We can add and subtract 4.5 in the left side to complete squares, then we can rewrite the quadratic equation as:
(x + 13)^2 = 4.5
How to rewrite the quadratic equation?Here we want to rewrite the quadratic equation:
x^2 + 26x + 164.5 = 0
To rewrite it in the desired way, we need to complete squares, remember that the perfect square trinomial is:
(a + b) = a^2 + 2ab + b^2
We can rewrite the given quadratic as:
x^2 + 26x + 164.5 = 0
x^2 + 2*13*x + 164.5 = 0
The missing term to complete squares is 13^2 = 169, so we can add and subtract 4.5 on the left side of that eqation to get:
x^2 + 2*13*x + 164.5 + 4.5 - 4.5 = 0
x^2 + 2*13*x + 169 - 4.5 = 0
(x + 13)^2 = 4.5
That is the equation we wanted to get.
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all else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.
true
false
The given statement " All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant. " is true.
The term t statistics refers the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.
Here we have the statement All else being equal, the further the t statistic falls from 0, either in the positive or negative direction, the more likely it is that the difference between two population averages is statistically significant.
And we need to identify whether the statement is true or not.
As per the definition of t statistics, we have identified that the t statistic falls from 0. which states that is goes on the negative direction.
Therefore, the more likely it is that the difference between two population averages is statistically significant.
So, the statement is correct.
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domain:1,2,3,4,5 range:68,71,74,77,80 what is a reasonable domain for this
The reasonable domain is { 1,2,3,4,5 }
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
The collection of all feasible independent variable values is known as the mathematical domain. The set of all independent variable values that are conceivable yet make sense in the context at hand is known as the reasonable domain.
Here, the situation is not given.
So, the reasonable domain is { 1,2,3,4,5 }
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In the diagram below, angle P is congruent to Angle S and Angle Q is congruent to angle T. Enter segments in the blanks provided that would result in a true equation.
Answer:
OP/PQ
Step-by-step explanation:
You need corresponding sides in triangle OPQ.
The ratio equivalent to the given ratio is OP/PQ
What are similar figures?Two shapes are said to be similar if their corresponding sides are in the same proportion and the corresponding angles are congruent.
Given are two triangles having two pairs of the corresponding angles equal,
So, according to the definition of the similar figures, we can say that the triangles are similar,
Also,
Their corresponding sides will be in the same proportion.
Therefore,
RS / OP = ST / QP = RT / QO
Hence, the ratio equivalent to the given ratio is OP/PQ
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A diameter of a circle has endpoints of (1, 4) and (5, 4). What is the equation of this circle?
The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0
A circle is what?A circle is a closed two-dimensional object in which every point in the plane is equally spaced from a certain point known as the "center" The symmetry line of reflection is formed by each line that traverses the circle. Additionally, it is rotationally symmetric about the center for all angles. In the plane, the circle formula is as follows:
The coordinate coordinates (x,y) are equal to (x-h)2 + (y-k)2 = r2.
The centre of a circle is located at (h,k), and its radius is measured in units of r.
The equation of a circle having end points of the diameter as (x1,y1) and (x2,y2) is (x−x1)(x−x2)+(y−y1)(y−y2)=0.
we have (1,4) and (5,4) as (x1,y1) and (x2,y2)
(x−(1))(x−(5))+(y−(4))(y−(4))=0
⇒ ([tex]x^{2}[/tex] -5x -1x + 5 ) + ( [tex]y^{2}[/tex] -4y -4y + 16 ) = 0
[tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0
The equation for the circle whose endpoints are A(1,4) and B(5,4) is written in diameter form [tex]x^{2} +y^{2}[/tex] -6x -8y + 21 = 0.
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the width of a confidence interval for a population mean depends on group of answer choices the sample proportion. the population size. the level of confidence chosen. the sample mean.
The width of a confidence interval for a population mean depends on group of answer choices the sample proportion is population size and sample mean .
Given :
What is population size ?
population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc.
What is sample mean ?
The sample mean from a group of observations is an estimate of the population mean .
so the width of a confidence interval is dependent on population size and sample mean .
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3x + 5y = 5
-2x-8y = 6
How can you eliminate the x-terms in this system?
