The simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given statement is "7-radical 7 over10+radical 3".
Write the statement in mathematical form and simplify:
[tex]\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\\\\\frac{7 - \sqrt{7}}{10 + \sqrt{3}}\times\frac{10 - \sqrt{3}}{10 -\sqrt{3}}\\\\\frac{(7 - \sqrt{7})(10-\sqrt{3})}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{100-3}\\\\\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex]
Hence, the simplified expression is [tex]\frac{70-7\sqrt{3}-10\sqrt{7}+\sqrt{21}}{97}[/tex].
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Find the volume v of the described solid s. The base of a solid s is the triangular region with vertices (0, 0), (4, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.
The volume of the solid S in the given question is 5.48unit³.
What is volume?A three-dimensional space's occupied volume is measured.
It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units.
The definition of length and volume are connected.
So, the volume of the solid S:
An equilateral triangle's sides are shown as a cross-section.
An equilateral triangle's height is determined by:
[tex]h = sSin60 = \frac{\sqrt{3} }{2} s[/tex]
Consequently, one triangle's area is:
[tex]A=\frac{1}{2} s h=\frac{1}{2} s \cdot \frac{\sqrt{3}}{2} s=\frac{\sqrt{3}}{4} s^2[/tex]
The line equation that depicts the diagonal is:
[tex]\begin{aligned}& x+y=1 \\& y=-x+1 \\& x=-y+1\end{aligned}[/tex]
This will indicate the s value integrate from 0 to 2 if we integrate along the y-axis.
[tex]\begin{aligned}& V=\int_0^2 \frac{\sqrt{3}}{4} s^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2(-y+1)^2 d x \\& =\frac{\sqrt{3}}{4} \int_0^2\left(y^2-2 y+1\right) d x \\& =\frac{\sqrt{3}}{4}\left[\frac{1}{3} y^3-y^2+y\right] \\& \left.=\frac{\sqrt{3}}{4}\left[\frac{1}{3}(2)^3-(2)^2+2\right)\right] \\& =5.48\end{aligned}[/tex]
Therefore, the volume of the solid S in the given question is 5.48unit³.
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Correct question:
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.
Tessa has a new beaded necklace. 18 out of the 45 beads on the necklace are blue. What
percentage of beads on Tessa's necklace are blue?
Answer: 40%
Step-by-step explanation: 18/45 = x/100
divide 100 by 45 and you get 2.22 repeating.
multiply 2.22 by 18 and you get 40%
Jack has 18 fewer points than Aria, who has x points.
Answer: x-18
Step-by-step explanation:
How do i do this? The real answer is supposed to be 1/16 but I don't know how to get there.
a) The student's work is False and the strategy is incorrect as the fraction should be 1/16
b) The fraction 1/16 as decimal is 0.0625
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be = A
Now the value of A is A = 6 1/4 %
The value of A = 6.25 %
Now , the value of 6.25 % = 6.25 / 100
The fractional form can be substituted by dividing the numerator and denominator by 25 , we get
A = 6.25 / 100
A = ( ( 6.25 ) / 25 ) / ( 100 / 25 )
A = ( 0.25 ) / 4
The value of A = 0.25 / 4
The value of A = 0.0625
And it can be represented in the fractional form as
A = 0.25 / 4
The value of 0.25 = 1/4
Substituting the value of 0.25 in the equation , we get
A = ( 1/4 ) / 4
A = 1/16
Therefore , the value of A = 1/16
b)
The decimal from of the number 1/16 is 0.0625
The mistake the student did was while dividing the number by 100 to convert the percentage , the student evaluated the number 625 instead of 6.25 , so after avoiding the error , we get the fraction as 1/16
The decimal from of the number 1/16 is 0.0625
Hence ,
a) The student's work is False and the strategy is incorrect as the fraction should be 1/16
b) The fraction 1/16 as decimal is 0.0625
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Calculate the unit rate for each option and determine which one is the BEST buy.
