1. the equation of the quadratic function is: y = (8/65)(x + 5)(x - 13)
2. The axis of symmetry is the line x = 0 (the y-axis).
What is quadratic function?
The quadratic equation with roots -5 and 13 can be written as:
y = a(x + 5)(x - 13)
where a is a constant that depends on the coefficient of the quadratic term.
To find the value of a, we can use the fact that the coefficient of the quadratic term is the sum of the roots, multiplied by -1:
a = -(sum of roots) / (product of roots)
a = -(-5 + 13) / (-5 * 13)
a = 8 / 65
Therefore, the equation of the quadratic function is:
y = (8/65)(x + 5)(x - 13)
What is symmetry?
2. The axis of symmetry is the line x = 0 (the y-axis).
To find the axis of symmetry, we can use the formula:
x = -(b / 2a)
where a and b are the coefficients of the quadratic function. In this case, a = 8/65 and b = 0, since there is no linear term.
Substituting these values, we get:
x = -(0 / (2 * (8/65)))
x = -0
Therefore, the axis of symmetry is the line x = 0 (the y-axis).
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hey uhm i need help with this table i have to make an equation
Natasha can run 5 km in 20 minutes. Eli can run 8 km in 32 minutes. Who is the faster runner? Explain you're thinking.
Answer:
Neither
Step-by-step explanation:
Find the unit rate
20/5 = 4/1
32/8 = 4/1
Neither
1. Which Quadrant is Point F in?
Answer:
point f is in quadrant 3 . . .
The minimum value of G in G ( x ) = 3 tan x is
The function G(x) = 3 tan(x) does not have a minimum value.
What are the relative extremas of a function?The relative extremas of a function are the values of x for which the derivative of the function assumes a value of zero.
The extremas are classified as local minimum or local maximum, as follows:
Local minimum: the function changes from decreasing to increasing.Local maximum: the function changes from increasing to decreasing.The tangent function does not have a local minimum, as it is increasing over it's entire domain.
The function G(x) = 3 tan(x) is a vertical stretch by a factor of 3 of the tangent function, which changes only the range, thus the function continues without a local minimum.
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In january of 2019, the american midwest experienced record-breaking freezing temperatures. A certain metropolitan area in wisconsin, with a residential population of over 1. 15 million, experienced daily average temperatures as low as minus 28 degrees fahrenheit. Hospitals saw a steady stream of patients reporting symptoms of frostbite. In the aftermath, a survey was conducted in order to estimate the true proportions of individuals afflicted by frostbite during the extreme weather. 289 residents were selected via simple random sampling and 273 reported not having any symptoms. What was the sample proportion obtained by the survey? give your answer to 3 decimal places. For help on how to input a numeric answer, please see instructions for inputting a numeric response.
The proportion of the sample obtained from the survey is 0.055
What is a percentage?
The percentage is a mathematical operation that is expressed with the symbol "%" is a relationship that allows us to know the portion of an initial value to represent a set.
It could also be defined as a representation of an original value that lets us know a certain number of elements that we want from that original value or set.
To solve this problem, we use a simple rule of three to find the percentage value of the sample.
289 -------- 100%
273 --------- x
x = (273 * 100%) / 289
x = 94.46%
100% - 94.46% = 5.53%
The ratio in propotion with 3 decimals is
5.53/100 = 0.055
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please help me dhdjjdjejejejdjejejejejejkenensndd
Answer: area=8cm
Step-by-step explanation:
Answer:
a) Area of shape = 8 square cm.
Step-by-step explanation:
Area of composite shape:
Area of shape = area of rectangle + 2* area of triangle
Rectangle:l = 3 cm ; w = 2 cm
\(\sf \boxed{\text{Area of rectangle = l *w}}\)
= 3 * 2
= 6 cm²
Triangle:
b = 2 cm
h = 1 cm
\(\sf \boxed{\text{Area of triangle=$\dfrac{1}{2}*b*h$}}\)
\(\sf = \dfrac{1}{2}*2*1\\\\\\ = 1 \ cm^2\)
Area of two triangles = 2 *1
= 2 cm²
Area of shape = 6 + 2
= 8 cm²
b) Area of rectangle ABCD = 4 * 2
= 8 cm²
Find the measure of each angle indicated. Round to the nearest whole degree.
