Answer:
Step-by-step explanation:
there is 1 dime and 12 quarters
A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.
Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that A is more effective than B.
Yes, because a difference in mean rating of 1.5 or more occurred only 23 out of 200 times, meaning the difference is statistically significant and there is convincing evidence that B is more effective than A.
No, because a difference in mean rating of 1.5 or less occurred 167 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
answer is D
The conclusion on if there is convincing evidence that the one detergent is better than the other is; Option D: No, because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
What is the conclusion of the sample research?We are told that, 25 pieces are randomly assigned to be cleaned with detergent A, while the remaining 25 pieces are cleaned with detergent B.
Therefore, we can say that the sample size for both detergent A and detergent B is same. We can also say that the sample is distributed randomly which means that the sample is unbiased (fair).
We are also told that the mean rating for detergent B is found to be significantly less than the mean rating for detergent A. Since we know that the mean is the average of a set of given numbers, then we can conclude that there is No evidence that the one detergent is better than the other because a difference in mean rating of 1.5 or more occurred 23 out of 200 times, meaning the difference is not statistically significant and there is not convincing evidence that one brand is better than the other.
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what is the y-intercept of a line that passes through the points (2, -2.5) and (4, -2)?
Answer:
Step-by-step explanation:
To find the y-intercept, we can use the slope-intercept form of a linear equation which is y = mx + b, where m is the slope of the line, and b is the y-intercept.
Since the line passes through the points (2, -2.5) and (4, -2), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line.
To find the slope(m) we can use the rise over the run formula ,
m = (y2 - y1) / (x2 - x1) = (-2 - (-2.5)) / (4 - 2) = -0.5
then we can substitute the values in point-slope form
y - (-2.5) = -0.5 (x - 2)
And now we can use x = 0,
y = -0.5(0-2) -2.5 = 1.5
so the y-intercept of the line is 1.5
Which equation represents a line that is perpendicular to the line with equation y = 2x - 8? Select all that apply.
Ay=1/2x+1
B. y=-1/2x+1
C. x + 2y = 5
D. -x + 2y = -3
E. -x-2y = 9
Step-by-step explanation:
credits are also on there
I dont know how to prove the equation below...pls help prove it with clear steps, i have no clue how does sin^2x can go into 1+cosx
Answer:
Answer:
Foci: (±5, 0)
Vertex: ( ±4 , 0)
Eccentricity: e = 5/4
Step-by-step explanation:
Hyperbola:
Write the equation of hyperbola in the form,
\boxed{\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1}
a
2
x
2
−
b
2
y
2
=1
9x² - 16y² = 144
Divide the entire equation by 144,
\begin{gathered}\sf \dfrac{9x^2}{144}-\dfrac{16y^2}{144}=\dfrac{144}{144}\\\\\\ \dfrac{x^2}{16}-\dfrac{y^2}{9}=1\\\\\\\dfrac{x^2}{4^2}-\dfrac{y^2}{3^2}=1\end{gathered}
144
9x
2
−
144
16y
2
=
144
144
16
x
2
−
9
y
2
=1
4
2
x
2
−
3
2
y
2
=1
a = 4 and b =3
Eccentricity: e
\boxed{e=\sqrt{1+\dfrac{b^2}{a^2}}}
e=
1+
a
2
b
2
\begin{gathered}\sf = \sqrt{1+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{16}{16}+\dfrac{9}{16}}\\\\=\sqrt{\dfrac{25}{16}}=\sqrt{\dfrac{5*5}{4*4}}\\\\\\=\dfrac{5}{4}\end{gathered}
=
1+
16
9
=
16
16
+
16
9
=
16
25
=
4∗4
5∗5
=
4
5
Foci:
(ae, 0) & (-ae , 0)
\begin{gathered}\sf \left(4*\dfrac{5}{4},0 \right) \ ; \ \left( -4*\dfrac{5}{4},0 \right)\\\\\\(5, 0) \ ; \ (-5,0)\end{gathered}
(4∗
4
5
,0) ; (−4∗
4
5
,0)
(5,0) ; (−5,0)
Vertex of hyperbola:
The vertex of the hyperbola is a point where the hyperbola cuts the axis. (-a , 0) ; (a , 0)
Vertex : (-4 , 0) ; (4 , 0)
Jasmine has $26 to spend on binders and one pack of pens. The pack of pens costs $4. 75. Each binder costs $5. Write an inequality to determine the maximum number of binders she can buy, (Define your variable. )
Jasmine can buy a average of 4 binders because the cost of the binders, multiplied by the number of binders she wants to buy, plus the cost of the pens, must not exceed her total budget of $26.
