Math Lab A - Section 203B Notebook Home Insert Draw View Class Notebook U abe А. = = A Styles ☆ ? The table shows the average mass, in kilograms, of different sizes of cars and trucks. Size Small Car Average Mass (kilograms) 1,354 1,985 Large Car Large Truck 2,460 Part A To the nearest hundred, how much greater is the mass of a large truck than the mass of a small car? Fill in the blanks to answer the question. To the nearest hundred, a large truck has a mass of kilograms, and a small car has a mass of kilograms. So, a large truck has a mass about kilograms greater than a small car.
Answers
Given:
Round the mass of the large car to the nearest thousand.
Because 1985 is between 1,000 and 2,000 and closer to 2,000 ,the number should round up to 2,000.
Option D is the correct answer.
Related Questions
Instructions: For the following quadratic functions, write the function in factored form and then find the -intercepts, axis of symmetry, vertex, and domain and range. Round to one decimal place, if necessary.
Answers
Factored form: y = (x+1)(x-8)
x-intercept: (-1, 0) and (8, 0)
Axis of symmetry: x = 7/2
Vertex: (7/2, -81/4)
Domain: All real numbers
Range: y ≥ -81/4
Explanations:Given the quadratic equation expressed as:
[tex]y=x^2-7x-8[/tex]Factorize
[tex]\begin{gathered} y=x^2-8x+x-8 \\ y=x(x-8)+1(x-8) \\ y=(x+1)(x-8)\text{ Factored form} \end{gathered}[/tex]The x-intercept is the point where y= 0. Substitute y = 0 into the factored form
[tex]\begin{gathered} (x+1)(x-8)=0 \\ x=-1\text{ }and\text{ }8 \\ The\text{ x-intercept are \lparen-1, 0\rparen and \lparen8, 0\rparen} \end{gathered}[/tex]The axis of symmetry of the equation is given as x = -b/2a where:
a = 1
b = -7
Substitute:
[tex]\begin{gathered} axis\text{ of symmetry:}x=\frac{-(-7)}{2(1)} \\ axis\text{ of symmetry: }x=\frac{7}{2} \end{gathered}[/tex]The vertex form of the equation is in the form (x-h)^2+k where (h, k) is the vertex. Rewrite in vertex form:
[tex]\begin{gathered} y=x^2-7x-8 \\ y=x^2-7x+(-\frac{7}{2})^2-(-\frac{7}{2})^2-8 \\ y=(x-\frac{7}{2})^2-\frac{49}{4}-8 \\ y=(x-\frac{7}{2})^2-\frac{81}{4} \end{gathered}[/tex]The vertex of the function will be (7/2, -81/4)
The domain are the independent values of the function for which it exists. The domain of the given quadratic function exists on all real number that is:
[tex]Domain:(-\infty,\infty)[/tex]The range of the function are the dependent value for which it exist. For the given function, the range is given as:
[tex]Range:[-\frac{81}{4},\infty)[/tex]What is the complement of a 54 1/2 degree angle
Answers
Two angles are complementary if their sum is 90 degrees
Therefore, to get a complement of 54 1/2 degrees, we will have to subtract it from 90 degrees
Let the complement of 54 1/2 be represented by x
[tex]\begin{gathered} x=90-54\frac{1}{2} \\ \\ x=90-\frac{109}{2} \\ \\ x=\frac{180-109}{2} \\ \\ x=\frac{71}{2} \\ \\ x=35\frac{1}{2}\text{ degrees} \end{gathered}[/tex]Therefore, the complement of angle 54 1/2 degrees is angle 35 1/2 degrees
Amanda is a fashion designer. She has 25 yards of silk material. The skirtAmanda is making requires 1 yards, the dress requires 4 yards, the shirtrequires 7 yards, and the pants requires yards.After making her pieces, how many yards of silk does Amanda have left?