HELP ME PLZZZZZ GUYS PLZZZZZZZZ
The answer for the following question is Option 1 - 700 + 9 + 0.1 + 0.004
Answer: 700+9+0.1+0.004
Step-by-step explanation:
700+9=709.000
0.1+0.004=0.104
709.000+0.104=709.104
Hope this helps :)
for brainiest:):):):):):)
Answer:
Just a rough try of the STRUCTURE, not the actual. Use a protractor.
What value of will make the triangles similar by the similarity theorem?
As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.
Similarity theorem:
In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.
Given,
Here we need to find the t value of will make the triangles similar by the similarity theorem.
For example, we are told that the 2 triangles are similar by SSS theorem.
Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem
Therefore, in the triangles ,applying the SSS postulate gives;
=> x/35 = 44/20
Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;
=> x = (44 * 35)/20
When we simplify this one then we get,
=> x = 77
Therefore, the value of x is 77.
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what do you think of france
Answer:
Baguette is very important
Step-by-step explanation:
they don't have bidet but baguette
Answer:
honestly i think its a pretty country, its pretty nice and wish i could go.
Step-by-step explanation:
For each scenario below, choose the graph that gives the best representation.Ali begins his jogging workout by running faster and faster for about a minute. Once he hits a comfortable pace, he runs at that pace for several minutes. Then he gradually slows down to a stop over the next few minutes.
Given:
Ali begins his jogging workout by running faster and faster for about a minute. Once he hits a comfortable pace, he runs at that pace for several minutes. Then he gradually slows down to a stop over the next few minutes.
Required:
Choose the graph that gives the best representation.
Explanation:
From second graph we can see that it is first increasing for few minutes after that moving constant then decresing.
It is defining Ali's scanario correctly.
Answer:
Second graph is correctly representing the scenario.
Write your equation in slope intercept form. Type your equation with no spaces and your slope should be written as a fraction and it’s a simplified form.
Answer:
:)
Step-by-step explanation:
What is the equation for the line of symmetry in this figure?
Answer:
y=3
Step-by-step explanation:
what is the solution to -6 - -25=
Answer:
19
Step-by-step explanation:
(-6)-(-25)=(-6) +25 = 19
The regular price of a dress is $80. The price
has been marked up by 23%. What is the
amount of markup?
[A] $18.40
[B] $57.00
[C] $23.00
[D] $61.60
Answer:
A
Step-by-step explanation:
Write an equation and solve for x if the area of the rectangle is 70 square units.
The equation is 70 = 7 (x + 4) and value of x is 6.
The area of rectangle is given by the formula -
Area of rectangle = length × width
Keep the value of length and width from the image.
70 = 7 (x + 4)
Performing multiplication on Right and Side of the equation
70 = 7x + 28
Rewriting the equation according to x
7x = 70 - 28
Performing subtraction on Right Hand Side of the equation
7x = 42
x = 42/7
Performing division on Right and Side of the equation
x = 6
Hence, the value of x is 6.
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The question image is attached in figure.
the hcf of 90 and x is 18. the lcm of 90 and x is 540. find the value of x.
The value of x is 108.
What is HCF?The highest common factor is defined as the set of numbers with the highest common multiple. The highest positive integer with more than one factor in the set is HCF.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
* Multiplication operation: Multiplies values on either side of the operator
For example 4*2 = 8
We have been given that the HCF of 90 and x is 18.
And the LCM of 90 and x is 540.
We have to determine the value of x.
Since the product of two numbers equals the product of their HCF and LCM.