16 pounds for $31.68
28 pounds for $49.56
The best buy will be;
''28 pounds for $49.56''
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The two options are,
16 pounds for $31.68
28 pounds for $49.56
Now,
Since, The two options are,
16 pounds for $31.68
28 pounds for $49.56
Hence, The unit rate for each are;
Since, The cost of 16 pounds = $31.68
Hence, The cost of 1 pounds = $31.68/16
= $1.98
And, The cost of 28 pounds = $49.56
Hence, The cost of 1 pounds = $49.56/28
= $1.77
Thus, The best buy will be;
''28 pounds for $49.56''
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a ladder is leaning against a wall. the ladder touches the wall 15 feet above the ground. how far is the bottom of the ladder from the wall if the length of the ladder is one foot more than twice its distance from the wall
The bottom of the ladder is at 8 feet from the wall.
The position of the ladder will form a right angled triangle with the wall. The perpendicular is 15 feet. Let the distance between ladder and wall be x. Thus, the length of the ladder will be 2x + 1. Forming a equation according to Pythagoras theorem.
(2x + 1)² = x² + 15²
Expanding the equation
4x² + 1 + 4x = x² + 225
Rewriting the equation
4x² - x² + 4x = 225 - 1
Performing subtraction
3x² + 4x = 224
3x² + 4x - 224 = 0
Factorizing the quadratic equation, we get -
x = -9.3 and 8
The distance can not be negative. Hence, the value of x is 8.
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A circle is centered at (−5, 8) and has a radius of 7. Which of the following is the equation of this circle? Group of answer choices (x + 5)2 + (x − 8)2 = 49 (x + 5)2 + (x − 8)2 = 7 (x − 5)2 + (x + 8)2 = 7 (x − 5)2 + (x + 8)2 = 49
The equation of the circle centered at (−5, 8) and having a radius of 7 is (x + 5)² + (y - 8)² = 49.
What is the equation of the circle centered at (−5, 8) and has a radius of 7?The standard form of the equation of a circle is expressed as;
x² + y² = r²
The horizontal (h) and vertical (k) translations represents the center of the circle.
Hence;
(x - h)² + (y - k)² = r²
Given the data in the question;
Center of the circle: (−5, 8)
h = -5k = 8r = 7Equation of the circle = ?Now, plug the values of h, k and r into the equation above and simplify,
(x - h)² + (y - k)² = r²
( x - (-5) )² + ( y - 8 )² = 7²
(x + 5)² + (y - 8)² = 49
Therefore, the equation of the circle is (x + 5)² + (y - 8)² = 49.
Hence, option A is the correct answer.
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50% of the tickets sold at a school carnival were early-admission tickets. If the school sold 64
tickets in all, how many early-admission tickets did it sell?
Answer: 32
Step-by-step explanation:
50% = x/2
50% of 64 = 64/2
50%=32
Answer: The correct answer is 32 tickets were early admission
Step-by-step explanation:
T = Total tickets sold
E = Early admission tickets
If 50% of the total tickets are for early admission, then our equation would be:
E = T * 50% (or .5)
Substitute 64 for the total tickets
E = 64 * .5
E = 32
given f (x) = 2x + 7 describe how the value of k affects the slope and y intercept of the graph of g compared to the graph of f 9 (x) = (2x +7) - 6
The slope of both functions remains the same, there is no effect of the value of k on a slope.
What is a slope?Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.
The given functions are :
f(x) = 2x + 5
g(x) = ( 2x + 5) -3
From the graph of both functions,
Let us consider two pairs of coordinates to find the slope,
For f(x)
(0,5) and ( -2, 1)
The slope of f(x)
m= ( 1- 5) / (-2 -0)
m= 2
For g(x) at (0,2) and (-1, 0) slope of g(x),
m = ( 0-2) / (-1-0)
m = 2
The slope remains unaffected.
y-intercept of f(x) , put x = 0
⇒ y = 5
y-intercept of g(x) , put x = 0
y =(0+ 5) -3
y = 2
Change in the value of y-intercept due to the value of k = -3.
Therefore, for the given function f(x) = 2x + 5 and g(x) = ( 2x + 5) -3, the effects of the value of k on slope and y-intercept are as follows:
The slope of both functions remains the same, there is no effect of the value of k on a slope.
