Using the t-distribution, it is found that since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 7 ounces, that is:
[tex]H_0: \mu = 7[/tex]
At the alternative hypothesis, it is tested if the mean is different of 7 ounces, that is:
[tex]H_1: \mu \neq 7[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given by:
[tex]\overline{x} = 7.04, \mu = 7, s = 0.17, n = 18[/tex]
Hence the value of the test statistic is found as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{7.04 - 7}{\frac{0.17}{\sqrt{18}}}[/tex]
t = 1
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with 18 - 1 = 17 df and a significance level of 0.1, the critical value is of [tex]t^{\ast} = 1.7341[/tex]
Since the test statistic is between -1.7341 and 1.7341, we do not reject(accept) the null hypothesis, hence there is not enough evidence to conclude that the true mean discharge differs from 7 ounces.
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What is the range of the function in the graph?
The range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
What is the Range and Domain of a Function?All the possible set of x-values that are plotted on the horizontal axis (x-axis) are the domain of a function. In order words, they are the inputs of the function.
On the other hand, all the corresponding set of x-values that are plotted on the vertical axis (y-axis) are the range of a function. In order words, they are the outputs of the function.
In the graph given below that shows a function, s is plotted on the vertical axis (y-axis), and its values starts from 20, up to 100. The range can be said to be all values of s that are from 20 to 100.
Therefore, the range of the function in the graph given can be expressed as: D. 20 ≤ s ≤ 100.
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Mia, Keela And Michelle are selling girl scout cookies.In all they have sold $800 worth of cookies. Mia sold 57 boxes, Keela sold 28 boxes and Michelle sold 15 boxes. How should the girls split the money so that they earn the same fraction as the boxes of cookies that they sold? Should Mia and Michelle get the same amount of money? Why Or Why not?
Answer:
the money should be split as per each girl sold. total boxes sold is 100.
Step-by-step explanation:
total boxes sold is 100. Mia sold 57/100 keela 28/100 and Michelle 15/100.
mia=456$
keela=224$
michelle=120$
calculated as boxes sold/100 x 800$
Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. what are the minimum and maximum possible values of f(8) − f(3)?
The minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.
Taking the given inequality as (i).
We are asked to find the minimum and maximum possible values of f(8) - f(3).
We multiply (i) by dx throughout, to get:
4dx ≤ f'(x)dx ≤ 5dx.
To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:
[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]
Thus, the minimum value of f(8) - f(3) is 20.
The maximum value of f(8) - f(3) is 25.
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if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z
(B) find x : y : z
Step-by-step explanation:
x:y=0.75:0.90
Here,
Dividing by the value of y=0.90,
x:y=0.75/0.90:0.90/0.90
=5/6:1
Similarly,
y:z=1/3:1/4
Dividing by 1/3,we get,
y:z=1:3/4
Now,
X:y:z=5/6:1:3/4
Multiplying by both value of y,0.90×1/3=3/10
x:y:z=5/6×3/10:1×3/10:3/4×3/10
By solving this,
x:y:z=1/4:3/10:9/40what is the parent function of g(x) = 3cos (x + 180°) + 1
The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
What are parent functions?Parent functions are the basic function that represents the entire family of that function family
How to determine the parent function?The function is given as;
g(x) = 3cos (x + 180°) + 1
As a general rule, the parent function of any function is the basic equation of the function family
The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)
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Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
The rate of change in the plant's height in terms of inches per week will be 1 2/3 inches.
How to calculate the rate?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.
The calculation for the rate of change is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.
The change in y (y being the height of the plant) over 4 weeks was 6 2/3 inches and there are four weeks. Therefore, the average height will be:
= 6 2/3 ÷ 4
= 1 2/3 inches
The average rate of change of the plant growth per week was 1 2/3 inches.
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Complete question:
Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.
a.+1 2/3B)-1 2/3C)+3/5D)-5/2
Gilbert plans to invest $14 000 into two types of bonds. one bond yields 8% interest each year and the other bond yields 12% interest each year. he needs to earn $1400 each year to consider the investment successful. how much should he invest in each bond?
invest in each bond = $7000
What is Profit and Loss?An income statement, also known as a profit and loss account, is one of a company's financial statements and displays the company's receipts and outlays for a specific time period. It explains how revenues are converted into net income or net profit.