Answers
To determine how much silk Amanda has at the end we need to substract the amount each pice need from the original amount:
[tex]\begin{gathered} 25-\frac{18}{7}-\frac{11}{2}-\frac{7}{4}-\frac{25}{7}=25-\frac{43}{7}-\frac{11}{2}-\frac{7}{4} \\ =25-\frac{86+77}{14}-\frac{7}{4} \\ =25-\frac{163}{14}-\frac{7}{4} \\ =25-\frac{652+98}{56} \\ =25-\frac{750}{56} \\ =\frac{1400-750}{56} \\ =\frac{650}{56} \\ =\frac{325}{28} \\ =11\frac{17}{28} \end{gathered}[/tex]Therefore Amanda has 11 17/28 yards of silk left.
What number is 2% of 35
Answers
Answer:
The 2% of 35 is;
[tex]0.7[/tex]
Explanation:
We want to find the 2% of 35
[tex]\begin{gathered} \text{ 2\% of 35 =} \\ \frac{2}{100}\times\text{ 35 = }\frac{70}{100}=0.7 \end{gathered}[/tex]Therefore, the 2% of 35 is;
[tex]0.7[/tex]
Answer:0.7
Step-by-step explanation:
35x2=70
70/100=0.7
polinomials (x + 3)2
Answers
Given the following question:
[tex](x+3)2[/tex](x + 3)2
First, we flip the polynomial:
(x + 3)2 = 2(x + 3)
2(x + 3)
Next, we apply the distributive law where we multiply 2 by x and 3.
2 × x = 2x
2 × 3 = 6
2x + 6
Expression cannot be simplified any further:
= 2x + 6
the radius of a circle is 4 centimeters. what is the diameter? give the exact answer in simplest form
Answers
we have that
the diameter is two times the radius
so
in this problem
D=2r
D=2(4)=8 cm
diameter is 8 cmhelp me asap please on this math question
Answers
Equations showing direct variations are 2x = y and y = 1.8c
Direct Variation exists between two variables when one variable is directly dependent to another variable means change in one variable will create change in other one also and vice versa.
Two variable increase or decrease by the same factor.
Suppose x and y is that are in direct variation then you can write
y ∝ x
where, "∝" denotes proportionality
removing proportionality sign by constant then you can write
y = k x , where k is constant and can hold any real value
From the following equation ,
2x = y with 2 as constant and
y = 1.8x with 1.8 as constant shows direct variations
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If 11 people each own of an acre of
2/19
land and they put all their land together
how much land, in acres, would they
Answers
If 11 people each own of an acre of 2/19 land, their land together is area of 22/19 of an acre.
If 11 people each own of an acre of 2/19
The area of land owned by 1 person = 2/9
To find the area of land owned by 11 persons altogether
We have to multiply 11 with the area owned by one person
11 x (2/19)
= 22/19
Therefore, If 11 people each own of an acre of 2/19 land, the they land owned by them altogether is area of 22/19 of an acre.
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Use the following function for questions # 1 - # 5:f(x) =x?- 14x + 44#1: Find the X value of the turning point.