So 90 × x= HCF × LCM
Substitute the values of given data,
⇒ 90×x = 18×540
⇒ 90×x = 9720
⇒ x = 9720/90
⇒ x = 108
Hence, the value of x is 108.
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If p and q are non-zero rational numbers, and s and t are irrational numbers, select all of the statements that are always false.
answer choices are
The product pq is irrational.
The product pt is irrational.
The quotient pq is irrational.
The product st is irrational.
The quotient st is rational.
Answer:
The false choices are A, C, and E
Step-by-step explanation:
Let's make an example:
p=1
q=2
s=sqrt(3)
t=sqrt(6)
Since pq=1*2=2, the answer is rational and A is false.
Since pt=1*sqrt(6)=sqrt(6), the answer is irrational and B is true.
Since p/q=1/2=0.5, the answer is rational and C is false.
Since st=sqrt(3)*sqrt(6)=sqrt(18), the answer is irrational and D is true.
Since s/t=sqrt(3)/sqrt(6)=sqrt(1/2), the answer is irrational and E is false.
The false statements are:
The product pq is irrational.
The quotient pq is irrational.
The quotient st is rational.
A rational number is a number can be expressed as a fraction of two whole numbers. While, an irrational number is a number that cannot be expressed as the fraction of two whole numbers.
Examples of rational numbers are: 6, 2,3
Examples of irrational numbers are: √2, √3
Let p and q be represented with 2 and 6 respectively.
The product of 2 and 3 = 2 x 6 = . The number is a rational number
Let p and t be represented with 2 and √2 respectively.
The product of 2 and √2 = 2 x√2 = 2√2. The product is irrational
The quotient of pq = 6 /2 = 3.
The quotient is rational.
Let s and t be represented with √2, √3. The product is √2 x √3 = √6. The product is irrational.
The quotient of s and t = √2 /√3.
The number is irrational.
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Solve the following for the value of the pro-numeral:
(c - 7) / 2 = -5
Answer:
\( \frac{(c - 7)}{2} = - 5 \\ c - 7 = - 5 \times 2 \\ c - 7 = - 10 \\ c = - 10 + 7 \\ c = - 3\)
I hope I helped you^_^
ore time on the Internet: A researcher polled a sample of 1012 adults in the year 2010 , asking them how many hours per week they spent on the Internet. The sample mean was 10.01 with a standard deviation of 13.90. A second sample of adults was taken in the year . For this sample, the mean was with a standard deviation of . Assume these are simple random samples from populations of adults. Can you conclude that the mean number of hours per week spent on the Internet differs between and
Sample 1: Mean=10.01, Standard deviation=13.90 Sample 2: Mean
=11.43, Standard deviation
=14.10
Sample size of 1st year = n1
= 1012Mean of 1st year sample
= X1 = 10.01Standard deviation of 1st year sample
= s1
= 13.90Sample size of 2nd year
= n2
= 1012Mean of 2nd year sample
= X2
= 11.43
Standard deviation of 2nd year sample = s2
= 14.10 Let us assume a significance level of α = 0.05, which implies that the critical region consists of 2.5% in both tails (since it is a two-tailed test).
Therefore, we do not have sufficient evidence to conclude that the mean number of hours per week spent on the Internet differs between 2010 and another year.
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A company sells running shoes. If the price of shoes. If the price of shoes in dollars is p the company estimates that it will sell 50,000-40p pairs of shoes. Write an expression that represents the revenue in dollars from selling running shoes if a pair of shoes is price at p dollars
Answer:
The revenue from selling a pair of running shoes at p dollars per pair is 50,000p - p^2
Step-by-step explanation:
Here in this question, we are interested in writing an equation that represents the revenue from selling a number of shoes.