According to the given data:
Let n be the amount invested at 8%
the amount invested at 12% would be : 14000-n
so,
8n+12(14000-n) = 1400
8n + 168000 - 12n = 1400 * 100
4n + 168000 = 140000
n = 28000/4
= 7000
Therefore,
At 12% amount invested
= 14000 - 7000
= $7000
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Viviana is tracking the number of calories she burns working out. Her watch
tracker says she burned 596 calories in 1 hour. Approximately how many calories
did she burn per minute? Round to the nearest tenth.
Answer:
9.93 calories
Step-by-step explanation:
If 596 calories = 1h
then ?? calories =1m
since 1h=60 min
>>( 1/60)×596
=9.93 calories
Which expression is equivalent to the given expression?
Assume the denominator does not equal zero.
a^3b^5 / a^4b
A. b^4 / a
B. a / b^4
C. 1 / ab^4
D. ab^4
The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.
Which of the answer choice represents an expression which is equivalent to the given expression?The given expression according to the task content is; a³b⁵/a⁴b.
It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;
a^(3-4)b^(5-1)
Consequently we have;
b⁴/a.
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Carly takes three steps to walk the same distance as jim walks in four steps. each of carly’s steps covers 0. 5 metres. how many metres does jim travel in 24 steps?
The distance travelled by Jim in 24 step is 9 miles by unitary method.
According to the given question.
The number of steps travelled by Jim = 24
Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".
Therefore, by unitary mehod we can say that
The number of steps walked by Carly = 3 × (24/4) = 3 × 6 = 18
So, the distance travelled by Carly in 18 steps
= 18 × 0.5miles
= 9 miles
Since, the Carly's 18 steps is equals to Jim's 24 steps.
Therefore, the distance travelled by Jim in 24 step is 9 miles.
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What is the slope of a line that is parallel to the line whose equation is y=45x−3?
The slope is (B) -5/4.
What is a slope?The slope is the inclination of a line relative to the horizontal as a numerical value. The slope of any line, ray, or line segment in analytic geometry is the ratio of the vertical to the horizontal distance between any two points on it ("slope equals rise over run").To find the slope:
We're going to assume that we don't mean, y = 45x -3; which has a perpendicular line with a slope of -1/45.Rather, we're going to assume that we mean, y = 4/5x -3; so that the slope of the perpendicular line is -5/4.Similarly, we're going to assume that the answer choices are supposed to represent fractions so that the above slope matches choice B.If the slope of a line is m, the slope of the perpendicular line is -1/m.The reciprocal of a fraction is the fraction that has the numerator and denominator swapped, -1/(4/5) = -5/4.Therefore, the slope is (B) -5/4.
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The complete question is given below:
What is the slope of a line that is parallel to the line whose equation is y=45x−3?
A. −4/5
B. −5/4
C. 5/4
D. 4/5
Select the equation of a straight line that is perpendicular to the line y = 3x - 2.
A y = 3x - 5
B 3y=x+2. C y=- -3x-2 D y= -x/3+2 E y=1\3x-2
[tex]y = mx + b \\ y = nx + c \\ for \: the \: two \: lines \: to \: be \: perpendicular \\ m.n = - 1[/tex]
[tex]m = 3 \\ \\ 3n = - 1 \\ n = \frac{ - 1}{3} [/tex]
Answer: D[tex]y = \frac{ - x}{3} + 2[/tex]
17. A bag contains 2x yellow counters, 4x + 6 red counters and 6x - 10 blue counters. a. Write an expression, in terms of x, for the total number of counters in the bag.
The total number of counters in the bag is 44.
b. Work out the number of blue counters in the bag.
c. How many more red counters are there than blue counters in the bag?