Answers
The given function is
f(x) = x^2 - 14x + 44
To find the turning point, we would differentiate the function, equate the derivative to zero and solve for x. We have
f'(x) = 2x - 14
Equating it to zero, we have
2x - 14 = 0
2x = 14
x = 14/2
x = 7
The value of x of the turnng point is 7
Find the value of b. * 4 b 6 Y 9 5.8 W
Answers
The smaller triangle has its hypotenuse as 4 units and the base as 6 units
The bigger triangle has its hypotenuse as 10 units, the height as 5.8 units and the other hypotenuse as 9 units
Using similarity properties, compare the ratio of the sides as;
Compare the ratio of the bigger triangle sides to that of the smaller traingle
First find the base of the bigger triangle using the sides given and applying the pythagorean relationship as;
10^2 - 5.8^2 = a^2
100 - 33.64 = a^2
66.36 = a^2
1/2 a= 8 .15 units
a= 16.30 units
Compare ratio
a/ 6 = 5.8 / b
16.30 /6 = 5.8/ b
16.30 b = { 6 * 5.8 }
b = {6 * 5.8} / 16.30
b = 2.13 units
Answer
2.13 units
#6) long division a. Let P(x) = 8x^3 + 27 and D(x) = 2x + 3
Answers
The functions are given to be:
[tex]\begin{gathered} P(x)=8x^3+27 \\ D(x)=2x+3 \end{gathered}[/tex]To evaluate:
[tex]P(x)\div D(x)[/tex]STEP 1
Divide the leading term of the dividend by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the dividend from the obtained result:
STEP 2
Divide the leading term of the obtained remainder by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the remainder from the obtained result:
STEP 3
Divide the leading term of the obtained remainder by the leading term of the divisor. Write down the calculated result in the upper part of the table. Multiply it by the divisor and subtract the remainder from the obtained result:
ANSWER
[tex]\frac{8x^3+27}{2x+3}=4x^2-6x+9[/tex]3 2 1 -3-2- 1 2 3 2 -3 Domain: (-3,3] Range: [-2, 2] Domain: (-2, 2] Range: [-3,3] Domain: (-2,-3) Range: (2,3) Domain: {-2, -1, 0, 1, 2} Range: {-3, -2, - 1, 0, 1, 2, 3} None of the above NON
Answers
The domain is [ -2, 2]
and the range is [-3, 3]
You flip a coin and roll a die. The table shows the sample space.12 3 4 5 6Heads(H) H-1 H-2 H-3 H-4H-5H-6Tails(T) T-1 T-2 T-3 T-4 T-5 T-6What is the probability of getting a head or a tail and anven number?Answer as a reduced fraction in the form ab.
Answers
You flip a coin and roll a die. The table shows the sample space.
1
2 3 4 5 6
Heads(H) H-1 H-2 H-3 H-4H-5H-6
Tails(T) T-1 T-2 T-3 T-4 T-5 T-6
What is the probability of getting a head or a tail and an
even number?
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
In this problem
the size of the sample space is (6+6+6)=18
the size of the event space is equal to (6+6+3)=15
REmember that an even number are (2,4 and 6)
so
the probability is equal to
P=15/18
simplify
P=5/6
therefore
the answer is5/6consider parallelogram JKLM below.use the information given in the figure to find m
Answers
Here, we have a parallelogram JKLM.
Given:
JK = 3x
LM = 3
m∠J = 106°
m∠KMJ = 34°
A parallelogram is a quadilateral that has equal opposite angles and the opposite sides are also equal.
Thus, we have:
• m∠L = m∠J = 106°
m∠L = 106°
• x:
Here, JK is opposite side LM. SInce they are opposite sides, they have equal length.
Thus, we have:
JK = LM
3x = 3
Divide both sides by 3:
[tex]\begin{gathered} \frac{3x}{3}=\frac{3}{3} \\ \\ x=1 \end{gathered}[/tex]x = 1
• m∠LKM:
Apply the alternate interior angles theorem. Alternate interior angles are congruent.
∠LKM and ∠KMJ are alternate interior angles. This means they are congruent.
Thus, we have:
m∠LKM = m∠KMJ = 34°
m∠LKM = 34°
ANSWER:
• m∠L = 106°
• x = 1
• m∠LKM = 34°
Hello! Thank you for helping me today, I need a little bit of assistance to understand the rest of this question please. (This is is not an active test, it is a book I am studying in order to take the ASVAB in a couple of weeks.)Options;A: 1/8B: 1/7C: 1/6D: 1/4
Answers
GIVEN:
We are told that in a certain class, 3 out of 24 students are in student organizations.
Required;
What is the ratio of students in student organizations to students not in student organizations?
Step-by-step solution;
We shall begin by dividing the entire students into the two given groups, and that will be;
In student organizations = 3
Not in student organizations = 21
Total number of all students = 24
To determine the ratio of one value to the other, we express them as follows;
[tex]\begin{gathered} Ratio\text{ }of\text{ }x\text{ }to\text{ }y=x:y \\ \\ OR \\ \\ Ratio\text{ }of\text{ }x\text{ }to\text{ }y=\frac{x}{y} \end{gathered}[/tex]Therefore, to express the ratio of students in organizations to students not in organizations, we will have;
[tex]\begin{gathered} Ratio=\frac{3}{21} \\ \\ Ratio=\frac{1}{7} \end{gathered}[/tex]ANSWER:
Therefore, the correct answer is option B
Y 3+ 2+ 1+ -4 -3 -2 -1 1 2 3 -1- -2 -3+ -4 47 What is the slope of the line?