Step 1: Define the variable. Let x represent the number of binders Jasmine can buy.
Step 2: Write the inequality. 5x + 4.75 ≤ 26
Step 3: Solve the inequality. 5x ≤ 21.25
Step 4: Isolate the variable. x ≤ 4.25
Step 5: The maximum number of binders Jasmine can buy is 4.
Let x represent the number of binders Jasmine can buy
5x + 4.75 ≤ 26
5x ≤ 21.25
x ≤ 4.25
Jasmine has a total of $26 to spend on binders and one pack of pens. The cost of the pens is $4.75, and each binder costs $5. To determine the maximum number of binders she can buy. The inequality we need to solve is 5x + 4.75 ≤ 26. We can solve this inequality by first multiplying both sides of the equation by 5, which gives us 5x ≤ 21.25. We can then isolate the variable by dividing both sides of the equation by 5, which gives us x ≤ 4.25. This means that the maximum number of binders Jasmine can buy is 4.
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is -0.0022 is smaller than -0.022
Answer: No, -0.0022 is not less that -0.022
Step-by-step explanation:
1. We know that the bigger the negative number the lesser it is ( 0.022 is a bigger number than 0.0022) but since it's a negative number it's less in value.
Find whether the following expressions are functions in the ranges they are defined.
The options that shows expressions which are functions in the ranges they are defined are;
Option A: f(x) = 2x + 5
Option B: f(x) = x² + 1
How to identify real numbers and Integers?Real numbers are defined as the combination of rational and irrational numbers, in the number system. This means that, all the arithmetic operations can be performed on real numbers and they can be represented in the number line.
Now, integers are defined as whole numbers that can be positive, negative or zero.
a) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = 2x + 5 will yield an output that is also a real number.
b) We are told that the input of real numbers must yield only real numbers. Yes this is true because any real number we put in for x in f(x) = x² + 1 will yield an output that is also a real number.
c) We are told that the input of real numbers must yield only real numbers. No this is not true because if we put -1 which is a real number for x in the denominator, we will get an undefined function.
d) We are told that the input of integers must yield only integers. No this is not true because if we put 1 for x which is an integer, we will get a fraction which is not an integer.
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, it can be inferred that the greatest possible quotient as required is; 25.
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Find the greatest common factor of $144$ and $405$.
Answer:
Step-by-step explanation:
Find the prime factorization of 144
144 = 2 × 2 × 2 × 2 × 3 × 3
Find the prime factorization of 405
405 = 3 × 3 × 3 × 3 × 5
To find the GCF, multiply all the prime factors common to both numbers:
Therefore, GCF = 3 × 3
Answer = 9
In a triple batch of spice mix, there are 6 teaspoons of garlic powder and 15 teaspoons of salt. Answer the following questions about the mix. If you get stuck, create a double number line.
In a double number line diagram, equal ratios are represented by two parallel number lines. On both number lines, the tick marks are in the same places. Though the other numbers are frequently varied, the tick marks labeled with 0 always line up.
How to create a double number line?According to question:-
How much more garlic powder than salt is in the triple batch?
Answer: 6 teaspoons of garlic powder - 15 teaspoons of salt = -9 teaspoons. So there is 9 teaspoons less garlic powder than salt in the triple batch.
How much spice mix is in the triple batch?
Answer: 6 teaspoons of garlic powder + 15 teaspoons of salt = 21 teaspoons of spice mix.
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Tyler is flying a kite on 100 feet spring how high is it above the ground if the horizontal distance between Tyler and the kite is 600 feet
If the horizontal distance between Tyler and the kite is 600 feet then the kite is 80 ft above the ground.
Pythagorean theoremPythagoras's Theorem is a fundamental result in Euclidean geometry that states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. This can be mathematically represented as:
[tex]c^2 = a^2 + b^2[/tex]
Where c is the length of the hypotenuse, and a and b are the lengths of the legs of the triangle.
