a. The decision rule for this question would be to reject the null hypothesis if test statistic is less than the critical value.
b. The test statistic is given as: -3.4091
What is the hypothesis?We have the null hypothesis as
h0 : μ ≥ 69
The alternate hypothesis is
H1 : μ < 69
a. The decision rule would be to reject the null if the test statistic is greater than the critical value
at α = 0.10 the degree of freedom = 36 - 1 = 35
the critical value is -1.306
The test statistic calculation
[tex]t =\frac{ x - u}{s/\sqrt{n} }[/tex]
[tex]t = \frac{64-69}{8.8/\sqrt{36} }[/tex]
t = -3.4091
The decision rule would be to Reject H0: µ ≥ 69 when the test statistic is less than -1.306.
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Suzanne is designing a garden for the Gateway Botanical Center. She used a scale of 1 : 600 to make the drawing below. 5 cm 15 cm What is the actual area of the garden, in square meters? (1m = 100 cm)
The given scale is 1:600.
The dimensions of the drawing are 5 by 15.
We just have to multiply each dimension by 600.
[tex]\begin{gathered} 5\times600=3000 \\ 15\times600=9000 \end{gathered}[/tex]So, the dimensions of the actual area are 3,000 cm and 9,000 cm. But, we know that 1 meter equals 100 centimeters, let's transform.
[tex]\begin{gathered} 3000cm\cdot\frac{1m}{100\operatorname{cm}}=30m \\ 9000\operatorname{cm}\cdot\frac{1m}{100\operatorname{cm}}=90m \end{gathered}[/tex]Then, we multiply the dimensions to find the area.
[tex]A=30m\times90m=2700m^2[/tex]Hence, the actual area is 2,700 square meters.5. A baker makes 275 wheat rolls.
He fills 9 boxes with 24 rolls in
each box. How many rolls are
not in boxes?
Answer:
59 rolls are not in boxes
Step-by-step explanation:
9×24=216-275=59
Jake and Joshua go to different theme parks during the day. Jake must pay a fee of $30 for a ticket and additional 4$ for every food/beverage. Joshua has to pay 50$ for a ticket and additional 6$ for the food and drinks. How many beverages and food would it take for Joshua to have the same amount of pay as Jake? Graph the item.Write a system of equations, graph them, and type the solution.
To answer this question, we will set a system of equations, and we will solve the system by the graphical method.
Let x be the number of times Jake buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=30+4x\text{.}[/tex]Its graph is:
Now, let x be the number of times Joshua buys drinks and food, then the total amount he will pay is determined by the following equation:
[tex]T=50+6x\text{.}[/tex]Graphing both equations we get:
The intersection of the graphs is the point,
These figures are similar. Thearea of one is given. Find thearea of the other.area=32 in?9 in12 in[ ? Jina
To find the area of similar figures whe you know the area of one of the figures and the length of corresponding sides:
1. Find the scale factor: in this case as you have the area of the largest figure find the scale factor for a reduction:
[tex]SF=\frac{small}{\text{big}}=\frac{9}{12}=\frac{3}{4}[/tex]2. Find the missing area: the area in similar figures is equal to the scale factor squared multiplied by the given area.
[tex]\begin{gathered} A=(\frac{3}{4})^2\cdot32in^2 \\ \\ A=(\frac{9}{16})\cdot32in^2 \\ \\ A=\frac{288}{16}in^2 \\ \\ A=18in^2 \end{gathered}[/tex]Then, the missing area is 18 square inchesan alloy contains copper and zinc in the ratio 3:7. find the mass of the metal in 750g of alloy
Given:
An alloy contains copper and zinc in a ratio of 3:7. The total mass of the alloy is 750g.
Required:
Find the mass of the metal in 750g of alloy.
Explanation:
Let the mass of the metal is x gm.
The weight of copper = 3x
The weight of zinc= 7x
Total weight
[tex]\begin{gathered} 3x+7x=750 \\ 10x=750 \\ x=\frac{750}{10} \\ x=75\text{ gm} \end{gathered}[/tex]
A building worth $829,000 is depreciated for tax purposes by its owner using the straight-line depreciation method.