3x + 5y = 5
Multiply by ? on both sides.
-2x8y=-6
Multiply by ?
on both sides.
Answer:
3x + 5y = 5
Multiply by 2 on both sides.
-2x - 8y = -6
Multiply by 3 on both sides.
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases} \;\;\:3x + 5y = 5\\-2x-8y = 6\end{cases}[/tex]
To eliminate the x-terms in the given system of equations:
Multiply 3x + 5y = 5 by 2 on both sides.Multiply -2x - 8y = 6 by 3 on both sides>3x + 5y = 5 → Multiply by 2 on both sides:
[tex]\implies 2(3x+5y)=2(5)[/tex]
[tex]\implies 6x+10y=10[/tex]
-2x - 8y = 6 → Multiply by 3 on both sides:
[tex]\implies 3(-2x - 8y) = 3(6)[/tex]
[tex]\implies -6x - 24y = 18[/tex]
Add them together to eliminate x:
[tex]\begin{array}{crcccc}&6x&+&10y&=&10\\+&(-6x&-&24y&=&18\\\cline{2-6} &&-&14y&=&28\end{array}[/tex]
On a coordinate plane, how are the location of the point (1 , -5) and (1 , 5) related?
Reflection across the y-axis on a coordinate plane.
What is the short definition of a coordinate plane?
Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is a single horizontal number line. The y-axis is a vertical number line, which is the other number line. A place known as the origin is where the two axes collide. The coordinate plane allows us to graph points, lines, and more.
What is reflaction of coordinate plane?
Transformation is the process of making each point in a shape appear at the same distance on the other side of a specified line.
The term "line of reflection" refers to introspection with relation to that line. A line is crossed to flip the image.
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(x2 – 2x – 37) ÷ (x2 – 3x – 40)
Answer:
If you divide:
[tex]1+\frac{x+3}{x^2-3x-40}[/tex]
If you simplify:
[tex]\frac{x^2-2x-37}{(x-8)(x+5)}[/tex]
Step-by-step explanation:
Line m has the equation y=−13x−2. Line k is parallel to line m and passes through the points (0,4) and (9,a) . What is the value of a ?
The required value of "a" would be 3.
What are the perpendicular lines?Perpendicular lines are two lines that cross one other and create a 90-degree angle.
As per the question, we have
Line m has the equation y = −13x − 2
Here slope of line m = -13
The slope of the given line m will be -13,
Line k passes through the points (0,4) and (9, a).
The slope of line k = (a - 4)/(9-0)
The slope of line k = (a - 4)/9
Given line m and line k are both perpendicular to each other,
We know that two lines are perpendicular if the product of their slopes is -1.
So, -13 × (a - 4)/9 = -1
⇒ -13a + 52 = 13
⇒ 13a = 52 - 13
⇒ 13a = 39
⇒ a = 39/13
⇒ a = 3
Therefore, the required value of "a" would be 3.
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Answer to what the value of x is
Answer: 17
Step-by-step explanation:
11x - 39 = 10x - 22
11x = 10x + 17
x = 17
nasa is conducting an experiment to find out the fraction of people who black out at g forces greater than 6. in an earlier study, the population proportion was estimated to be 0.43. how large a sample would be required in order to estimate the fraction of people who black out at 6 or more gs at the 99% confidence level with an error of at most 0.03? round your answer up to the next integer.
The sample size of 502 should be the required size to perform the experiment.
The confidence interval (1 - alpha )% for population percentage p is as follows,
CI =p +- z √pq/n
The following formula is used to determine the margin of error,
MOE = z * √pq/n
The information provided is, with a margin of error of 0.03 and = 0.32.
The z-value for an 85% degree of confidence is,
For the z-value, use a z-table.
The sample size n is then determined by,
MOE = z * √pq/n
= 1.44 √ 0.32( 1 - 0.32 ) ²/ 0.03
= ( 22.392 )²
= 502
Therefore, a sample of size 502 would be needed to assess the percentage of subjects that experience blackouts at 6 or more Gs.
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HELP!!!!!
I put a picture down below!
