The answer is C)
You can do this by several ways. The more direct is to realize that (x-5)(x+5) is a factorization of a difference of squares.
Also, you can apply the distributive propierty:
\(\begin{gathered} x\cdot x=x^2 \\ x\cdot5=5x \\ -5\cdot x=-5x \\ (-5)\cdot5=-25 \end{gathered}\)Now, you add everithing up:
\(\begin{gathered} (x-5)(x+5)=x^2+5x-5x-25=x^2-25 \\ \end{gathered}\)And then you get the answer C)
what is 4.25% as a decimal
Answer:
0.0425
Step-by-step explanation:
Answer:
0.0425
Step-by-step explanation:
hope this helped ^^
6)
25
20
15
Height (inches)
10
S
10
15
20
25
Length (inches)
Find the rate of change for the ramp represented in the graph.
My Answer:
Answer:
the change is 5.
Step-by-step explanation:
pls mark brailyist
Find the lowest common denominator (multiple). Type the equivalent fractions. Then, add or subtract. Simplify your answer. 1
2
1
3
Answer:what
Step-by-step explanation:what does this mean
The grades on a history midterm at Gardner Bullis are roughly symmetric with μ = 69 μ=69mu, equals, 69 and σ = 3.5 σ=3.5sigma, equals, 3, point, 5. Ishaan scored 65 6565 on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
Answer:
-1.14
Step-by-step explanation:
The given information in statement is
mean=μ=69
standard deviation=σ=3.5
Let X be the Ishaan's exam score
X=65
The Z score can be computed as
\(z=\frac{x-mean}{standard deviation}\)
\(z=\frac{65-69}{3.5}\)
z=-1.1429
z=-1.14 (rounded to two decimal places).
Thus, the computed z-score for Ishaan's exam grade is -1.14.
Answer:
-2.67
Step-by-step explanation:
khan academy
What is the property of -10+3 = 3+(-10)
Answer: −7 = −7
Step-by-step explanation:
Answer:
Commutative Property of Addition
Step-by-step explanation:
Commutative Property of Addition states that A + B = B + A
Suppose that the scores on a reading ability test are normally distributed with a mean of 65 and a standard deviation of 8. a) If one student is chosen at random, what is the probability that the students score is less than 81 points on this test? b) If 500 students took reading ability test how many would expect to earn score less than 81 points? c) Find the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68.
The probability that a student's score is less than 81 points on the reading ability test is 0.9772. We would expect approximately 489 students to earn a score less than 81 points if 500 students took the reading ability test. The probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.
To find the probability that a student's score is less than 81 points, we need to standardize the score using the z-score formula:
z = (x - μ) / σ
where x is the student's score, μ is the mean score, and σ is the standard deviation. Plugging in the values, we get:
z = (81 - 65) / 8 = 2.00
Using a standard normal distribution table or calculator, we can find the probability of a z-score less than 2.00 to be approximately 0.9772. Therefore, the probability that a student's score is less than 81 points is 0.9772.
Since the distribution is normal, we can use the normal distribution to estimate the number of students who would earn a score less than 81. We can standardize the score of 81 using the z-score formula as above and use the standardized score to find the area under the normal distribution curve. Specifically, the area under the curve to the left of the standardized score represents the proportion of students who scored less than 81. We can then multiply this proportion by the total number of students (500) to estimate the number of students who would score less than 81.
z = (81 - 65) / 8 = 2.00
P(z < 2.00) = 0.9772
Number of students with score < 81 = 0.9772 x 500 = 489
Therefore, we would expect approximately 489 students to earn a score less than 81 points.
The distribution of the sample mean reading ability test scores is also normal with mean μ = 65 and standard deviation σ / sqrt(n) = 8 / sqrt(35) ≈ 1.35, where n is the sample size (number of students in the sample). To find the probability that the sample mean score is between 66 and 68, we can standardize using the z-score formula:
z1 = (66 - 65) / (8 / sqrt(35)) ≈ 0.70
z2 = (68 - 65) / (8 / sqrt(35)) ≈ 2.08
Using a standard normal distribution table or calculator, we can find the probability that a z-score is between 0.70 and 2.08 to be approximately 0.2190. Therefore, the probability of randomly selecting 35 students (all from the same class) that have a sample mean reading ability test score between 66 and 68 is approximately 0.2190.