The value of the building, y, after x months of use, is given by y=829,000-2700x dollars. After how many years will
the value of the building be $699,400?
The value of the building would be $699,400 in 4 years.
What will be the value of the building?Depreciation is the when the value of an asset reduces as a result of wear and tear. Straight line depreciation is a method used in depreciating the value of an asset linearly with the passage of time.
The equation that can be used to determine the value of the building with a straight line depreciation is:
Value of the asset = initial value of the asset - (number of months x deprecation rate)
y = 829,000 - 2700x
The first step is to determine the number of months it would take for the building to have a value of $699,400.
$699,400 = 829,000 - 2700x
829,000 - 699,400 = 2,700x
129,600 = 2,700x
x = 129,600 / 2,700
x = 48 months
Now convert, months to years
1 year = 12 months
48 / 12 = 4 years
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Instructions:Prepare a written response to the prompt below using a word processor. Please save your file in .doc or .docx format. Yourresponse should be in complete sentences.*To view the grading rubric for this assignment, click on the name of the assignment and click "View Rubric"Assignment Prompt:1. Explain, using the numeric expression below, how to use Order of Operations to compute a numeric value of anexpression.70-2052 - 22)3 +5.(-2)2. Why is it important to have an agreed upon set of rules to determine the order of how we add, subtract, multiply.divide, etc.?3. Please submit your document by clicking on the name of this assignment (above) and attaching your file on the nextscreen.4. If you have any questions, please ask your professor.
We need to solve the following expression:
[tex]70-2(5^2-22)^3+5(-2)[/tex]The order of operations is a rule that tells the correct sequence of steps for evaluationf a math expression. We can remember the order using PEMDAS: Parenthesis, Exponents, Multiplication and Division (from left to right).
Then, in our expression, we must solve parenthesis first. It yields
[tex]\begin{gathered} 70-2(25-22)^3-10 \\ 70-2\times3^3-10 \end{gathered}[/tex]The next step is to raise exponents,
[tex]70-2\times27-10[/tex]and now, the multiplication step
[tex]70-54-10[/tex]then, we get 70-64 and the solution is 6.
helpppppp plssssssssssssssssssss
Answer:
No.
Step-by-step explanation:
Pre-SolvingWe are given the following inequality:
[tex]76 < 5-\frac{136}{s}[/tex]
And we want to know if s=2 is a solution, meaning if s is 2, will the inequality still be true?
SolvingWe can substitute 2 for s in the inequality to test it.
Replace s with 2.
[tex]76 < 5-\frac{136}{2}[/tex]
First, let's divide 136 by 2.
136/2 = 68
The inequality is now:
76 < 5 - 68
Subtract 68 from 5.
76 < -63
The inequality reads "76 is less than -63", which is a false statement (76 is positive, -63 is negative, and positive numbers are greater than negative numbers).
Ergo, s = 2 is not a solution to the inequality.
kenny has red marbles, 3 blue marbles,and 4 black marbes. Which ration compares a part to the whole? Please help me
A ratio comparing a part to the whole must then have 9 as the second number.
In this question, we have been given Kenny has red marbles, 3 blue marbles, and 4 black marbles.
We need to find the ratio that compares a part to the whole.
Here, the total number of marbles are:
2 red + 3 blue + 4 black = 9 marbles.
Let x be either number of marbles (either red marbles or blue marbles or black marbles)
Then the ratio that compares a part to the whole would be,
x : 9
Therefore, a ratio comparing a part to the whole must then have 9 as the second number.
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helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:f(x) = 1/4x
Step-by-step explanation:
Assuming this is a linear equation, we simply use the two points given to find the slope (or gradient depending on where you’re from), to find the equation. So just do rise over run:
Edited: I divided backwards, apologies!