Answer:
d) y = -3x-3
e) y = -3x - 1
f) y = -3x + 2
Step-by-step explanation:
Knowledge Needed:
Slope-Intercept Form: y = mx + b
y and x stay as variables so you can solve for the intercepts and graph.
m is the slope, or the constant amount that the y-value on a line changes when the x-value increases by 1.
b is the y-intercept, or when t he line has an x-value of 0.
When lines are parallel, they have the same slope.
Question
d)
Examine the line: At what y-value does the line have a x-value of 0?
y-value: -3
Alternatively, you could also solve be getting a set of points on the line and plugging in.
(1,0)
Our equation for line d:
y = -3x - b
0 = -3(1) - b
0 = -3 - b
0 + 3 = -3 + 3 - b
3 = -b
b = -3
d) y = -3x-3
e)
Repeat the same steps.
y-intercept: -1
Because they are parallel, they have the same slope.
e) y = -3x - 1
f)
Repeat the same steps.
y-intercept: 2
Because they are parallel, they have the same slope.
f) y = -3x + 2
At the carnival,the ratio of people who won the ring toss game to lost was 8:5.if 24 people won,how many people would have lost?
Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company
.
Answer:
Step-by-step explanation:
Sophie was offered a job after college earning a salary of $30,000. She will get a raise of $2,000 after each year working for the company. Answer the questions below regarding the relationship between salary and the number of years working at the company.
Let p: it is raining
Let q: robert is laughing.
Assume p is true. select two statements that must logically be true.
A. p ∨ q
B. p ∧ q
C. q → p
D. p → q
E. q ↔ p
The two statements that are logically true as per the given data is q=>p and p ∧ q .
p = raining
q = Robert is laughing
q=>p this is because the entire proposition is logically true when the conclusion of the condition is true.
and
p ∧ q means that it is raining and Robert is laughing which is again logically true.
If two logical statements have the same truth value in all circumstances, they are said to be comparable. This fact can occasionally be used to demonstrate a mathematical result by switching out one expression for an equivalent one while maintaining the original compound proposition's truth value.
Propositional types based on Truth values
tautologycontradictioncontingency.To learn more about proportional equivalence
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Theo drove 240 miles in 4 hours. Lex drove 183 miles in 3 hours. At those rates, could either man drive 118 miles in 2 hours? Complete the explanation. Show your work pls
Answer:
Yes, both men could drive at the rate of 112 miles in 2 hours. This is because you need to find the unit rate. For Theo's unit rate it is 57 miles per hour while Lex could drive at 62 miles per hour. Finally, the last statement ask if they could drive at a unit rate of 56 miles per hour and yes both men can.
Step-by-step explanation:
Answer: Theo's speed is 240 miles / 4 hours = <<240/4=60>>60 mph.
Lex's speed is 183 miles / 3 hours = <<183/3=61>>61 mph.
To determine whether Theo can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 60 mph: 118 miles / 60 mph = <<118/60=1.97>>1.97 hours.
Since 1.97 hours is less than 2 hours, Theo could drive 118 miles in 2 hours.
To determine whether Lex can drive 118 miles in 2 hours, we can calculate the time it would take him to travel 118 miles at his speed of 61 mph: 118 miles / 61 mph = <<118/61=1.93>>1.93 hours.
Since 1.93 hours is less than 2 hours, Lex could also drive 118 miles in 2 hours.
Therefore, both Theo and Lex could drive 118 miles in 2 hours.
7) what are the coordinates of the vertices with the base b and the height h?
8) solve for the measures of angles 1, 2, and 3
The coordinates of the vertices with the base b and the height h is O(0, 0), W(b, 0), T(b, h) and S(0,h).
What is rectangle?
An example of a quadrilateral with equal and parallel opposite sides is a rectangle. It is a polygon with four sides and four angles that are each 90 degrees. A rectangle is a shape with only two dimensions.
The rectangle with base b and height h.
We know that:
The point O is shown in the graph is at Origin.