Change in the value of y-intercept. For f(x) y-intercept is 5 and for g(x) y-intercept is 2.
The graph is attached.
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In someone infected with measles, the virus level N (measured in number of infected cells per mL of blood plasma) reaches a peak density at about t = 12 days (when a rash appears) and then decreases fairly rapidly as a result of immune response. The area under the graph of N(t) from t = 0 to t = 12 (as shown in the figure) is equal to the total amount of infection needed to develop symptoms (measured in density of infected cells x time). The function N has been modeled by the function f(t) = -t(t - 21)(t + 1). Use this model with six subintervals and their midpoints to estimate the total amount of infection needed to develop symptoms of measles.
The total amount of infection needed to develop symptoms of measles is 7840
Consider the model,
N(t)= f(t)=-t(t-21)(t+1).
The area of the graph of N(t) from t=0 to t = 12 is,
N(t)dt
Use six subintervals and their midpoints to estimate the above as follows:
Here, a=0,b=12, n=6
The length of each subinterval is,
h= b-a/n = 12-0/6
=2
So, the midpoints of each subinterval are 1, 3, 5, 7, 9, and 11.
Use Midpoint Rule,
A = [N(t)dt]
= At[ƒ (1) + ƒ (3) + ƒ (5) +ƒ(7)+ƒ(9)+ƒ(11)] =2[40+216+480+784+1080+1320]
= 7840
Thus, the total amount of infection needed to develop symptoms of measles is 7840.
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why are we able to solve the wason task with examples (whether one is 21 and drinking alcohol) rather than letters and numbers? group of answer choices
The Wason selection test measures a person's ability to recognize information that challenges a certain hypothesis, in this case, a type of conditional hypothesis. if P, then Q.
Given,
Wason's Card;
A popular tool for studying problem resolution that was developed in 1966 by English psychologist Peter C(athcart) Wason (1924–2003). The uppermost faces of the four cards, which are arranged on a table, display the letters and numerals E, K, 4, and 7.
What is demonstrated by the Wason selection task?
As a result, the Wason selection test gauges how well people can spot evidence that refutes a certain hypothesis, in this case, a conditional hypothesis of the type. P, then Q if.
For example;-
The majority of people have no trouble choosing the proper cards ("16" and "drinking beer") if the rule is "If you are drinking alcohol, then you must be over 18" and the cards contain an age and beverage on one side, respectively.
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PLS HELP I'M VERY CONFUSED IT"S DUE 2DAY!!!! 100PTS!!!! NO SCAM ANSWERS!!!
In the following activity, match each pair of equivalent expressions.
(IT'S IN THE PICTURE)
The equivalent expressions of each number are respectively;
1) 2(x - 2) = -7 + 6x - 4x + 3
2) (x + 14) - (8 - 2x) = 9x - 2(3x - 3)
3) 3(x + 5) = -2x + 9 + 5x + 6
4) -4(x + 1) + 5x = (7 - 2x) + (3x - 11)
5) (7 + 5x) + (4x - 1) = -3x + 6 + 4x
How to use algebraic properties?The properties of algebra include associative property, distributive property, Identity property, Inverse property, e.t.c.