-3 - (-2)/-8 - (-12) = -5/-20 = 1/4x.
write each percent as a decimal 1%
You have the following percentage:
24.1%
In order to determine the associated decimal to this fraction you proceed as follow:
Find all numbers whose absolute value is .4]
The numbers 4 and - 4 have an absolute value equal to 4.
What numbers are associated to a given absolute value?
In this question we need to find all the numbers such that absolute value is equal to 4. This can be found by using the definition of absolute value:
|x| = x for x ≥ 0.|x| = - x for x < 0.Absolute values are functions that contains only the magnitudes of the numbers, that is, their distances with respect to zero. Then, if the absolute value is 4, then, the number may be 4 or - 4.
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The absolute value is 4, then, the number may be 4 or - 4.
What are Absolute values?Absolute value describes the distance from zero that a number is on the number line, without considering direction
To find all the numbers such that absolute value is equal to 4.
By definition of absolute value we have
|x| = x for x ≥ 0.
|x| = - x for x < 0.
Absolute values contains magnitude which does not have direction.
|4|=4 for 4≥ 0.
|4| = -4 for x < 0.
Then, if the absolute value is 4, then, the number may be 4 or - 4.
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3t^2-2t+5; find the company revenues last month if t=-1
Given revenue function is:
[tex]R=3t^2-2t+5[/tex]Now revenue at t=(-1)
[tex]\begin{gathered} R=3(-1)^2-2(-1)+5 \\ R=3+2+5 \\ R=10 \end{gathered}[/tex]So the revenue at t=-1 is 10.
I need help with this Tyler’s mom purchased a saving bond for Tyler. The value of the savings bond increases by 4% each year one year after it was purchased, the value of the savings bond was $156.00 find the value of the bond when Tyler’s mom purchased it. Explain your reason
Let x = value of the bond when Tyler’s mom purchased it.
After one year, this value increased by 4%. This new value is calculated as follows:
[tex]\text{new value = }x\cdot1.04[/tex]The new value is $156.00, then
[tex]\begin{gathered} 156.00=x\cdot1.04 \\ \frac{156.00}{1.04}=x \\ 150.00=x \end{gathered}[/tex]The value of the bond was $150.00 when Tyler’s mom purchased
Which is a way to model 9485 with base ten blocks
The most appropriate way to model 9485 with the base ten blocks is
9 - thousand, 4 - hundred, 8- ten, and 5 - once.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Base ten block implies the number of blocks according to the digit representation,
For the given question,
The number represents there are 9485 cubes, which can be represented as 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
Thus, the most appropriate way to model 9485 with the base ten blocks is 9 - thousand, 4 - hundred, 8- ten, and 5 - once.
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Use any strategy to determine a combination of apples
and pineapples that will balance the scale.
Explain how you know it will balance.
1 Pine- apple equal to 9 Apples.
What is Ratio proportion?The divisional comparison of two quantities yields a ratio, and the equality of two ratios yields a proportion.
A ratio is commonly written as "x: y," though it can also be read as "x is to y" or "x/y."
In terms of comparison, a proportional equation says that two ratios are equal.
When x: y: z: w is used to represent a ratio, it is understood to mean that x is to y as z is to w.
In this case, w and Y are not equal to 0, therefore x/y Equals z/w.
6 Apples = 4 Pomegranates
6 Pomegranates = 1 Pine- apple
1 Pine- apple = 9 Apples.
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Benny is flying a kite directly over his friend Frank, who is 125 meters away.When he holds the kite string down to the ground, the string makes a 39° anglewith the level ground. How high is Benny's kite?Draw a sketch depicting the situation above.b.)Use trigonometry to determine the height of Benny's kite.
Solution
Let us draw a diagram to illustrate the information
Using SOHCAHTOA
[tex]\begin{gathered} tan\theta=\frac{opposite}{adjacent} \\ \\ tan39=\frac{h}{125} \\ cross\text{ multiply} \\ h=125\times tan39 \\ \\ h=101.2230041 \\ \\ h=101.22m\text{ \lparen to two decimal places\rparen} \end{gathered}[/tex]Please find the coordinates and graph the points on the graph and rotate the image.Please demonstrate the pre image and the rotated image on the graph after finding the coordinates.