So, its coordinates are O(0, 0)
Since, the height of the rectangle is h,
as S and T are h units away from the x-axis.
and the base of the rectangle is b, T and W are b units away from the y-axis.
thus the coordinates of the other vertices are:
S(0, h), T(b, h) and W(b, 0)
Therefore, the coordinates of the vertices of the following rectangle with base b and height h are:
O(0, 0), W(b, 0), T(b, h) and S(0,h)
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A multiple-choice quiz has 5 questions. Each question has 3 possible answers. A student guesses the answer to each question. Find the probability that the student answers exactly 1 question correctly.
The probability that the student answers exactly 1 question correctly is
[tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]
What is the binomial coefficient?
In combinatorics, the binomial coefficient is used to denote the number of possible ways to choose a subset of objects of a given numerosity from a larger set.
There are a total of [tex]$3^5=243$[/tex] possible ways that the student can answer the quiz. To count the number of ways that the student can answer exactly 1 question correctly, we can use the binomial coefficient formula:
[tex]\binom{5}{1}=5[/tex]
This counts the number of ways that the student can choose which 1 question to answer correctly.
For each of these 5 ways, there are 3 ways to choose the incorrect answer for each of the other 4 questions, so the total number of ways that the student can answer exactly 1 question correctly is
[tex]$5\cdot 3^4=135$[/tex].
Therefore, the probability that the student answers exactly 1 question correctly is
[tex]$\frac{135}{243}=\boxed{\frac{5}{9}}$[/tex]
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Tanisha has 54 m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. (The fourth side of the enclosure would be the river.)
'The area of the land is 280 square meters. List each set of possible dimensions (length and width) of the field.
13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.
What are dimensions?Height, length, and width are the three dimensions that all of the places we dwell and things we utilize on a daily basis have.
Height, depth, and other dimensions are examples of dimensions.
The dimensions of a line, a square, and a cube are each one, two, and three, respectively.
However, we consider the Universe to have one temporal dimension and three spatial dimensions (north-south, east-west, and up-down).
So, we have the area (A):
A = (54 – 2x)x
A = 54x - 2x²
Differentiate to obtain: dA/dX = 54 - 4x
We shall differentiate and equate to zero for a maximum Area, so dA/dx = 0.
54 – 4x = 0
x = 54/4
x = 13.5 m
It covers 280 m². Consequently, the other potential dimension:
w = 280/13.5
w = 20.74 m
Therefore, 13.5m × 20.74m or 20.74m × 13.5m can be the possible dimensions.
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An item is regularly priced at $83. It is on sale for 35% off the regular price.
Answer: $53.95
Step-by-step explanation:
Original Price: $83
Discount: 35%
35%=0.35
$83 x 35%, or 83 x 0.35
=29.05
$83-29.05
=$53.95
If 80% of 120 students passed the test, and (1)/(4) of these students received an A on the test, how many students received an A?
A 20 students
B 22 students
C 24 students
D 26 students
24 students received an A on the test.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
If 80% of 120 students passed the test, the number of students who passed is 120 * 80% = 96 students.
If (1)/(4) of these students received an A on the test, the number of students who received an A is (1)/(4) * 96 = 24 students.
Therefore, 24 students received an A on the test.
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Determine the monthly periodic interest rate on a credit card with a 24.99% APR. Write your answer as a percent, rounded to the nearest hundredth.
The monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .
The average interest rate for new credit card offers is lower than the 24.99% APR on a credit card. If the cardholder keeps a balance on the credit card for the entire year, the APR of 24.99% means that the balance will rise by around 24.99%. If the APR is 24.99%, for instance, and you carry a $1,000 balance for a year, you would end up owing about $246.48 in interest.Fortunately, if you pay the entire balance before the due date each month, you won't be subject to the 24.99% APR. But you'll end up spending a significant amount in interest if you carry a balance from month to month.This is because interest costs accumulate every day the balance is outstanding. In other words, interest is applied to your principal balance as well as any accumulated interest from prior days.The credit card company will divide the APR using a daily periodic rate (DPR) to calculate the amount of interest you'll pay for a specific billing cycle because some months have more days than others. Simply divide a credit card's APR of 24.99% by 365 to obtain the DPR. The rate that results is 0.0685% each day. Until the payment is paid in full, daily interest charges are assessed.Hence, the monthly periodic interest rate on a credit card with a 24.99% APR is 0.0685% .