Answer: 12x-4, 14 counters, 8 more counters
Step-by-step explanation: There are 2x yellow, 4x+6 red, and 6x-10 blue counters. We need to add all of this up to get the total number of counters. We first add the x's : 2x+4x+6x = 12x. Then we add the numbers. 6+ (-10) is -4. So, our expression is 12x-4. Next, we need to find out how many blue counters are in the bag. We know that there are 44 total counters and we need to find x because all the counters have x in them. 12x-4 = 44. We first add 4 to both sides to get 12x= 48 and x = 4. blue has 6x-10 counters so, blue has 24-10 = 14 counters. Red has 16+6 = 22 counters. 22-14 = 8 more counters
Find the perimeter of the shaded figure. PLS ASAP
Answer:
54
Step-by-step explanation:
im having trouble with this question! pls help
Using a proportional relationship, it is found that the unit rate of change is of 9.
The relation d = 9t is graphed at the end of the answer.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, we have d as a function of t, hence the relationship is:
d = kt.
When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:
k = d/t = 1.8/0.2 = 9
The relation d = 9t is graphed at the end of the answer.
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graph the function
g(x)=3x^2+1
Answer:
x=1, y=4;
x=2, y=13
Step-by-step explanation:
What is the total number of common tangents that can be drawn to the circles
The total number of common tangents that can be drawn to the circles is 2.
What is a tangent?A tangent serves as line that touches the circle at a single point whereby the point where tangent meets the circle is the tangency.
A tangent to a circle can be described as the straight line that touches the circle at only one point.
Therefore, from the definition, The total number of common tangents that can be drawn to the circles is 2.
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Miguel created the ratio table below to show how he uses the money he earns at work.
Miguel’s Money
Money Earned
(dollars)
Money Saved
(dollars)
10
8
50
40
120
?
150
120
How much money will he save if he earns 120 dollars?
The amount of money that Miguel would save when he earns $120 is $96.
How much would Miguel save?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
A ratio table can be described as table that shows equivalent values between two or more numbers and helps us to understand the relationship between the numbers.
The first step is to determine the ratio between the money earned and the money saved.
Ratio = money saved / money earned
8/10 = 0.8
Now, multiply the ratio gotten in the previous step by the amount earned to determine the amount saved.
Amount saved = amount earned x ratio
0.8 x 120 = $96
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Answer:
96
Step-by-step explanation:
I took the quiz edge 2022
Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic
The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.
According to the statement
We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.
So,
According to this representation,
A linear representation is a representation on a category of vector spaces or similar.
The other meaning is that when the growth increases linearly or at the constant speed.
In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.
linear representation explain this graph perfectly.
So, Linear model suits best to this graphical representation.
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A 105
5) How will you educated, uneducated people in your locality
about the environment problems of your locallly.
I will educated uneducated people on my locality
Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community.
How to improve the uneducated people in our locality about the environmental problems of our local?Get your associates, neighbors, friends, family, or even your local government concerned. It's much more comfortable and more useful to apply environmental attention and create a local project if you cooperate with others in our community. Encouraging environmental awareness exists a vital aspect of being an environmental guardian.
Facilitate knowledge transfer from workers approaching retirement to workers of all ages. Work with families to support children in school and control illiteracy. Provide young people from deprived backgrounds the norms to study. Improve access to education for Aboriginal people.
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How many solutions does the equation −3y 3y 4 = 4 have? none infinitely many one four
A given linear equation has infinitely many solutions.
What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that make a linear equation true and plot those values on a coordinate grid.As much as possible, reduce the equation to y = mx + b. Verify the exponents in your equation. It is nonlinear if it has exponents. Your equation is linear if there are no exponents in it.The definition of a linear equation is an equation with a maximum degree of one.Given: −3y 3y 4 = 4
3y+4=3y+4
The given linear equation satisfies any value of 'y'.
So, A given linear equation has infinitely many solutions.
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Find x. A. 4–√6 B. 16√6/3 C. 4√6/3 D. 32√3/3
Answer:
Step-by-step explanation:
12
Line segment st is dilated to create line segment s't' using the dilation rule dq,2.25. point q is the center of dilation. line segment s t is dilated to create line segment s prime t prime. the length of q t is 1.2 and the length of q s is 2. the length of s s prime is x and the length of t t prime is 1.5. what is x, the distance between points s' and s?
The distance between points S' and S is 2.5 units.
What is proportionality theorem in triangles?If a line is drawn parallel to any one side of a triangle so that it intersects the other two sides in two distinct points, then the other two sides of the triangle are divided in the same ratio.