We have that the general rule for a counterclockwise rotation of 270 degrees is given by the following expression:
[tex]R_{270}(x,y)=(y,-x)[/tex]then, in this case,we have the following:
[tex]\begin{gathered} R_{270}(4,5)=(5,-4)=D^{\prime} \\ R_{270}(6,-2)=(-2,-6)=E^{\prime} \\ R_{270}(1,-2)=(-2,-1)=F^{\prime} \end{gathered}[/tex]and the graph would look like this:
Is the number -3.7 a natural number, a whole number, an integer, a rational number, an irrational number or a real number?
ANSWER
Rational number and Real number
EXPLANATION
We want to identify what type of number -3.7 is.
A natural number is a number that is a positive integer, used in counting things. Examples are 4, 7 and 55.
A whole number is a number that is used in counting, including 0 i.e. natural numbers including 0.
An integer is a whole number but the difference is that an integer can be positive, negative or zero.
A rational number is a number that can be expressed as a fraction of two integers i.e. a/b while an irrational number is one that cannot be expressed as a fraction of two integers.
A real number is any number that can be found as a distance between two points on the number line.
From the definitions above, we see that we can classify -3.7 as a rational number and a real number.
It is not a natural number, whole number, irrational number or an integer.
A pair of bikes cost $89.99 and the sales tax is 8%.What is the total cost of the shoes including tax?
Answer
Total Cost of the bike including tax = $97.1892
Explanation
Cost of the bike = $89.99
Sales Tax = 8% of Cost of bike = 8% (89.99) = 0.08 (89.99) = $7.1992
Total Cost of the bike = (Cost of the bike) + (Sales Tax)
= 89.99 + 7.1992
= $97.1892
Hope this Helps!!!
which is the new equation written in the slope-intercept form
he slope-intercept form is
y = mx + c
here, m = slope of the line and C is intercept on y axis.
4(y – 4) = 8 O A. -2 O B. 2 0 C. 4 D. 6
To find the value of y
4(y – 4) = 8
Divide both-side of the equation by 4
y - 4 = 2
Add 4 to both-side of the equation
y = 2 + 4
y = 6
D is the correct option
need help with this as soon as possible, answer quick
Answer:
Given points are,
A'(2,3) and A(3,-4), under the translation.
we get the graph as,
where B is A(3,-4) and A is A'(2,3).
A translation by 1 unit left and 7 units up.
Answer is:
A translation by 1 unit left and 7 units up.
2625÷32 long division way
Answer: 82 R1 or decimal form 82.031
Step-by-step explanation:
0082
. --------
-0
26
. - 0
. 262
. -256
65
-64
. 1
On Friday, you and your friends took a 140 mile road trip to go to a concert.On Sunday you returned home and calculated that the round trip was 7 hours.What was your average speed?Your answer
20 miles per hour
1) Gathering the data from the question:
S=140 miles
Time spent =7 hours
Average speed=?
2) The average speed is calculated using a ratio:
[tex]A\text{ =}\frac{140}{7}=\text{ 20}[/tex]Since the units are in a standard usual way, we don't need to do any conversion so, the answer is
20 miles per hour
write the linear equation that passes through the two given points (2,-2) and (0,-1)
Given the points:
(x1, y1) ==> (2, -2)
(x2, y2) ==> (0, -1)
To find the linear equation, use the form:
y = mx + b
where m is the slope.
To find the slope, use the formula below:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Thus, we have the slope as:
[tex]m=\frac{-1-(-2)}{0-2}=\frac{-1+2}{0-2}=\frac{1}{-2}=-\frac{1}{2}[/tex]Input 2 for x, -2 for y, and -1/2 for b to find b.
