Answer:
GCF of 12 and 100 by Prime Factorization
Prime factorization of 12 and 100 is (2 × 2 × 3) and (2 × 2 × 5 × 5) respectively. As visible, 12 and 100 have common prime factors. Hence, the GCF of 12 and 100 is 2 × 2 = 4.
GCF of 12 and 100 by Listing Common FactorsFactors of 12: 1, 2, 3, 4, 6, 12Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
There are 3 common factors of 12 and 100, that are 1, 2, and 4. Therefore, the greatest common factor of 12 and 100 is 4.
please, if you write an absurd anwser i will report it
a) The function is continuous in it's entire domain.
b) The increasing and decreasing intervals for the function are given as follows:
Increasing: (0,2).Decreasing: (2,10).What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
In this problem, we have a piece-wise function which has the definition changing at x = 2, hence the continuity must be studied at x = 2.
The lateral limits for the function in this problem are defined as follows:
[tex]\lim_{x \rightarrow 2^-} A(x) = \lim_{x \rightarrow 2} x^2 + 2 = 2^2 + 2 = 6[/tex][tex]\lim_{x \rightarrow 2^+} A(x) = \lim_{x \rightarrow 2} \frac{-3x + 30}{4} = 0.25(-3(2) + 30) = 6[/tex]The second limit is also equals to the numeric value at x = 2, due to the equal sign in the definition, hence the function is continuous at x = 2 and for all other values in the domain.
The intervals of increase and decrease are given as follows:
Increasing: (0,2). -> y = x² increases for x > 0, the 2 changes just the range.Decreasing: (2,10). -> decreasing line, due to the negative slope.TranslationThe function for this problem is the piece-wise function A(x).
Item a asks if the function is continuous.
Item b asks when the function is increasing and when it is decreasing.
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A manufacturer receives parts from two suppliers. A simple random sample of 400 parts from supplier 1 finds 20 defective. A simple random sample of 200 parts from supplier 2 finds 20 defective. Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Test whether the defective rates of the parts from two suppliers are significant different at the 1% significance level. Conduct a hypothesis testing. Answer the next three questions. 12. Test statistic
Answer:
The test statistic is [tex]z = -2.1[/tex]
The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A simple random sample of 400 parts from supplier 1 finds 20 defective.
This means that:
[tex]p_1 = \frac{20}{400} = 0.05, s_1 = \sqrt{\frac{0.05*0.95}{400}} = 0.0109[/tex]
A simple random sample of 200 parts from supplier 2 finds 20 defective.
This means that:
[tex]p_2 = \frac{20}{200} = 0.1, s_2 = \sqrt{\frac{0.1*0.9}{200}} = 0.0212[/tex]
Let p1 and p2 be the proportion of all parts from suppliers 1 and 2, respectively, that are defective. Test whether the defective rates of the parts from two suppliers are significant different at the 1% significance level.
At the null hypothesis, we test if they are equal, that is, if the subtraction of the proportions is 0. So
[tex]H_0: p_1 - p_2 = 0[/tex]
At the alternate of the null hypothesis, we test if they are different, that is, if the subtraction of the proportions is different of 0. So
[tex]H_a: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the sample proportions:
[tex]X = p_1 - p_2 = 0.05 - 0.1 = -0.05[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0109^2 + 0.0212^2} = 0.0238[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.05 - 0}{0.0238}[/tex]
[tex]z = -2.1[/tex]
P-value of the test and decision:
The p-value of the test is the probability that the sample proportion differs from 0 by at least 0.05, that is, P(|z| < 2.1), which is 2 multiplied by the p-value of Z = -2.1.
Z = -2.1 has a p-value of 0.0179
2*0.0179 = 0.0358.
The p-value of the test is 0.0358 > 0.01, which means that the defective rates of the two suppliers are not significant different at the 1% significance level.
Equations of Exponential Functions
The table of values below represent an exponential function.
Write an exponential equation that models the data.
a. y = 18.2(1.7)× c. y = 26(0.7)×
b. y = 12.71(1.3)× d. y = 12.74(0.7)×
Please select the best answer from the choices provided
The initial value where x=0, y is 12.74 and the exponential function is
y = 12.74(0.7)×.
Option D is correct.
