The volume of gasoline in the tank as a function of time can be determined as,
[tex]V=2t[/tex]The time taken to fill the tank can be determined as,
[tex]\begin{gathered} 16=2t \\ t=8 \end{gathered}[/tex]Thus, the requried domain is,
[tex]t\in\lbrack0,8\rbrack[/tex]The range of the function can be determined as,
[tex]V\in\lbrack0,16\rbrack[/tex]Thus, the above expressions gives the required domain and range of the function.
Your family used 27.5 gallons of gas to drive 654.5 miles. how many miles did you drive for each gallon?
Answer:
total distance = 654.5
Total gas used = 27.5
Distance per gallon = 654.5 ÷ 27.5 = 23.8
We drove 23.8 miles for each gallon of gas
The following shape consists of a rectangle and a triangle. Determine its area.
Answer:
72 cm²
Step-by-step explanation:
You want the area of a shape consisting of a rectangle and a triangle. The rectangle is 7 cm long and 8 cm high. The triangle has a base of 8 cm and a height of 4 cm.
AreaThe area of the rectangle is ...
A = bh
A = (8 cm)(7 cm) = 56 cm²
The area of the triangle is ...
A = 1/2bh
A = 1/2(8 cm)(4 cm) = 16 cm²
Total areaThe total area is the sum of the areas of the parts:
total area = rectangle area + triangle area
= (56 cm²) +(16 cm²) = 72 cm²
The area of the shape is 72 cm².
__
Additional comment
You can see from the area formula that the area of a triangle is half the area of its enclosing rectangle. That is, the 4 cm high triangle on the right side of the figure effectively adds the area of a 2 cm wide rectangle with the same base.
The figure's area is equivalent to that of a rectangle 7+(4/2) = 9 cm wide and 8 cm high: (9 cm)(8 cm) = 72 cm², as above.
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Lines a and b are parallel. Line c is perpendicular to line a. Must it also be perpendicular to line b? Explain your thinking.
Line c is also perpendicular to line a.
Suppose that c and b are perpendicular. This implies that:
option 1) b and a are the same line or,
option 2) b is parallel to a
Since we know that a and b are different lines, hence, the option 2 is the correct.
Assume the TV warranty or replacement times for TV sets are normally distributed with a mean of 9.2 years and a standard deviation of 1.1 years. Find the probability that a randomly selected TV will have a replacement time of less than 6 years.
Firstly, let's draw a picture of the distribution:
Graphically, we want to calculate the blue area. To put it differently, we want to calculate
[tex]P(X<6).[/tex]To do this, we need to find the z-score associated with 6. We can calculate it by
[tex]\begin{gathered} z=\frac{6-\mu}{\sigma}\Rightarrow\begin{cases}\mu=\operatorname{mean} \\ \sigma=\text{standard deviation}\end{cases}, \\ \\ z=\frac{6-\mu}{\sigma}=\frac{6-9.2}{1.1}\approx-2.91. \end{gathered}[/tex]Now, we must check our favorite z-score table and look for the probability associated with the z-score we just found. It's 0.0018.
AnswerThe probability that a randomly selected TV will have a warranty of less than 6 years is 0.0018.
May I please get help with this. I have tried multiple times to get the correct answer for this but still could not seem to get the right one.
Answer:
42
Explanation:
Recall that two triangles are said to be similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.
Given that triangles ABC and XYZ are similar, to be able to determine missing side length, we have to set up proportions as seen below;
[tex]\begin{gathered} \frac{AB}{XY}=\frac{AC}{XZ} \\ \frac{30}{5}=\frac{AC}{7} \end{gathered}[/tex]Let's cross multiply;
[tex]\begin{gathered} 5\cdot AC=30\cdot7 \\ 5AC=210 \end{gathered}[/tex]Let's divide both sides of the equation by 5;
[tex]\begin{gathered} \frac{5AC}{5}=\frac{210}{5} \\ AC=42 \end{gathered}[/tex]So the missing side length is 42
A car rental company charges an initial fee plus an additional fee for each mile driven. The charge depends on the type of careconomy luxury The charge E dollars) to rent an economy car is given by the function E = 15.95 + 0.60M where M is the number of miles drivenThe charge (dollars) to rent a luxury car is given by the function L = 18.20 + 1.25M be how much more it costs to rent a luxury car than an economy car (in dollars)an equation relating C to Simplify your answer as much as possible
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
C=34.15+0.65M
ExplanationGiven
[tex]\begin{gathered} E=15.95+0.60M \\ L=18.20+1.25\text{ M} \\ where \\ E\text{ is the cost to rental an Economy car} \\ Lis\text{ the total cost to rental an Luxury car} \\ M\text{ is the number of miles traveled} \end{gathered}[/tex]so
to Know C, how much more it costs to rent a Luxuy can than an economc, we need to do a subtraction, hence
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ \end{gathered}[/tex]so, replace and simplify
[tex]\begin{gathered} C(M)=L(M)-E(M) \\ C=18.20+1.25M-(15.95+0.60M) \\ C=18.20+1.25M-15.95-0.60M \\ C=34.15+0.65M \end{gathered}[/tex]therefore, the answer is
C=34.15+0.65M
I hope this helps you
6V
6V
I
I₁
R₁ =
6Ω
IT
B₁
1₂
R₂
352
B₂
Series or parallel?