The theorem is named after the ancient Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof, although it is often argued that the theorem may have been known to the Babylonians and Indians over a thousand years earlier.
Pythagoras's theorem is widely used in mathematics and physics, especially in trigonometry and in the study of triangles and their properties, and it's also used to find the distance between two points in a two-dimensional space, for example, in cartesian coordinates.
Hypotenuse2 = Perpendicular2 + Base2
c2 = a2 + b2
We apply the Pythagorean Theorem to determine the kite's height, h
the problem can solve if the kite is 60feet
[tex]h^2 = 100^2 - 60^2\\h^2 = 10000 - 360\\h^2 = 6,400\\h=\sqrt{6400} \\h=80[/tex]
h =80 ft (we take the positive solution since the height can not be negative number)
The kite is 80 ft above the ground.
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A college biology lab selected 65 women and 65 men at random and recorded their body temperatures (in degrees Fahrenheit). The distributions of their temperatures are shown below.Which statement gives an accurate comparison of the body temperatures of women and men shown?
Question 5 options:
1.)The mean body temperature for women is less than for men and women's temperatures vary more than men's temperatures.
2.)The mean body temperature for women is greater than for men and women's temperatures vary less than men's temperatures.
3.)The mean body temperature for women is less than for men and women's temperatures vary less than men's temperatures.
4.)The mean body temperature for women is greater than for men and women's temperatures vary more than men's temperatures.
Answer: Choice 2
Step-by-step explanation:
Willl mark you brainlieestttt
Answer:
√28 and √11
Step-by-step explanation:
Note : -
Irrational number is any real number that cannot be expressed as the quotient of two integers.
Here,
√28 = 5.291.......
5.291.... is an infinite number, it keeps going, it cannot be expressed in terms of a fraction.
Similarly,
√11 = 3.316......
Hence,
√28 and √11 are irrational numbers.
Yara is 8 years old. Yara's mother is 4n times older than Yara. How old
was Yara's mother 5 years ago in terms of n?
Yara's mother was 32n-5 years old 5 years ago in terms of n.
Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:
Mother's age = 4n * 8 years
We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:
Mother's age 5 years ago = 4n * 8 years - 5 years
Now we can simplify this equation:
Mother's age 5 years ago = 32n - 5 years
Now we can substitute the value of n to find the mother's age in terms of n.
To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.
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for k(x)=4÷5x-6,determine k^-1(8)
The value of k⁻¹(8) in for k(x) = 4 ÷ 5x - 6 is 2/35.
What is an inverse function?First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.
We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.
Given, k(x) = 4 ÷ 5x - 6.
k(x) = (4/5x) - 6.
Let, y = k(x).
y = (4/5x) - 6.
(4/5x) = y + 6.
1/x = 5(y + 6)/4.
x = 4/{5(y + 6)}.
y = 4/{5(x + 6)}.
k⁻¹(x) = 4/{5(x + 6)}.
k⁻¹(8) = 4/{5(8 + 6)}.
k⁻¹(8) = 4/{5(14)}.
k⁻¹(8) = 4/70.
k⁻¹(8) = 2/35.
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PLEASE HELP!
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails. The manager found that 0.3 pounds of nails in the sample were defective. They were either bent, the heads were damaged, or they had been clipped too short during manufacture. How many pounds of defective nails should the manager expect the 350-pound delivery to contain? Round your answer to the nearest tenth of a pound.
There are 23.33 pounds of defective nails should the manager expect the 350-pound delivery to contain.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The manager of a hardware store took a random sample of 4.5 pounds of nails from a delivery of 350 pounds of nails.
And, The manager found that 0.3 pounds of nails in the sample were defective.
Since, The manager found that 0.3 pounds of nails in the sample were defective.
Hence, Amount of pounds of defective nails should the manager expect the 350-pound delivery to contain is,
⇒ 350 × 0.3 / 4.5
⇒ 23.33 pounds
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Vanessa will sell yogurt for $2.50 a cup. Fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt.
Answer:
2.50 × 19 = 47.5
Therefore, she would get $47.5 if she sold 19 cups.
Suppose that you have 8 cards. 5 are green and 3 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 3 yellow cards are numbered 1, 2, and 3. The cards are well shuffled. You randomly draw one card. G
The necessary probabilities are 3/8, 1/3, 9/64, and 37/64.