What is Exponential Function?The formula f(x) = [tex]a^x[/tex] defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x.
The quantity drops rapidly at first, then slowly in Exponential Decay. The rate of change slows over time. As time passes, the rate of change slows.
We know the formula for an exponential function is
y= a [tex]b^x[/tex]
where a is initial value and b is growth factor.
Now, we have to find the growth factor as
We can observe from the table that the values of y decrease as x increases.
That is an example of an exponential decay function.
In an exponential decay function, the value of a growth/decay factor b is always smaller than 1.
Thus, the initial value a= 12.74 and growth factor b=0.7 that is less than 1.
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WILL MARK BRAINLIEST!
Answer:
D
Step-by-step explanation:
Both lines are not intersecting each other so that means they don't share a solution
What are terms and common rations ? Can someone explain to me how to solve
For the arithmetic sequence 4 - 2(n - 1), we have that:
The first term is 4.The second term is 2.The third term is zero.The fourth term is -2.The fifth term is -4.The common difference is -2.For the geometric sequence 6 x 3^(n - 1), we have that:
The first term is 6.The second term is 18.The third term is 54.The fourth term is 162.The fifth term is 486.The common ratio is 3.How to model the arithmetic sequence?An arithmetic sequence is a sequence of numbers in which there is a common difference of the numbers, that is, the subtraction between consecutive terms of the sequence is always constant.
The nth term of an arithmetic sequence is given by the equation presented as follows:
[tex]a_n = a_1 + d(n - 1)[/tex]
In which:
[tex]a_1[/tex] is the first term.d is the common difference.The sequence in this problem is defined as follows:
4 - 2(n - 1)
Which has first term 4 and common difference -2, hence the terms are:
4, 2, 0, -2, -4, -6 and so on...
What is a geometric sequence?A geometric sequence is a sequence of numbers in which there is a common ratio of the numbers, that is, the quotient between consecutive terms of the sequence is always constant.
The nth term of a geometric sequence is given by the equation presented as follows:
[tex]a_n = a_1 \times q^{n - 1}[/tex]
In which:
[tex]a_1[/tex] is the first term.q is the common ratio.The sequence for this problem is given as follows:
6 x 3^(n - 1)
Which has first term of 6 and common ratio of 3, hence the terms are given as follows:
6, 18, 54, and so on...
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What is the equation of the
function y = x translated 3 units
up and 4 units left?
Answer:
Step-by-step explanation:
y=(x+4)+3
Answer:
y = x + 7
Step-by-step explanation:
Since y = x is a linear function, it may be confusing when using the translation tips you learned from class to solve it. However, there is an easy way to go about it.
1. Remember that when a function moves left, we use + inside of the parenthesis.
4 units left:
y = (x + 4)
2. Remember that when a function moves up, we use + outside of the parenthesis.
3 units up:
y = (x + 4) + 3
3. Add 'em up
y = x + 7
Since the function is linear, it may be confusing to see whether the graph moved up or left. However, by following the origin (0,0) of y = x and moving 4 units left and 3 units up, you will see that the origin has moved from (0,0) to (-4, 3), representing 4 units to the left and 3 units up on a graph.
Hope this helps :)
Clothing donations are collected to help a family in need. The function g(x) represents the number of items collected where x is the number of people who donated. Does a possible solution of (60,10) make sense for this function? Explain yojr answer
Answer:
No g(x) = x/6 for (60, 10) to be a possible solution
by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments
Step-by-step explanation:
g(x) number of items
x number of people
the data point (60, 10) make sense as a possilbe solution NO
g(x) = number of items x = 60 g(x) = 10
g(60) = x/6 = 10
= 60/10
by this function 60 people would have to donate 1/6th of a garment each to achieve 10 full garments
Please please someone help me
[tex]1000ml = 1l \\ 5000ml = \frac{5000}{1000} l = 5l[/tex]
So option C, 5 litres.
Answer:
5 liters
Step-by-step explanation:
So, lets go over what we know:
There is 5000 milliliters.
There are 1000 milliliters in a liter.
To find the amount of liters, we have to divide 5000 by 1000, or total millilileters by millilileters per liter:
5000/1000
=
5
Hope this helps!
carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game. how many points did carlos score in his first game?