Answers
To find the slope of the line, we will follow the steps given below:
Step 1: select two points on the graph
(0, -1) and (4,2)
Step 2: Apply the slope formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]=>
[tex]\text{slope}=\frac{2-(-1)}{4-0}=\frac{2+1}{4}=\frac{3}{4}[/tex]The slope of the graph is:
[tex]\frac{3}{4}[/tex]Complete the function table for the given domain, and plot the points on the graph. (t) = -12 + 2.1 + 5 -1 0 1 2 3 Drawing tools Click on a tool to begin draving. EK Select f(x) Point Click on the Graph to place a Point HHHH 6 2 2 10 0
Answers
f(x) = -x^2 + 2x + 5
x -1 0 1 2 3
f(x) 2 5 6 5 2
What is the measure of
Answers
In the parallelogram ABCD,
Angle D is 145 degree.
In the parallelogram adjacent angles sum is 180 degree.
In the given parallelogram ABCD , angle D and angle C are adjacent.
[tex]\begin{gathered} \angle D+\angle C=180^{\circ} \\ 145^{\circ}+\angle C=180^{\circ} \\ \angle C=180^{\circ}-145^{\circ} \\ \angle C=35^{\circ} \end{gathered}[/tex]Answer: Option B) 35 degree.
According to the graph, what is the value of the constant in the equation below? 2- 18+ Height = Constant Wiat 16+ (0.5,1.6) 12+ Height (0.8.1) 0.8 + (1.6.05) (2.0.4) 12 14 16 18 2
Answers
Liyah, this is the solution:
• Height = Constant/Width
,• Height * Width = Constant (you need to multiply each ordered pair )
Therefore,
Constant = 1.6 * 0.5
Constant = 0.8
Constant = 0.4 * 2
Constant = 0.8
The correct answer is C. 0.8
Ruth used a spinner to perform 10 to the probably of having the children whyes • Is Ruth's estimated probably representative of the theoretical probaby of having the children were? • Provide the estimated probability from this on and the theoretical probably of having them Respond in the space provide
Answers
Keshawn, this is the solution to part B:
P (blue) = 25% = 1/4
P (brown) = 75% = 3/4
If Ruth performs 10 trials, the theoretical probability would be:
P (blue) = 25% = 2.5/10
P (brown) = 75% = 7.5/10
Upon saying that, the outcome of 1 of having three children with blue eyes isn't a theoretical probability, it is a experimental probability.
Finally, the theoretical probability of having three children with blue eyes is:
P (3 chlildren with blue eyes) = 1/4 * 1/4 * 1/4 = 1/64
12x+18 rewrite using distributive property
Answers
we have
12x+18
REmember that
12=(2^2)*(3)
18=(2)*(3^2)
substitute
(2^2)*(3)x+(2)*(3^2)
Factor (2)*(3)=6
6(2x+3)
therefore
the answer is
6(2x+3)John drank 18 fluid ounces of juice. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
We know that 1 cup is equivalent to 8 fluid ounces. Then, we can establish the following rule of three:
[tex]\begin{gathered} 8\text{ fluid ounces ----- 1 cup} \\ 18\text{ fluid ounces ------ x} \end{gathered}[/tex]Then, by cross multiplying these quantities, we have
[tex]x\times8\text{ fluid ounces= 1 cup}\times\text{ 18 ounces}[/tex]By dividing both sides by 8 fluid ounces, we get
[tex]x=\frac{1\text{ cup}\times18\text{ ounces}}{8\text{ fluid ounces}}[/tex]which gives
[tex]x=\frac{18}{8}\text{ cups}[/tex]Now, we need to convert this simple form to a mixed form, that is,
Then, by simplifying this mixed form, the answer is:
[tex]2\frac{1}{4}\text{ cups}[/tex]Five fair tetrahedral (four-sided) dice are rolled at the same time. The values on the faces of each die are 1, 2, 3, and 4.a. What is the theoretical probability of rolling a 1 on all five dice?b. Zavier conducted an experiment in which he rolled five fair tetrahedral dice 50 times. He rolled a 1 on all five dice once. What is the experimental probability of rolling a 1 on all five dice?