Now, let us simplify the terms on the right;
a) (7 - 2x) + (3x - 11)
Expanding the brackets gives us;
7 - 2x + 3x - 11
= x - 4
This can also be expressed as;
-4(x + 1) + 5x
b) -7 + 6x - 4x + 3
Simplifying gives;
2x - 4
= 2(x - 2)
c) 9x - 2(3x - 3)
Simplifying gives;
9x - 6x + 6
3x + 6
It can also be written as;
(x + 14) - (8 - 2x)
d) -3x + 6 + 4x
Simplifying gives;
x + 6
This can also be expressed as;
(7 + 5x) + (4x - 1)
e) -2x + 9 + 5x + 6
This can also be expressed as;
3x + 15
3(x + 5)
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Answer:
[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]
[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]
[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]
[tex]\boxed{5.} \quad -3x+6+4x[/tex]
[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]
Step-by-step explanation:
Simplify the given expressions numbered 1 through 5:
[tex]\begin{aligned}\textsf{1.} \quad 2(x-2)&=2 \cdot x + 2 \cdot (-2)\\&=2x-4\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{2.} \quad (x+14)-(8-2x)&=x+14-8+2x\\&=x+2x+14-8\\&=3x+6\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{3.} \quad 3(x+5)&=3 \cdot x + 3 \cdot 5\\&=3x+15\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{4.} \quad -4(x+1)+5x&=-4 \cdot x -4 \cdot 1+5x\\&=-4x-4+5x\\&=5x-4x-4\\&=x-4\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{5.} \quad (7+5x)+(-4x-1)&=7+5x-4x-1\\&=5x-4x+7-1\\&=x+6\end{aligned}[/tex]
Simplify the given answer expressions:
[tex]\begin{aligned}(7-2x)+(3x-11)&=7-2x+3x-11\\&=3x-2x+11-11\\&=x-4\end{aligned}[/tex]
[tex]\begin{aligned}-7+6x-4x+3&=6x-4x+3-7\\&=2x-4\end{aligned}[/tex]
[tex]\begin{aligned}9x-2(3x-3)&=9x-2 \cdot 3x-2 \cdot (-3)\\&=9x-6x+6\\&=3x+6\end{aligned}[/tex]
[tex]\begin{aligned}-3x+6+4x&=4x-3x+6\\&=x+6\end{aligned}[/tex]
[tex]\begin{aligned}-2x+9+5x+6&=5x-2x+9+6\\&=3x+15\end{aligned}[/tex]
Therefore, the matching pairs of equivalent expressions are:
[tex]\boxed{4.} \quad (7-2x)+(3x-11)[/tex]
[tex]\boxed{1.} \quad -7+6x-4x+3[/tex]
[tex]\boxed{2.} \quad 9x-2(3x-3)[/tex]
[tex]\boxed{5.} \quad -3x+6+4x[/tex]
[tex]\boxed{3.} \quad -2x+9+5x+6[/tex]
"A scientist uses a submarine to study ocean life. She begins at sea level, which is an elevation of 0 feet. She travels straight down for 90 seconds at a speed of 3.5 feet per second. She then travels directly up for 30 seconds at a speed of 2.2 feet per second. After this 120 second period, how much time, in seconds, will it take for the scientist to travel back to sea level at the submarine's maximum speed of 4.8 feet per second? Round your answer to the nearest tenth of a second." I need this done soon, please help.
It will take 51.9 seconds to return to sea level.
What is speed?The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.
Using the speed - distance relationship, the time taken for the scientist to travel back to sea level would be 51.9 seconds
Distance = Speed × time
First travel :
Distance covered = 90 × 3.5 = 315 feet
Second travel :
Distance covered = 30 × 2.2 = 66 feet
Net change in position from sea level :
(315 - 66) feet = 249 feet
Maximum speed = 4.8 feet per second
Time taken = Distance / speed
Time taken = 249 ÷ 4.8 = 51.875 seconds
Hence, it will take 51.9 seconds to return to sea level.
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Given the equation V/7.9 equals 14.6, solve for v.
The required value of V for the given equation is 115.34
What is a simple equation?
A simple equation is a mathematical formula that, on both sides of the "equal to" sign, expresses the relationship between two expressions. It primarily consists of a variable, sometimes with a numerical constant in addition. There cannot be a simple equation without a variable. A known, fixed quantity that is used in a straightforward equation is referred to as a constant.
Given an expression, V/7.9 equals 14.6
or, V/7.9 = 14.6
or, V = 14.6*7.9
or, V = 115.34
Hence, the required value of V is 115.34
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a test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test. at what percentile (rounded off) would this client's score place her?
As per the concept of z - score, the percentile would this client's score is 0.4772
Z - score:
In statistics, z - score is also termed the standard score, is used to determine how much each data point position is away from its mean. Where as in other words, it measures the deviation of x (data point) in terms of the standard deviations. Here the percentage of the population above or below the score can be obtained using z tables.
Given,
A test has a mean of 100 and a standard deviation of 15. a client scores 130 on the test.