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5. A farmer's field has the dimensions shown. He needs to find the area of the field so that he knows how much seed to buy. 1 km w 21 km 2 II square kilometers
ok
\(\begin{gathered} \text{ 2}\frac{3}{4}\cdot\text{ 1}\frac{1}{3}\text{ = }\frac{8\text{ + 3}}{4}\cdot\text{ }\frac{3\text{ + 1}}{3}\text{ } \\ \text{ = }\frac{11}{4}\cdot\text{ }\frac{4}{3} \\ \text{ = }\frac{44}{12} \\ \text{ = 3 }\frac{8}{12} \\ \text{ = 3}\frac{4}{6}\text{ or} \\ \text{ = 3}\frac{2}{3}km^2 \end{gathered}\)The answer is the last line.
PLEASE HELP PLEASE
Answer:
Median?
Step-by-step explanation:
Question is kinda unclear.
Mean: Average of the data values
Median: Middle of all the data values
Mode: Amount of times a value appears
Range: Difference between largest and smallest values.
THIS IS MY LAST QUESTION I HAVE TO DO, PLEASE HELP ME!
Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.
To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.
On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.
Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.
Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.
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2.
Classify the following Polynomial: -3ab^5cd^3*
(3 Points)
6th degree Monomial
6th degree Binomial
5th degree Binomial
10th degree Monomial
Answer:
10th degree Monomial
Step-by-step explanation:
\( - 3ab^{5}cd^{3} \)
a=1
b=5
c=1
d=3
1+5+1+3 = 10
What is equivalent to 6 exponent 8
bjorn is trying to estimate a difference in average sugar content in two different types of donut: one that is fat free, and one that is full fat. in order to do this, he collects 60 donuts to test: 22 donuts are fat free, 38 that are full fat. he says this satisfies his assumptions. is he right? if not what's wrong? (select all that apply)
The correct answers are His sample was not drawn at random ,he ought to purchase more fat-free donuts, he may look at the data's histogram to see whether it is roughly typical.
Given that, Bjorn is attempting to calculate the difference between the average sugar level of two distinct kinds of donuts: a fat-free kind and a full-fat variety.
He gathers 60 donuts to test in order to do this: There are 22 fat-free donuts and 38 full-fat donuts. The correct answers are A, D and E He did not get a random sample He should get more fat free donuts He could check the histogram of the data to see if it's approximately normal
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Calculate how long it would take for an investment of R9000 to double if the simple interest rate is 11% per annum.
Answer:
9.09 years
Step-by-step explanation:
Use the simple interest formula
A=P(1+rt)
18000=9000(1+.11*t), solve for t
t = 9.0909
1
A power line is connecting the top of a building to the ground 251.8 meters away from the base of the building. At what angle is the wire connected at the
building (angle of depression) if the wire is 371.9 meters long?
Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). it is called by ____
Grouping symbols, Exponents, Multiply & Divide, Add & Subtract (GEMDAS). It is called by GEMS.
An effective acronym for teaching pupils the hierarchy of operations is PEMDAS.
The PEMDAS rule explains to pupils how to solve multi-step arithmetic problems and in what sequence to complete the operations to arrive at the right solution.
Groupings, Exponents, Multiplication or Division, Subtraction or Addition is referred to as GEMS. All grouping symbols, including parentheses, brackets, and braces, are referred to as groupings. The acronym GEMS has been adopted to take the role of PEMDAS. These can be used in place of one another.
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find the perimeter of the triangle? what does 2 represent in the triangle?
Answer:
i got 11.8 and what do u mean by the 2, do u mean the 2 strokes, that means that they are equal
Step-by-step explanation:
Answer:
6 + 5\(\sqrt{5}\)
Step-by-step explanation:
Since the triangle is isosceles then the 2 marked sides are congruent.