[tex]\begin{gathered} -2=-\frac{1}{2}(2)+b \\ \\ -2=-1+b \\ \\ -2+1=b \\ \\ -1=b \end{gathered}[/tex]Therefore, the linear equation is:
[tex]y=-\frac{1}{2}x-1[/tex]ANSWER:
[tex]y=-\frac{1}{2}x-1[/tex]I I need help solving problem number 8 please :)
Answer:
(8, -1)
Explanation:
Given the below system of equations;
[tex]\begin{gathered} y^2+x^2=65\ldots\ldots\ldots\text{.Equation 1} \\ y+x=7\ldots\ldots\ldots\ldots\text{.Equation 2} \end{gathered}[/tex]Let's go ahead and test each of the given solutions and see which of them is the correct one;
For (8, -1), we have x = 8 and y = -1;
Substituting the above values in Equation 1, we have;
[tex]\begin{gathered} (-1)^2+(8)^2=65 \\ 1+64=65 \\ 65=65 \end{gathered}[/tex]Substituting the values into Equation 2;
[tex]\begin{gathered} (-1)+8=7 \\ -1+8=7 \\ 7=7 \end{gathered}[/tex]We can see that (8, -1) is a solution to the given system of equations
Graph the inequality. Then write the solution set in interval notation.
Representing intervals as we are doing for your question means we will represent all the possible values of x. To do that we will colour in blue all possible values of x but there is a detail we must to consider. The limits of the interval. for that we have two symbols, [ that means "closed on the value" and ( that means "opened on the value". So if there is a [ on a number it means that number makes part of the interval, but if there is a ( it means that number is not in the interval.
Now, for our inequality we have
Once x can be equal or superior to 2 it means 2 is part of the interval because x can be this value, but x is inferior to 8 but it can not be 8 so 8 is not on the interval. Once we know that, know we can represent our interval as follows:
And that is our final answer.
For an interval notation we can write [2,8).
Find the slope of the line that goes through the given points.
(-3,-2) and (– 15,13)
Answer:
Answer:
Slope m= [tex]-\frac{5}{4}[/tex]
As a decimal:
m = -1.25
Step-by-step explanation:
[tex]m=\frac{Rise}{Run} =\frac{y}{x} \\m=\frac{y2-y1}{x2-x1} \\m=\frac{13--2}{-15--3} \\m=\frac{15}{-12} \\m=-\frac{5}{4}[/tex]
Finding a time to reach the limit in a word problem on exponential growth or decay
We are told that each year the value of the laptop is 75% of the value of the value of the previous year. This means that every year the current value of the laptop is multiplied by 0.75. Then if v is the original value of the laptop its value after t years is given by:
[tex]V(t)=v0.75^t[/tex]We need to find after which year V(t) is equal to 500 or less then we have V(t)≤500 and since the original value of the laptop was 4200 we have v=4200:
[tex]4200*0.75^t\leq500[/tex]We divide both sides by 4200:
[tex]\begin{gathered} \frac{4200\times0.75^t}{4200}\leqslant\frac{500}{4200} \\ 0.75^t\leq\frac{5}{42} \end{gathered}[/tex]Then we apply the logarithm to both sides:
[tex]\log_{10}(0.75^t)\leqslant\log_{10}(\frac{5}{42})[/tex]Then we use the property of logarithm regarding exponents:
[tex]\begin{gathered} \operatorname{\log}_{10}(0.75^{t})\leqslant\operatorname{\log}_{10}(\frac{5}{42}) \\ t\log_{10}(0.75)\leq\operatorname{\log}_{10}(\frac{5}{42}) \end{gathered}[/tex]And we divide both sides by the logarithm of 0.75 (we change the inequality symbol because log(0.75) is negative):
[tex]\begin{gathered} \frac{t\operatorname{\log}_{10}(0.75)}{\operatorname{\log}_{10}(0.75)}\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \\ t\ge\frac{\log_{10}(\frac{5}{42})}{\operatorname{\log}_{10}(0.75)} \end{gathered}[/tex]Then we get:
[tex]t\ge7.398[/tex]So the laptop's value is less than $500 after 7.398 years.
AnswerSince we are requested to write a whole number as the answer and the smallest whole number that is bigger than 7.398 is 8 we have that the answer is 8 years.