Here we need to find at what percentile (rounded off) would this client's score place her.
As per the formula of z score, here we have the values,
mean = 100
standard deviation = 15
Score = 130
Therefore, the z score is calculated as,
=> z score = (130 - 100) / 15
=> z score = 30 / 15
=> z score = 2
According to the z score table the resulting value is 0.4772.
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7 the cost of a pen and a notebook used to be the same, but recently the cost of the pen was increased by $44, whereas, the cost of notebook became $66 less than 55 times its original value.after the revised cost, if the pen was more expensive than the notebook, what could have been the possible original value of both the products, if the initial price was a natural number?
x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
Given that,
Pens and notebooks used to cost the same, however recently the price of the pen went up by $4 while the price of the notebook went down by $6 from its previous value of $5.
We have to find what might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
We know that,
We get the equation as
x+4>5x-6
By solving the x
The inequality with x<2.5
So, natural number, n=2
x>2
Therefore, x>2 might the original value of both goods have been if the initial price had been a natural number and the pen had been more expensive than the notebook.
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a couple plans to have three children. all arrangements are (approximately) equally likely. let x be the number of girls the couple has. what the probability that x is greater than or equal to 2
The probability that the couple will have more than 2 girls is 1/2.
Here, we are given that a couple is planning to have 3 children.
Let us list down all the possible combination of outcomes-
GGG, GGB, GBB, BBB
Here G stands for a girl and B for a boy.
Thus, there are a total of 4 outcomes. We need to find the probability that the number of girls is greater than or equal to 2.
Out of the listed outcomes, 2 combinations- GGG and GGB have number of girls ≥ 2.
We know that probability = Number of favorable outcomes/ total number of outcomes
P(x ≥ 2) = 2/4
= 1/2
Thus, the probability that the couple will have more than 2 girls is 1/2.
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the mean of five positive integers is 1.5 times their median. four of the integers are 8, 18, 36 and 62, and the largest integer is not 62. what is the largest integer?
The largest number of the five positive integers is 146.
Mean:
The mean is the mathematical average of a set of two or more numbers. The arithmetic mean and the geometric mean are two types of mean that can be calculated. The formula for calculating the arithmetic mean is to add up the numbers in a set and divide by the total quantity of numbers in the set.
Median:
The median is the middle value in a set of data. First, organize and order the data from smallest to largest. To find the midpoint value, divide the number of observations by two. If there are an odd number of observations, round that number up, and the value in that position is the median.
Here we have to find the largest integer.
Data given:
Four of the five integers are 8, 18, 36, and 62.
It is given that mean of five numbers 1.5 times their median.
mean = (8+18+36+62 + x)/5
median = 36
mean = 1.5 × median
(124 + x) / 5 = 1.5 × 36
124 + x = 5 × 54
x = 270 - 124
= 146
Therefore we get the largest number as 146.
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Step by step please help asap !!!!!!!
Answer:
3,31
Step-by-step explanation:
i dont got steps for this but i think thats the right answer
Solve each inequality. Use the number line provided to test intervals.
Thank you!! :)
Answer: x ∈ {-0.5, -5, -12.5}
Step-by-step explanation: To solve the inequality 2x³ + 21x² + 60x + 25 > 0, we first need to find the values of x that make the inequality true. We can do this by setting the expression equal to 0 and solving for x.
We can start by factoring the expression to make it easier to solve. Notice that 2x³ + 21x² + 60x + 25 is a polynomial with a leading coefficient of 2 and a constant term of 25. This means that it has the form (x + a)(x + b)(x + c), where a, b, and c are constants.
We can start by factoring out the common factor of 2x from the first two terms: 2x³ + 21x² + 60x + 25 = 2x(x² + 10.5x + 12.5). Now we can see that the expression has the form (x + a)(x + b)(x + c), where a = 0.5, b = 5, and c = 12.5.
So, we can rewrite the expression as (x + 0.5)(x + 5)(x + 12.5) = 0. Now we can solve for x by setting each factor equal to 0 and solving for x:
x + 0.5 = 0 => x = -0.5
x + 5 = 0 => x = -5
x + 12.5 = 0 => x = -12.5
Therefore, the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5.