What is probability?The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
S = { G1, G2, G3, Y1, Y2, Y3, Y4, Y5 }
G = { G1, G2, G3 }
P(G) = 3/8
E = { G2, Y2, Y4 }
P(G|E) = 1/3
P(G and E) = P(G)*P(E) = (3/8)*(3/8) = 9/64
P(G or E) = P(G) + P(E) - P(G and E) = (3/8) + (3/8) - (9/64) = (6/8) - (9/64) = (48/64) - (9/64) = 37/64
The required probability is 3/8, 1/3, 9/64 and 37/64.
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How do you create a function in forex?
A trader can create their own automated trading strategies in forex by writing a script or program in a programming language, such as MQL4 or Python. This script will contain instructions to execute trades according to specific criteria defined by the trader. They can then backtest the strategy to see how it performs.
1. Decide on a trading strategy. This could include things like setting entry and exit points, calculating position sizes, and setting stop losses and take profits.
2. Choose a programming language that is compatible with the trading platform you are using, such as MQL4 or Python.
3. Write the script or program that will contain the instructions for the trading platform to follow in order to execute the trading strategy.
4. Test the script or program to make sure it works properly.
5. Run a backtest to see how the trading strategy performs.
6. If the results of the backtest are satisfactory, you can deploy the trading strategy on the trading platform.
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How does the parabola open? Is the vertex a minimum or maximum value?
f(x) = 5x²-3x
The parabola is open upward direction. The vertex is the minimum value of the parabola.
What is a parabola?
A parabola is a planar curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits various seemingly disparate mathematical descriptions, all of which can be shown to define the same curves. A point and a line are two ways to describe a parabola.
Given quadratic function is
f(x) = 5x² -3x
The leading term of the given function is 5x².
The sign of the leading term is positive, thus it is open upward direction.
Rewrite the given function in the form f(x) = a(x - h)² + k
f(x) = 5x² -3x
f(x) = 5( x² - 3/5 x)
f(x) = 5( x² - 3/5 x + 9/100 - 9/100)
f(x) = 5( x² - 3/5 x + 9/100) - 5 × 9/100
f(x) = 5( x - 3/10)² - 9/20
f(x) = 5( x - 3/10)² + (-9/20)
The vertex of the parabola is (3/10, -9/20).
Since the parabola opens upward direction, thus the vertex of the parabole is a minimum value.
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The square on the right is a scaled copy of the square on the left. Identify the scale
factor. Express your answer as a whole number or fraction in simplest form.
8
8
4
Writing the whole number in the numerator and 1 in the denominator. Fraction in simplest form is 8
In the simplest form, how do you write an answer as a fraction?How to Find the Most Basic Form
Determine the GCF of the fraction’s numerator and denominator.
Divide the created GCF by the numerator and denominator.
Fill in the blanks with the simplified fraction of the supplied fraction.
The most basic form, If the top and bottom have no common components other than 1, the fraction is in its simplest form. In other words, the top and bottom cannot be divided any further and still remain full numbers. You may sometimes hear the phrase “lowest terms” when referring to the simplest form.
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What are the x-intercept and the y intercept of the graph of 6x - 3y = 36?
The x-intercept and the y intercept of the graph of 6x - 3y = 36 are x = 6 and y = -12
How to determine the x-intercept and the y intercept of the graph?
From the question, we have the following parameters that can be used in our computation:
6x - 3y = 36
Set y to 0 to determine the x-intercept
So, we have the following representation
6x = 36
Divide by 6
x = 6
Set x to 0 to determine the y-intercept
-3y = 36
Divide by -3
y = -12
hence, the intercepts are x = 6 and y = -12
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Starting with a randomly selected box of cereal from the manufacturing line every 50th box of cereal is removed and weighed the mode weight of a days sample us calculated
Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.
what is mode ?The value that consistently appears in a given set is known as the mode in statistics. The mode or modal value is the value or number that appears most frequently in a data set and has a high frequency. Along with mean and median, there are three other ways to measure central tendency. The mode can be calculated quite easily. After sorting the numbers in a set according to their order—lowest to highest or highest to lowest—count how many times each number appears in the group.
given
Example: 50th box of cereal
All cereal boxes are lined up in the population
Example Parameter: The cereal box's average weight
Population metric: The cereal on the line's average weight
Sample Parameter: The population's weight and the average weight of the cereal box The grain on the line's average weight is the parameter.