Given that,
line segment ST is dilated to create line segment S'T' using the dilation rule DQ.
Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5 units, SS' = x units.
We need to find the value of x, the distance between points S' and S.
Since the line ST is dilated to S'T' with center of dilation Q, so the triangles STQ and S'T'Q must be similar.
We know that the corresponding sides of two similar triangles are proportional.
So, from ΔSTQ and ΔS'T'Q, we get
[tex]\frac{SQ}{S'Q} =\frac{TQ}{T'Q}[/tex]
[tex]\frac{SQ}{SQ+S'S} =\frac{TQ}{TQ+T'Q}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{1.2+1.5}[/tex]
[tex]\frac{2}{2+x} =\frac{1.2}{2.7}[/tex]
[tex]\frac{2}{2+x} =\frac{12}{27}[/tex]
[tex]\frac{1}{2+x} =\frac{6}{27}[/tex]
12+6x = 27
6x = 15
x = 2.5
Hence, Thus, the required value of x is 2.5 units.
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Type the missing number in this sequence: 4, , 144, 864, 5,184, 31,104
The missing number in the given series is 24.
What is missing number in the given sequence?Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.
Given the series,
4, ?, 144, 864, 5184, 31104
Multiplying with 6 in each term in the given sequence.
4×6 = 24
24×6 = 144
144×6 = 864
864×6 = 5184
5184×6 = 31104
Following the above sequence, we get the 2nd term is 24.
Hence the missing number is 24.
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Mrs. Wood is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 716 books had no damage, 68 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 36,500 books in the collection should Mrs. Wood expect to have major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.
Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For this problem, the proportion of books with major damage is:
43/(716 + 68 + 43) = 0.051995.
Hence, out of 36,500 books, the expected amount of books with major damage is:
0.051995 x 36,500 = 1898.
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A certain type of thread is manufactured with a mean tensile strength of kilograms and a standard deviation of kilograms. How is the variance of the sample mean changed when the sample size is
In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
What occurs if the variance increases?Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.
Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.
Therefore, In the case above:
(a) If there is an increased from 64 to 196, then the variance decreases.
(b) If there is a decreased from 784 to 49, then the variance increases.
See full question below
A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?
What is the variance about?
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Please helppppp!!
Question #1 (Question un ) : What is the smallest positive integer k such that k/660 can be expressed as a terminating decimal?
Give BRAINLIST IF ANSWER!!!!!
Answer:
k = 33
Step-by-step explanation:
Terminating decimal numbers: Decimals that have a finite number of decimal places.
For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5. As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.
Prime factorization of 660:
⇒ 660 = 2 × 2 × 3 × 5 × 11
⇒ 660 = 2² × 3 × 5 × 11
Therefore:
[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]
The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out. To do this, their lowest common multiple must be the numerator:
⇒ LCM of 3 and 11 = 3 × 11 = 33
[tex]\implies \sf \dfrac{33}{660}[/tex]
[tex]\implies \sf k=33[/tex]
Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.
Answer:
33
Step-by-step explanation:
Evaluate f(-3) for f(x) = 2^x
a. 1/8
b. -8
c. 8
d. -6
Answer:
A
Step-by-step explanation:
f(-3) = 2^-3
to get rid of a negative in an exponent, move the whole thing to the denominator.
1/(2^3)
2^3 = 2×2×2
1/(2×2×2)
1/8
In the accompanying diagram, three vertices of parallelogram ORST are O(0,0), R(b,d), and T (a,0). What are the coordinates of S
Based on the coordinates of the vertices of the parallelogram ORST, the coordinates of S can be found to be (a + b, d).
What are the coordinates of point S?As this is a parallelogram, the horizontal distance between O and R would be the same as the horizontal distance between S and T.
The horizontal distance between O and R is represented by "b".
The horizontal distance between T and S would therefore be:
= a + b
The fact that R and S are on the same plane would mean that the y-value of S is the same as that of R which is d.
The coordinates of S is:
( a + b, d).
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Which of the following shapes could be formed by taking a longitudinal section perpendicular to the base of a rectangular prism?
The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.
What is a three dimensional shape?A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.
A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.
A rectangular prism is a three-dimensional shape, having six faces, where all the faces are rectangles.
The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.
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