Now we need to determine which of these values make the inequality 2x³ + 21x² + 60x + 25 > 0 true. To do this, we can substitute each of the values of x into the inequality and see which ones make the inequality true.
When x = -0.5, the inequality becomes 2(-0.5)³ + 21(-0.5)² + 60(-0.5) + 25 > 0, which simplifies to -0.5 + 5.25 - 15 + 25 > 0. This is true, because the left-hand side is 29 > 0.
When x = -5, the inequality becomes 2(-5)³ + 21(-5)² + 60(-5) + 25 > 0, which simplifies to -125 + 525 - 300 + 25 > 0. This is also true, because the left-hand side is 225 > 0.
When x = -12.5, the inequality becomes 2(-12.5)³ + 21(-12.5)² + 60(-12.5) + 25 > 0, which simplifies to -391.25 + 1181.25 - 750 + 25 > 0. This is also true, because the left-hand side is 1147.5 > 0.
Therefore, the solution to the inequality is x ∈ {-0.5, -5, -12.5}. This means that the values of x that make the inequality true are x = -0.5, x = -5, and x = -12.5. The inequality is satisfied when x is any of these values.
Simpliy. 4x+2(2+5)+1
Answer:
4x + 15
Step-by-step explanation:
1. Add the numbers
4x + 2(2 + 5) + 1
4x + 2(7) + 1
2. Multiply the numbers
4x + 2(7) + 1
4x + 14 + 1
3. Add the numbers
4x + 14 + 1
4x + 15
Solution:
4x + 15
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A common guideline for constructing a 95% confidence interval is to place upper and lower bounds one standard error on either side of the mean.
True
False
False. Because a 95% confidence interval is two standard errors on either side of the mean.
What is a 95% confidence interval?
If 100 separate samples were taken and a 95% confidence interval was calculated for each sample, then around 95 of the 100 confidence intervals would contain the actual mean value (), according to the definition of a 95% confidence interval.
For a 95% confidence interval, the value lies within 2 standard deviations of the normal distribution.
For upper and lower bounds one standard error on either side of the mean is 68%.
So, the 95% confidence interval is two standard errors on either side of the mean.
Hence, the given statement is False.
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So far, you proved that one pair of parallel sides in a parallelogram
must be congruent. Add to your proof to prove that both pairs of
parallel sides in a parallelogram must be congruent.
Geometry
Both the pairs of opposite sides in a parallelogram are parallel and congruent.
According to the question,
We've proved that one pair of sides in parallelogram must be congruent
Let ABCD is a parallelogram ,
We know that AB // CD
Here, AC is transversal for the parallel lines AB and CD
So, ∠BAC = ∠DCA (Using interior angle property) --------(1)
Similarly , We also know that BC // AD
=> ∠BCA = ∠DAC -----------(2)
Now , In ΔABC and ΔADC,
∠BAC = ∠DCA from (1) AC is common side∠BCA = ∠DAC from (2)Therefore , ΔABC ≅ ΔADC (as per ASA congruence rule)
Therefore , AB = CD and BC=AD (Corresponding sides of congruent triangles are equal)
Hence , Both the pairs of opposite sides in a parallelogram are parallel and congruent.
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Please answer. Question below!
Answer:
Solution = (5, 2)
Step-by-step explanation:
Step 1: Solve for y in 9x + 2y = 49
1. 9x + 2y = 49 → 2y = -9x + 49 → y = -4.5x + 24.5
Step 2: Substitute -4.5x + 24.5 for y in -3x + 5y = -5
2. -3x + 5(-4.5x + 24.5) = -5
Step 3: Solve for x
3. -3x - 22.5x + 122.5 = -5 → -25.5x + 122.5 = -5 → -25.5x = -127.5 → x = 5
Step 4: Substitute 5 for x in -3x + 5y = -5
4. -3(5) + 5y = -5 → -15 + 5y = -5 → 5y = 10 → y = 2
Hope this helps :)
samples of size 5 are selected from a manufacturing process. the mean of the sample ranges is 0.50. what is the estimate of the standard deviation of the population? (round your answer to 3 decimal places.)