Using the rule of radicals
\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)
Thus perimeter (P) is the sum of the 3 sides
P = \(\sqrt{20}\) + 3 + \(\sqrt{20}\) + 3 + \(\sqrt{5}\)
= 2\(\sqrt{20}\) + 6 + \(\sqrt{5}\)
= 2(\(\sqrt{4(5)}\) ) + 6 + \(\sqrt{5}\)
= 2 ( \(\sqrt{4}\) × \(\sqrt{5}\) ) + 6 + \(\sqrt{5}\)
= 2(2\(\sqrt{5}\) ) + 6 + \(\sqrt{5}\)
= 4\(\sqrt{5}\) + 6 + \(\sqrt{5}\)
= 6 + 5\(\sqrt{5}\)
Find the volume of the cone.
9 cm
r = 6 cm
V = [?] cm3
Round to the nearest tenth.
Step-by-step explanation:
\( \frac{1}{3} \pi {(6)}^{2} (9) \\ \frac{1}{3} \pi(36)(9) \\ \frac{1}{3} \pi(324) \\ 108\pi \\ 339.3 {cm}^{3} \)
Find (f0f)(81)
f(x)=sqrt{x},g(x)=(x−7)^2
From the given function f(x) the value of expression f(f(81)) is equal to 3.
Let's see how to find the answer to the question:
Find (f0f)(81)
In the given question, we need to find the value of (f0f)(81). This notation means (f◦f)(81).
Given that f(x)= sqrt(x) and g(x) =\((x - 7)^2\).
We know that to find (f◦f)(x), we need to evaluate f(f(x)).
This means we need to first evaluate f(x), and then evaluate f(f(x)).
To find (f◦f)(81), we need to find f(f(81)).
Using the function f(x), we find f(81):
f(81) = sqrt(81) = 9
Now, we use the function f(x) again to find f(f(81)):
f(f(81)) = f(9)
= sqrt(9)
= 3
Thus, we have found that
(f◦f)(81) = f(f(81))
= 3
Hence, the value of (f0f)(81) is 3.
Therefore, the value of (f0f)(81) is 3.
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Find the value of x please show work
Answer:
x =98
Step-by-step explanation:
Extend the line in the upper part.
By Alternate interior angle theorem, the alternate interior angle would be 62°.
By Linear pair theorem the angle beside 144° is supplementary, and therefore is equal to 36°.
Finally, the line would create a triangle, which means that we can use that to solve for the linear pair of x°
Recall that the sum of the interior angle of a triangle is 180°
Therefore that angle is
36° + 62° + third angle in triangle = 180°
98° + third angle in triangle = 180°
third angle in triangle = 180° - 98°
third angle in triangle = 82°
Now that we know the measurement of the linear pair of x°, we can conclude that
x° + 82° = 180°
x° = 180° - 82°
x° = 98°
Therefore, x° = 98°
(If you have any question please let me know)
In a data set, the number of elements will always be the same as the number of: a. data point b. independent variable c. dependent variable d.observation
The number of elements will always be the same as the number of observations.
How to find the mean of a data set?
Mean is the ratio of the sum of the values of the data set to the total number of values available in the data set.
Thus, we get;
\(\rm Mean = \dfrac{\text{Sum of the observations of the data set}}{\text{Total number of observations}}\)
We are given that;
the number of elements=number
Now,
From observation we can say that the number of elements is equal to the number of observations.
Therefore, by mean the answer will be observation.
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I need help with 12 I don’t need a explanation I only need the answer I think i did something wrong in my work
Since Sahil got 28 questions right and Angelina got 7 more wrong answers, therefore Angelina's score is 7 lesser than Sahil. The equation will be 28 - 7 = Angelina's score. And based on the choices, it is a + 7 = 28.
Angelina's score is 21 and that is a.
So, if you substitute a with 21 to the second equation which is:
a + 7 = 28
21 + 7 = 28.
SOMEONE PLEASE HELP ME WITH THIS!!
IMAGE DOWN BELOW!!
ILL GIVE YOU BRAINLIST ANSWER!!
Answer:
5.735
pythagorian theorem is a^2 + B^2 = c^2
C is the longest side of the right triangle
Louis filled his 275.2-gallon pool with water in 8.6 hours. How many gallons per hour did he use?
To find the gallons per hour Louis used to fill his pool, we divide the total number of gallons by the total number of hours.