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What is 2/3 + 1/6 + 2/8
Answer:
2/3 + 1/6 + 2/8
=(2×8+1×4+2×3)/24
=(16+4+6)/24
=26/24
=13/12
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need help with #7 a and b. i’m in Algebra 1 and this is lesson 5 Exponential Algebra and Functions.
There is no upper limit if the ratio raises x to a higher power. The limit is 0 if the ratio causes the power of x to be reduced to zero.
A ratio is what?A ratio is an expression for an ordered pair of numbers, a and b, where b is not equal to zero and the expression is written as a/b. A ratio is created by combining two ratios. Assuming a ratio of one boy to three girls, this would suggest that 3/4 of the population is female and only 1/4 is male. A part can be an amount, a percentage, or the difference between two or more objects.
Here,
The ratio of, say, the highest-degree words serves as the upper bound as x grows.
There is no upper bound on how much the ratio can raise the power of x. The limit is 0 if the ratio causes the power of x to be reduced to zero.
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Please help asap! Appreciate everyone!
Answer:
b and c
Step-by-step explanation:
b is basically saying flip it up and turning the whole thing left which will put it on top of pnms and c is saying rotate it where line sr and sm would be side by side then flip it right
difference between -0.4 and 44.4
Answer:
44.8
Step-by-step explanation:
44.4 - (-0.4) = 44.8
Is the area of an equilateral triangle is 196 root 3 cm square then each of its side is?
Therefore , In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.
What is triangle?
Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.
What is polygons ?A polygon is a closed two-dimensional geometric shape that has three or more straight sides. The sides of a polygon are called edges and the points where the edges meet are called vertices.
Here,
We must apply the mathematical procedure for computing an equilateral triangle's area.
An equilateral triangle's area is equal to 3/4 of each side; assume that each side is x cm long.
[3/4 (a)2] cm2 is the equilateral triangle's surface area.
In light of the information mentioned in the query,
√3/4 × (a)² = 196√3
a²/4 = 196√3/√3
a²/4 = 196
a² = 196×4
a² = 784
a = √784
a = 28
In the instance of an equilateral triangle, each side's length (3 sides are equal) is equivalent to 28 cm.
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Use the distributive property to rewrite each expression. Then evaluate. 14 (102)
Using the distributive property to rewrite the expression, gives (14 x 10) + ( 14 x 2). When evaluated, the result would be 168.
What is the distributive property?According to the distributive property, it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.
This means that with the formula given, 14 (10 + 2):, the distributive property makes it:
= 14 (10 + 2)
= (14 x 10) + ( 14 x 2)
The evaluation gives :
= (14 x 10) + ( 14 x 2)
= 140 + 28
= 168
In conclusion, using the distributive property gives (14 x 10) + ( 14 x 2).
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The first rule is add 4 starting from 2. The second rule is subtract 4 starting from 28. What is the second ordered pair using the terms in each sequence? A (2, 28) B(6, 24) C (14, 16) D (10, 20)
The second ordered pair using the terms in each sequence is B (6, 24).
THE SEQUENCE PAIRThe first rule says to add 4 to the first term of the ordered pair, starting from 2. So the first term of the second ordered pair would be 2+4 = 6.The second rule says to subtract 4 from the second term of the ordered pair, starting from 28. So the second term of the second ordered pair would be 28-4 = 24.
Therefore, the second ordered pair using the terms in each sequence is B (6, 24).
The third ordered pair using the terms in each sequence would be C (14,16) and the fourth ordered pair would be D (10,20)This is because:
C (14,16) can be obtained by adding 4 to first term of B(6,24) which is 6+4 = 10 and subtracting 4 from second term of B(6,24) which is 24-4=20.
D (10,20) can be obtained by adding 4 to first term of C(14,16) which is 14+4 = 18 and subtracting 4 from second term of C(14,16) which is 16-4=12.
So the sequence list of ordered pair would be:
First order: A (2,28)
Second order: B(6,24)
Third order: C (14,16) D (10,20)
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