The estimate value of the standard deviation of the population ( manufacturing process) is 0.125..
The standard deviations is estimated to be one fourth of the sample range (as most of data values are within two standard deviations of the mean).
We have given that,
A sample of manufacturing process.
Sample size, n = 5
Mean of sample ranges = 0.50
we have to calculate the estimate of standard deviations of population.
thus , we estimate the standard deviations as fourth of the mean of the sample ranges is
S = Mean of sample ranges/4
=> S = 0.50/4
=> S = 0.125
Hence, the standard deviation of the population is estimated as 0.125..
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Use the probability distribution and histogram found here to select the correct probability for each statement.
The probability that a randomly selected student has fewer than 4 siblings is P(X<✓4)=0. 89
The probability that a randomly selected student has at least 5 siblings is P(X≥ ✓ 5
The probability that a randomly selected student is not an only child is P(X # 0) = 0. 75
☐
4
=✓0. 04✓
The probabilities are given as follows:
Fewer than 4 siblings: P(X < 4) = 0.737.At least 5 siblings: P(X >= 5) = 0.111.Not an only child: P(X > 1) = 0.734.How to obtain the probabilities?The probabilities are called identifying the desired outcomes from the distribution of the number of children per parent.
Hence the probability of fewer than 4 siblings is of:
P(X < 4) = P(X = 1) + P(X = 2) + P(X = 3) = 0.266 + 0.322 + 0.149 = 0.737.
The probability of at least 5 siblings is of:
P(X >= 5) = P(X = 5) + P(X = 6) + P(X > 6) = 0.059 + 0.032 + 0.02 = 0.111.
The probability that the student is not an only child is given as follows:
P(X > 1) = 1 - P(X = 1) = 1 - 0.266 = 0.734.
Missing InformationThe distribution is given as follows:
P(X = 1) = 0.266.P(X = 2) = 0.322.P(X = 3) = 0.149.P(X = 4) = 0.152.P(X = 5) = 0.059.P(X = 6) = 0.032.P(X > 6) = 0.02.More can be learned about probabilities at https://brainly.com/question/14398287
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Find the slope of the line through (7,-6),perpendicular to y=4x+2
Answer:
4y+x+17=0Step-by-step explanation:
y=4x+2
For a point to be perpendicular to a line
then the product of the two gradients must be negative one (I.e, m1×m2=-1)
where m1= 4
m2=-(1/m1)
m2=-1/4
point (7,-6)
x1=7 y1=-6
from the general equation of a line
y-y1=m(x-x1)
y-(-6)=-1/4(x-7)
y+6=-1/4(x-7)
y+6=-1/4x+7/4
y+1/4x=(7/4)-6
y+1/4x=-17/4
y+1/4x+17/4=0
4y+x+17=0
I need help with this asap please
Answer: C
Step-by-step explanation:
-2 and 2 add up to 0
Answer:
c
Step-by-step explanation:
-2 + 2 =0
Solve the equation for y.
x = 4y-2
y=
Answer:
Step-by-step explanation:
a food server examines the amount of money earned in tips after working an 8-hour shift. the server has a total of $95 in denominations of $1, $5, $10, and $20 bills. the total number of paper bills is 26. the number of $5 bills is 4 times the number of $10 bills, and the number of $1 bills is 1 less than twice the number of $5 bills. write a system of linear equations to represent the situation. (assume x
The solution to the system equation is (x, y, z, w) = (23, 12, 3, 1).
What is equation?
An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =
Main body:
Here is a system of linear equations that represents the situation.
x +5y +10z +20w = 133 . . . total amount earned
x +y +z +w = 39 . . . . . . . . . total number of bills
y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s
x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s
_____
We can substitute for x and z in the first two equations:
... (2y-1) +5y +10(y/4) +20w = 133
... (2y-1) +y +(y/4) +w = 39
These simplify to
... 9.5y +20w = 134
... 3.25y +w = 40
Solving by your favorite method, you get
... y = 12
... w = 1
So the other values can be found to be
... x = 2·12 -1 = 23
... z = 12/4 = 3
hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).
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