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in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
HELP ME
The number of bacteria after 4 hours is 800
How to determine the number of bacteria after 4 hours?The complete question is added at the end of this solution
Given that,
Initial population = 50Reproduction = splitting every hourThis means that the rate of production is by doubling
So, we have the following parameters
a = 50
r = 2
An exponential function is represented as
A(n) = arⁿ
Substitute the known values in the above equation, so, we have the following representation
A(n) = 50(2)ⁿ
We have to find,
Find the number of bacteria after 4 hours.
This means that n = 4
So, we have
A(4) = 50(2)⁴
Evaluate
A(4) = 800
Hence, the population is 800
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Complete question
in a biology lab, a population of 50 bacteria reproduce by splitting. Every hour, on the hour, each bacterium splits into two bacteria.
Find the number of bacteria after 4 hours.
Which statement about the graph of y=12·(1/2)x is true?
The graph has an asymptote at y = 0.
Option (A) is correct.
What is the asymptote of the graph?
An asymptote is a straight line that constantly approaches a given curve but does not meet at an infinite distance. In other words, an Asymptote is a line that a curve approaches as it moves toward infinity.
The given function is:
[tex]y = 12.(\frac{1}{2})^x[/tex]
Now let's draw the graph for this given function,
By observing the graph we can conclude that the graph has an asymptote at y = 0 cause it is not meeting to the x-axis when it is approaching infinity.
Hence, the graph has an asymptote at y = 0.
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(a) Find m ZK.
40°
6
m2K =°
K
6
Step-by-step explanation:
it is an isoceles triangle (both legs are equally long).
that means also both base angles are equal :
angle J = angle L = 40°
the sum of all angles in a triangle is always 180°.
so,
180 = angle J + angle L + angle K = 40 + 40 + angle K
angle K = 180 - 40 - 40 = 100°
Help please ASAP !!!!!
Answer: S
Step-by-step explanation:
Tori bought one share of Chipotle stock on Nov 1, 2016 for $396.33.
Then, four years later, she sold it at the closing price of $778.38.
a) How much money did she gain/lose with this stock?
b) What was Tori's return on investment?
a) The amount of money that he earned with the stock was of: $382.05.
b) The return on the investment was of: 96.40%.
How to obtain the amount of money earned and the return on the investment?The amount of money earned is obtained by the subtraction of the price that the stock was sold by the price the stock was bought. If this amount is negative, it means that money was lost, otherwise money was earned.
Considering the values on the problem, the amount that he earned with the stock is given as follows:
778.38 - 396.33 = $382.05.
The return on the investment is given by the amount earned/lost divided by the initial value, and multiplied by 100% to obtain the value as a percentage, hence it is of:
382.05/396.33 x 100% = 96.40%.
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The parent function f(x) = x is transformed to g(x) = f(-x)-2 which graph represents g(x)
Answer:
g(x) will be the line y=x, reflected across the y-axis and shifted down 2 units.
Step-by-step explanation:
The -x negates every x-value, which has the effect of reflecting the graph across the y-axis. The -2 moves the graph down 2 units.
What is the major difference between the alternate hypothesis and the null hypothesis?.
The null hypothesis of a test always predicts no effect or no association between variables, but the alternative hypothesis reflects the effect or relationship that your research predicts.
Hypothesis;-
A put forward explanation for a phenomenon is called a hypothesis (plural: hypotheses).
A hypothesis cannot be called a scientific hypothesis unless it can be tested using the scientific process. Observations from the past that cannot be fully explained by the body of knowledge at this time often serve as the foundation for scientific ideas.
A scientific hypothesis is distinct from a scientific theory, despite the fact that the phrases "hypothesis" and "theory" are sometimes used interchangeably.
A working hypothesis is a theory that has been accepted provisionally and is put forth for further investigation[1], beginning with an educated guess or way of thinking.
As a result, the alternative hypothesis of a test indicates the effect or relationship that your research predicts, whereas the null hypothesis of a test always predicts that there will be no effect or no association between variables.
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Michael is 3 more than twice leon's age if michael is 35 how old is leon
Answer:
16 years old
Step-by-step explanation:
2x+3=35
-3. -3
2x=32
/2. /2
x=16
Leon is 16 years old
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