Given:
Pool capacity: 275.2 gallons
Time taken: 8.6 hours
The rate at which Louis used water can be calculated as:
\(\[\text{{Rate}} = \frac{{\text{{Total gallons}}}}{{\text{{Total hours}}}}\]\)
Substituting the given values:
\(\[\text{{Rate}} = \frac{{275.2 \, \text{{gallons}}}}{{8.6 \, \text{{hours}}}}\]\)
Simplifying the expression, we find:
\(\[\text{{Rate}} \approx 32 \, \text{{gallons per hour}}\]\)
Therefore, Louis used approximately 32 gallons per hour to fill his pool.
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The functions f(x) = x2 – 2 and g(x) = –x2 + 5 are shown on the graph.
There are two stiff transforms to use:
Vertical movement 7 units to the plus side.reflection along the y = 5 line.The fact that the real domain is the domain of quadratic functions makes it possible to identify the solution set.
How can rigid transformations be used?Thus, we must decide which rigid transformations to apply to f(x) in order to produce g(x). Rigid transformations are transformations applied to geometric loci in the field of Euclidean geometry so that Euclidean distances within the latter are conserved (x).
Following thorough consideration, we come to the conclusion that the two stiff transformations listed below must be used:
Vertical translation 7 units to the plus side.
reflection along the y = 5 line.
The collection of x-values necessary for the function to exist is represented by the solution set. Due to the fact that both functions are quadratic equations, the entire real domain is described by their solutions.
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Select the correct answer from each drop down menu. In the figure, AB=__inches and AC=___
10" inches
Answer: In the figure AB is about 8.4 inches and AC is about 13.05 inches.
Step-by-step explanation: We can use cosine to find the hypotenuse. \(cos(40)=\frac{10}{x} \\cos(40) (x)=\frac{10}{x}(x)\\cos(40) (x) =10\\\frac{cos(40) (x)}{cos (40)} =\frac{10}{cos (40)} \\x=\frac{10}{cos(40)}\)
Using a calculator x is about 13.05
Using tangent we can find the length opposite of <C
\(tan(40)=\frac{x}{10} \\tan(40) (10)=\frac{x}{10}(10)\\tan(40) (10) = x\)
Using a calculator x would be about 8.4
Answer:
Step-by-step explanation:
(15 Points Guaranteed) Find The Surface Area Of This Cube. Be Sure To Include The Correct Unit In Your Answer.
Answer:
486 Yards
Step-by-step explanation:
Area of a Cube = 6a^2
6 * 9^2
6 * 81
486
Can you help me plz on this
Answer: A
Step-by-step explanation: I think it's point A.
Multiplying Polynomials
Find each product.
1) 6v(2v + 3) 2) 7(−5v − 8)
3) 2x(−2x − 3)
A polynomial is an equation made up of coefficients and in determinates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables.
Multiplying Polynomials Find each product. 1) \(6v(2v + 3) 2) 7(-5v - 8)3) 2x(-2x -3)6v(2v + 3)\)
To distribute the 6v over the binomial 2v + 3, we multiply 6v by each term inside the parenthesis:
\(6v(2v) + 6v(3)\)
\(= 12v^2 + 18v7(-5v - 8)\)
To distribute the 7 over the binomial -5v - 8, we multiply 7 by each term inside the parenthesis:
\(7(-5v) + 7(-8)= -35v - 562x(-2x - 3)\)
To distribute the 2x over the binomial -2x - 3, we multiply 2x by each term inside the parenthesis:
\(2x(-2x) + 2x(-3)= -4x^2 - 6x\)
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The number of calories burned y
after x
minutes of kayaking is represented by the linear function y=4.5x
How many more calories are burned by doing the activity in part (a) than the other activity for 45 minutes?
The number of calories burned y after x minutes of kayaking is
How to find the number of calories burned y?You should know when we eat and drink more calories than we use up, our bodies store the excess as body fat. If this continues, over time we may put on weight
For kayaking Linear function is y=4.5x
In 45 minute means x=45
so, y=4.5x
45*45
= 20.25
That means in kayaking will burnt 20.25 calories in 45
minutes
Therefore, hiking burns more calories.
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