m
VT=
V Branches
1₁ =
1₂=
IT =
RT =
P =
Answer:
12
Step-by-step explanation:
8 times the quantity of X and 8 Translate it into expression
Given
8 times the quantity of X and 8
Find
Translate into an expression
Explanation
Quantity be X
so , according to the question ,
8 (X + 8)
Final Answer
Hence , the required expression is 8 (X + 8)
Let g(x) be the transformation of f(x) = IxI so that the vertex is at (-1, -3). Identify the rule for g(x) and its graph.
EXPLANATION
Since the vertex is at (-1, -3), the only appropriate option is to translate the function one unit to the left, and again translating 3 units down, with the following form:
g(x) = |x+1| - 3
Therefore, the solution is the last option.
professor horvat designs a study to assess the work satisfaction and home-life satisfaction of a group of graduate students. she administers the same measures of work and home-life satisfaction on two occasions, 1 year apart. she finds at both the first time point and the second time point there is a strong correlation between work satisfaction and home-life satisfaction. which type of correlations are these?
The type of correlation founded in the study by assessing the work and home life satisfaction measure identically at two occasions, a year apart, is a cross-sectional correlation.
Cross-sectional correlation is a non-experimental research design that uses data collected from a single time point. It is used to generate a static portrait of research variables. As opposed to serial correlation which is a correlation of one variable at different times, cross- sectional correlation is a correlation of two variables at the same time.
In the given study, professor measured the work satisfaction and home-life satisfaction at one time point and repeated it after a year at the second time point. She found a strong correlation between variable at both time points. Hence, it is cross-sectional correlation.
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3y=x-6 in standard form
Answer: x-3y=6
Step-by-step explanation:
so first subtract x to get -x+3y = -6 because standford is ax+by = c
and then multiply by -1 since x has to be positive
x-3y = 6 That is your answer
Are null and alternative hypotheses statements about samples, about populations, or does it depend on the situation? explain.
The null and alternative are always claims about the population. That's because the goal of hypothesis testing is to make inferences about a population based on a sample.
Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
1. What is the value of 18 + (-7) – (-5)
Answer:
16
Step-by-step explanation:
Two negatives make a positive:
18-7+5
Solve the problem left to right:
18-7=11
11+5=16
Dr. Choi just started an experiment. He will collect data for days. How many hours is this?
The data collected in [n] days is collected in 24n hours.
What is the SI unit of time?
The SI unit of time is Seconds. In 1 second, there are (1/60) minutes.
Given is Dr. Choi who just started an experiment and he will collect data for days.
Assume that he collects the data for [n] number of days. In one day, we have 24 hours. Therefore, in [n] number of days, there will be total of 24n hours.
Therefore, the data collected in [n] days is collected in 24n hours.
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The shaded portion in each glass represents an amount of grape drink Martin's glass of grape drink has a weaker tasting grape flavor than Tia's glass of grape drink.
The stronger flavor of grape is in Tia's glass.
Given,
Martin's glass of grape drink has weaker tasting grape flavor
Tia's glass of grape drink has stronger tasting grape flavor
3 ounces of water is added to Martin's glass
One table spoon of grape mix is added to Tia's glass
We have to find the glass which contain the stronger grape flavor
Already in Martin's glass flavor is low. When we add water again to his glass, the flavor will again dissolves with water.
In Tia's glass grape flavor is stronger. By adding one tablespoon of grape mix the flavor will become more stronger.
That is,
The stronger flavor of grape is in Tia's glass.
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Question 12
I just want the answer :)
Given the information marked on each figure below, select all classifications that must be true.
Note that each figure is drawn like a rectangle, but you should not rely on the way the figure is drawn in determining your answers.
If necessary, you may learn what the markings on a figure indicate.