Carlos's score in his first game was 14.
What is addition?Addition in maths, a process of combining two or more numbers.
Given that, Carlos scored a total of 60 points in his last three basketball games. be improved in each game by scoring 6 more points than in the previous game.
Let the first score be x,
x+x+6x+6+6=60
3x+18 = 60
3x = 42
x = 14
Hence, Carlos's score in his first game was 14.
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PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS HEEEEEEEEEEEEEEEEEEEEEEEELLLLLLLLLP ILLLLLLLLLLLLL BIVE brainleist
Answer: 195
Step-by-step explanation:
(0.3x + 66) + (0.1x + 36) = 180. ( 180 because thats the angle of a straight line)
0.3x + 0.1x + 66 + 36 = 180
0.4x + 102 = 180
0.4x = 180 - 102
0.4x = 78
x = 195
5,430 is 181% of what number?
Answer:
3000
Step-by-step explanation:
5430=1.81x
solving for x, we take 1, which is equal to 100%, and divide it by 1.81 to get 1/1.81 or 0.55248618
multiply 1/1.81 by 5430 to get 3000
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before. If you list the number of tickets sold over time, what kind of sequence will you see?
tysm ;-;
The kind of sequence that you will obtain when you list the number of tickets sold over time is given as follows:
A geometric sequence.
How to classify the sequence?A sequence can be classified as either arithmetic or geometric, as follows:
Arithmetic sequence: the difference between consecutive terms is constant.Geometric sequence: the ratio between consecutive terms is constant.If none of these statements is true, then the function is neither arithmetic or geometric.
A growing amusement park is able to sell 7 times as many tickets each year as it did the year before, which means that there is a constant ratio of 7 between the amounts of tickets sold each year, and thus this sequence is a geometric sequence.
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What is the equation of the line that passes through the points (-2, 3) and (2, 7)? (5 points)
O x-y=-1
Ox-y=-2
Ox-y=-5
O x-y=-6
The equation of the line that passes through the points (-2,3) and (2,7) is:
x-y=-5
Therefore, option(C) x-y= -5 is correct answer.
Step-by-step solution:
The algebraic representation of a line's equation is the collection of points that make up the line in a coordinate system.
Given the line passes through the points (-2,3) and (2,7)
So, the equation of the line passing through the two points is given by:
[tex]\frac{y-y_{1} }{y_{2}-y_{1} } =\frac{x-x_{1} }{x_{2} -x_{1} }[/tex]
[tex]\frac{y-3 }{7-3} } =\frac{x-(-2) }{2-(-2) }[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{2+2}[/tex]
[tex]\frac{y-3}{4} =\frac{x+2}{4}[/tex]
[tex]y-3 = x+2[/tex]
Now rearranging the above equation:
x - y + 3 + 2 = 0
x - y + 5 =0
Therefore, the equation of the line passing through the points (-2,3) and (2,7) is: x-y=-5
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If these two shapes are similar, what is the measure of the missing length j?
Answer:
45ft is the missing length j.
How can you use this pattern to find 3°
Number pattern, sequence, finding the algebraic rule and using a ... To illustrate this, consider the following sequence of numbers {1, 3, 5, 7, 9, …}.
What is Number pattern?Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers.Here, we get the numbers in the pattern by skip counting by 5. Given are the steps to identify a number pattern.To solve the problems of number pattern, we need first to find the rule being followed in the pattern.
To find out the rule, we need to see the first few numbers in the series.Try to see the difference between consecutive numbers, it will help us understand the relationship between the numbers.Number pattern is a pattern or sequence in a series of numbers. This pattern generally establishes a common relationship between all numbers. For example: 0, 5, 10, 15, 20, 25, … Here, we get the numbers in the pattern by skip counting by 5.
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The complete question is -
How can you use this pattern to find 3° of the number in Series ?
What is the approximate volume of this cone?
3.14 as your approximation for π
Enter your answer as a whole number, like this: 42
Answer:
942
I wish you luck! :D
give person above me brainliest since he/she/non-binary answered first
Answer:
942
Step-by-step explanation:
I just did this on a test and got 100% so I can verify this is right!
help me.. pls pls pls pls
Answer:
the other side is 5 i think
What is the average rate of change between (4,1) and (3,5)
the price of a sandwich decreases from $8 to $6 what is the percentage decrease in the price of the sandwich
Answer:
The percentage decrease is 25%.