Mathematically;
Revenue = Number of shoes sold * Price of one shoe
From the question, the number of shoes sold at price P dollars is 50,000 - 40p
The price of a single pair is P dollars
So the revenue in this case will be ; p * (50,000 - 40p)
= (50,000p - 40p^2) dollars
The expression that represents the revenue in dollars is \((50000p-40p^{2} )\)
Algebraic expression :We have to find an expression that represents the revenue in dollars
So that,
Revenue = Number of shoes sold * Price of one shoe
It is given that the number of shoes sold at price P dollars is \((50000 - 40p)\)
and the price of a single pair is P dollars
Thus, the revenue expression is,
\(= p * (50000 - 40p)\\\\=50000p-40p^{2}\)
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QUESTION 3 ??? I NEED HELP FAST ITS SO CONFUSING
Answer:
1024
--------
8
Step-by-step explanation:
Answer:
2⁷
Step-by-step explanation:
2¹⁰/2³
2¹⁰ ÷ 2³
10-3= 7
2⁷
y/5-2=-7 what is the solution of the equation.
Answer: mg they left u hanging for some time here hol up,
y=−25
Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y/5-2-(-7)=0
y/5
(y/5 - 2) - -7 = 0
Subtracting a whole from a fraction
Rewrite the whole as a fraction using 5 as the denominator :
2 = 2/1=2.5/5
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
y - (2.5/5 5)=y - 10
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
y+25
———— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
y+25 = 0
4.2 Solve : y+25 = 0
Subtract 25 from both sides of the equation :
y = -25
Zeyad has a bag of 40 marbles. 10 of them are red. 12 are blue. 18 are white. He reaches into the bag without looking. What is the probability that Zeyad will select a white marble?
Answer:
9/20
Step-by-step explanation:
There are 40 marbles
18 are white
P( white marble) = number of white marbles / total number of marbles
= 18/40 = 9/20
(b) Estimate each using the normal approximation for the distribution of (outcome - point spread).
The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5
What is Normal Distribution?
An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center of the range.
Reason:
The number of trials n in the binomial setting and the constant success probability p for each of these trials decide the proper normal distribution to choose. Our binomial variable has a mean of np and a standard deviation of (np(1 - p)0.5, which approximates a normal distribution.
It can be demonstrated using simple mathematics that there are a few circumstances in which we must apply a normal approximation to the binomial distribution. To ensure that both np and n(1 - p) are higher than or equal to 10, the number of observations n must be sufficient, as must the value of p. This is a generalization that is supported by statistical theory. The standard approximation can always be used, however it may not be a very accurate approximation if these requirements are not met.
The normal approximation for the distribution of (outcome - point spread is (np(1 - p)0.5
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Please help, thank you
A researcher claims that 45% of students drop out of college. She conducts a hypothesis test and rejects the null hypothesis. What type of error could have been committed here?
A.
Power of the test
B.
Type II
C.
There are never errors in hypothesis testing
D.
Type I
The type of error that could have been committed in this scenario is a Type I error.
In hypothesis testing, a Type I error occurs when the null hypothesis is rejected, even though it is true. It means that the researcher incorrectly concludes that there is a significant result or effect when there is actually no real effect present in the population. In this case, if the researcher rejects the null hypothesis that the dropout rate is 45% and concludes that it is different, she might be committing a Type I error if the null hypothesis is actually true.
A Type II error, on the other hand, occurs when the null hypothesis is not rejected, even though it is false. It means that the researcher fails to detect a significant result or effect when there is actually a real effect present in the population. The question states that the null hypothesis is rejected, so a Type II error is not relevant in this situation.
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elise says, "if you subtract 16 from from my number and multiply the difference by -5, the result is -35." what is elise's number?
Answer:
23
Step-by-step explanation:
1. (x-16)-5=-35
2. (x-16)=-35/-5
3. x-16=7
4. x=16+7
5. x=23
What is the equation of a line of a line passing through (-3,7) and having a slope of - 1/5?
Answer:
y = -1/5x + 6.4
Step-by-step explanation:
Use the point-slope formula.
y-y₁ = m(x -x₁)
so...
y-7 = -1/5(x - (-3))
y = -1/5x+ 32/5
and you need you can change 32/5 to 6.4
Hope this helps!