1. Quadrilateral.
The quadrilateral is not necessarily a parallelogram since the diagonals don't necessarily bisect each other.2. Rectangle.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.The parallelogram is a rectangle because there is one right angle.3. Parallelogram.
The quadrilateral is a parallelogram because there is one pair of congruent and parallel sides.Using positive integers between 1 and 9 and each positive integer at most once, fill in values
to get two constraints so that x = 7 is the only integer that will satisfy both constraints at
the same time.
☐ x+☐ < ☐ x + ☐
☐x+ ☐ > ☐ x+ ☐
Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
To get two constraints so that x = 7 is the only integer that will satisfy both constraints at the same time. Upon analysing it can be seen that to the coefficients of x in eaxh equation shouch be two consecutive number. The coefficient on the lesser than side should be lower than the coeffiecient present on the greater than side.
To make the equation in such a way that only 7 satisfy it, the lesser than sides are added with numbers higher than 7 that is 8 and 9.
Therefore, Using positive integers between 1 and 9 and each positive integer at most once,
2 x+ 9 < 3 x + 1
6x+ 4 > 5 x+ 8
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1. What is the center of the hyperbola?
(y+3)^2/9 − (x−2)^2/2 = 1
Enter your answer by filling in the boxes.
The center of the hyperbola given as (y + 3)²/9 − (x − 2)²/2 = 1 is (2, -3)
How to determine the center of the hyperbola?From the question, the equation of the hyperbola is given as
(y + 3)²/9 − (x − 2)²/2 = 1
As a general representation, a hyperbola is represented as
(y - k)²/a² − (x − h)²/b² = 1
From the above general representation, the coordinates of the center of the hyperbola is
Center = (h, k)
By comparing the equations (y - k)²/a² − (x − h)²/b² = 1 and (y + 3)²/9 − (x − 2)²/2 = 1, we have the following representstion
(h, k) = (2, -3)
This means that
Center = (2, -3)
Hence, the center is (2, -3)
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Answer:
(2,-3) See question 10
Step-by-step explanation:
Either Table A or Table B shows a proportional relationship.
Plot the points from the table that shows a proportional relationship.
Table A shows a proportional relationship
What is proportional relationship?
When the value of independent variable changes the value of dependent variable changes. that means if the value independent variables is increase the value of dependent variable will also be increased.
In the figure we are given 2 tables
We plot both the curve on the graph we get
Table A shows a linear relationship where are Table b Does not shows a proportional relationship
Hence Table A shows a proportional relationship
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Answer:
Step-by-step explanation:
23 - x < 23(1 + 7x)
What does x equal???
[tex]23 - x < 23 + 161x \\ - x - 161x < 23 - 23 \\ - 162x < 0 \\ \frac{ - 162x}{ - 162} < \frac{0}{ - 162} \\ x > 0[/tex]
without given any restriction x is all the numbers greater than 0.
NOTE THAT THE SIGNS >< CHANGE DIRECTION WHEN YOU MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.
Select the correct answer.
Which of the following represents a function?
B. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}
C. x -5 -1 9 8 -1
y 1 7 23 17 1
The relation which represents a function is the mapping diagram.
What is a function?A function can be defined as a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value).
In this scenario, the same x-value of the given ordered pairs (3, 2) and (3, 4) have the different output variable (y-value) and as such does not represent a function. Similarly, the table of values has the same x-value (-1) which outputs different numerical values.
Based on the ordered pairs and table shown above, we can reasonably and logically deduce that it is only the mapping diagram that represents a function.
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Find an equation for the line that passes through the points (3, -4) and (-3, -1).
Answer:
That is my own idea and I hope it is very helpful
Can Some one help PLEASEE
The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.
How to find the variable associated to the measure of two angles in a parallelogram
Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,
13 · x + 7 · x = 180°
Now we clear the variable x:
20 · x = 180°
x = 9
And the missing angles are:
13 · 9 = 117°
7 · 9 = 63°
The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.
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Linear ApplicationThe function V(x) = 20.6 +2.2x gives the value (in thousands of dollars) of an investmentafter a months.Interpret the Slope in this situation.The value of this investment is decreasing✓at a rate ofdollars per year V
SOLUTION:
Case: Interpreting slopes from linear equations
Method:
V(x) = 20.6 + 2.2x
Compared to
y = mx + b
Where m is the slope and it is being interpreted as the rise for every single run on the line graph.
As it applies,
V(x) = 20.6 + 2.2x
m = 2.2 thousand ie. 2200
It is interpreted as the amount the value increases by each month.