Step-by-step explanation:
The difference in price is $2:
$8 - $6 = $2
Now to find the percentage decrease, we use the formula decrease in price divided by original price (or new/old) times 100:
2/8 * 100.
This equals 200/800 which is 25%.
For what value of a does (1/9)^a+1 = 81^a+1 • 27^2-a
Answer: a = -4
Step-by-step explanation:
If r=1 and 0=7pi/6, what is the approximate arc length?
Answer:
3.665
Step-by-step explanation:
A 45°-45°-90° triangle has a hypotenuse that is
[tex]16 \sqrt{2} [/tex]cm long. Each leg of the triangle is ___ cm long.
Explanation:
For any 45-45-90 triangle, if each leg is x units long, then the hypotenuse is x*sqrt(2) units long. Comparing that with 16*sqrt(2) must mean x = 16.
find the area and circumference of a circle with a radius 5 m. use the value 3.14 for radius, and do not round your answers. Be sure to include the correct units in your answers.
Area and circumference of the circle are 78.5 m² and 31.4 m respectively.
What is a circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Given that, a circle have a radius 5 m
Area of a circle = π × radius²
Circumference = 2π×radius
Area = 3.14 × 5² = 3.14 × 25 = 78.5 m²
Circumference = 3,14 × 2 × 5 = 31.4 m
Hence, area and circumference of the circle are 78.5 m² and 31.4 m respectively.
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Someone pls help!!
Construct a circle through points
X, Y, and Z.
By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.
What is a circle?It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)
How can you create a circumcircle?First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.
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12. Remove the bracket and simplify
4y (6x-8)
Answer:
24xy - 32y
Step-by-step explanation:
4y × 6x =24xy
4y × -8 = -32y
brainliest plz? i got 1000+ points deleted
Answer:
4y(6x-8)
[tex]4y \times (6x - 8)[/tex]
[tex]4y \times - 6x + 8[/tex]
[tex] - 24xy + 8[/tex]
[tex] - 32xy[/tex]
Answer
What is the solution of the inequality shown
below?
a+5>-7
The required solution for the inequality a + 5 > -7 is (-12, ∞).
What is inequality?Inequality shows relation between two expression which are not equal to each others.
The given inequality is,
a + 5 > -7
To find the solution for the inequality,
Simplify the inequality,
a + 5 > - 7
a > - 7 - 5
a > -12
The value of a is greater than -12, implies that,
The solution for the value of the given inequality is (-12, ∞).
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please help will give brainliest
Zachary's car used 15 gallons to travel 645 miles. At what rate does the car use gas, in miles per gallon?
On the double number line below, fill in the given values, then use multiplication or division to find the missing value.
Lindsay wishes she's she could have four times the amount of jelly beans Lisa has. Which expression shows Lindsay's wish?
A) 4 + b
B) 4 - b
C) 4 divided by b
D) 4b
Answer:
D) 4b
Step-by-step explanation:
6. What is the range of this sequence? 5, 10, 16, 3, 8, 11, 7, 10, 2 a. 14 b. 12 c. 11 d. 13
9514 1404 393
Answer:
d. 13
Step-by-step explanation:
The smallest number is 3.
The largest number is 16.
The range is the difference between these values:
16 -3 = 13 . . . range of the data
Enter the distance between each pair of islands. Use
the sketch tool if it helps with your thinking.
Press I'Find the Coconuts" to check your work.
Island
Distance Between Islands
(miles)
A(10,10)
B(18,4)
C(25,-5)
9514 1404 393
Answer:
AB = 10
BC ≈ 11.40
Step-by-step explanation:
The distance formula is useful for finding distances between points.
d = √((x2 -x1)² +(y2 -y1)²)
AB = √((18 -10)² +(4 -10)²) = √(8² +(-6)²) = √100
AB = 10
__
BC = √((25 -18)² +(-5-4)²) = √(7² +(-9)²) = √130
BC ≈ 11.40
_____
A sketch tool can be useful for finding or checking the answer.