Final answer:
The value of this investment is increasing at a rate of $2200 each month
suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of inches and a standard deviation of inches. what proportion of woodlice have antenna lengths that are more than inches? round your answer to at least four decimal places.
Proportion = 0.2119
P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119
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Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Which choice represents the sample space, S, for this event?
S = {PQR}
S = {PQR, PRQ, QPR, QRP, RPQ, RQP}
S = {PQ, PR, QR}
S = {PQ, QP, PR, RP, QR, RQ}
The resulting sample space of the given situation is S = {PQ, QP, PR, RP, QR, RQ}
Sample space:
Sample space refers the collection or a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Given,
Patty, Quinlan, and Rashad want to be club officers. The teacher who directs the club will place their names in a hat and choose two without looking. The student whose name is chosen first will be president and the student whose name is chosen second will be vice president.
Here we need to find the sample space for the event.
Let us consider,
P represents Patty
Q represents Quinlan
R represents Rashad
And through the question we have know that, the teacher drawn two card at a time,
So we have consider that the teacher is going to draw out of the hat one first, without replacement, and then draw another one.
The first chosen one will be the president, and that could be P, Q or R, Now, the chosen second one is the Vice president, and already one has already being drawn, that could only be two fellows.
Therefore, the total of likely outcomes is PQ,QP, PR, RP, QR, RQ, one paired up with either of the two remaining in the hat.
So, the resulting sample space is
S = {PQ, QP, PR, RP, QR, RQ}
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The Smiths have decided to put a paved walkway of uniform width around their swimming pool. The pool is a rectangular pool that measures 12 feet by 20 feet. The area of the walkway will be 60 square feet. Find the width of the walkway.
***NOTE*** This is a Quadratic Word Problem, so please the Quadratic Method!! Extra 20 BRAINLIST will be reward if work is shown step by step CORRECTLY!!
Answer:
Step-by-step explanation:
12 times 2 =24 60 into 10 so i think it will be 6
PLEASE HELP ME FIND X
Answer:
28°
Step-by-step explanation:
AB and CD are straight lines, all angles in a straight line add up to 180
May someone please help me?
Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]
Answer:
y = 5x + 7 ---1
y = 7x + 8 ---2
Substitute either one of the equations into the other.
I will substitute 1 into 2.
5x + 7 = 7x + 8
Simplify and solve for x.
2x = -1
x = -1/2
Substitute x into either one of the equations to find y.
I will substitute x into 1.
y = 5(-1/2) + 7
= 9/2
Hence, x = -1/2, y = 9/2
15:4y2 – 30:23 + 4554The quotient of517is7. When this quotient is divided bythe result is 3-35-5I3y – 25y2 + 3
We are given the following expression:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}[/tex]To determine the quotient of the expression we will factor the numerator. To do that we take the Greatest Common Multiple of the denominator.
The denominator is the following expression:
[tex]15x^4y^2-30x^2y^3+45xy[/tex]To get the greatest common multiple we need to determine the multiples of the coefficients first.
For 15 we have:
[tex]factors\text{ 15= 1, 3, 5, 15}[/tex]For 30 we have:
[tex]\text{factors 30 = }1,2,3,5,6,10,15,30[/tex]For 45 we have:
[tex]\text{factors 45 =}1,3,5,9,15,45[/tex]We notice that the factors that are repeated for each of the numbers are:
[tex]\text{repeated = 1,3,5,15}[/tex]The greatest of the repeated factors is 15, therefore, the greatest common factor is 15.
Now, we take the variables that are repeated in the expression and we take the ones with smaller exponents. The variables repeated are:
[tex]xy[/tex]Of these, the ones with smaller exponents are:
[tex]xy[/tex]Now, combining the two parts we get that the greatest common factor of the denominator is:
[tex]15xy[/tex]We take out that factor and re arrange the expression, like this:
[tex]\frac{15x^4y^2-30x^2y^3+45xy}{5xy}=\frac{15xy(x^3y-2xy^2+3)}{5xy}[/tex]Now, we cancel out the "xy" and simplify 15/5:
[tex]\frac{15xy(x^3y-2xy^2+3)}{5xy}=3(x^3y-2xy^2+3)[/tex]And thus we get the quotient.
We notice that the quotient is multiplied by 3, therefore, if we divide by 3:
[tex]\frac{3(x^3y-2xy^2+3)}{3}[/tex]We can cancel out the 3 and we get:
[tex]\frac{3(x^3y-2xy^2+3)}{3}=x^3y-2xy^2+3[/tex]Therefore, the quotient is divided by 3.