Answers
Solution:
The probability of an event is the ratio of number of outcome of the event to the total outcome of events.
Thus;
(a) The theoretical probability of rolling a 1 on all five dice is;
[tex](\frac{1}{4})^5[/tex](b) In the experiment, he rolled five fair tetrahedral dice 50 times. Thus, the experiment probability of rolling a 1 on all five dice is;
[tex]\frac{1}{50}[/tex]A __ is a polynomial with one term.
Answers
Answer:
Monomial
Step-by-step explanation:
A polynomial that consists of exactly one term is called monomial.
Examples are 3, 10x², xy,...
So the answer is: Monomial
Consider the following simple statements: p: Your shirt is tucked into your pants. q: Your pants are tucked into your shirt.What is the symbolic form of the statement: "If your shirt isn't tucked into your pants then your pants are tucked into your shirt."Select the correct answer below:∼q⟹p∼q⟹∼pp⟹∼q∼p⟹q
Answers
SOLUTION
We are asked the symbolic form of "If your shirt isn't tucked into your pants then your pants are tucked into your shirt."
This simply means the negation of p implies q.
p implies q is represented as p⟹q
Then the negation of p implies q will be ∼p⟹q.
Therefore, the correct answer is ∼p⟹q
A 104° sector of a circle has an area of 56 square centimeters. Tothe nearest centimeter, what is the diameter of the circle?
Answers
The diameter is 8cm
Explanation:Given the following:
[tex]\begin{gathered} \theta=104^o \\ \\ \text{Area(}A)=\pi r^2=56cm^2 \\ \text{Diameter(D)}=2r=\text{?} \end{gathered}[/tex]From the area of the circle, we can have the value for the radius, r as follows:
[tex]\begin{gathered} \pi r^2=56 \\ r^2=\frac{56}{\pi} \\ \\ r=\sqrt[]{\frac{56}{\pi}}\approx4cm \end{gathered}[/tex]We can now obtain the diameter by multiplying the radius by 2
[tex]D=2r=2\times4=8cm[/tex]9. At last Friday's soccer game there were a total of 673 fans in attendance, including students and non-students.Let x represent the number of students, and y represent non-students. Which of the following statements couldrepresent the number of fans in attendance. Select all that apply.a. x + y = 673b. 335 and 138c. 335 and 338d. x=y - 673e. y = -x + 673f. 273 and 400
Answers
The answer is A
From the question:
Total fans in attendence = 673
x = number of students
y= non - students
Total of fans in attendance =
x + y= 673
The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticketLet S represent the number of stops that Julia buys.1) Which inequality describes this scenario?A. 5+2.75•S ≤ 21 B. 5+2.75•S ≥ 21 C. 5+2.75•S ≤ 50 D. 5+2.75•S ≥ 502) What is the largest number of stops that Julia can afford?
Answers
Let's begin by listing out the information given to us:
Initial fee = $5
Fee per stop = $2.75
Amount with Julia = $21
What is the highest number of stops she can make?
S = the number of stops Julia bought
Julia pays the initial fee of $5. We subtract this from the $21, we have
$ (21 - 5) = $16
Julia has $16 left to buy her stops. She cannot spend beyond the amount of money with her (altogether $21). She spends lesser than or equal to $21 (≤ $21)
The inequality that describes this scenario is given by:
initial fee + fee per stop * number of stops ≤ 21
5 + 2.75 * S ≤ 21
Hence, option A is the correct answer
What is the largest number of stops that Julia can afford?
This is gotten by dividing the amount left after subtracting the initial fee by the fee per stop
n = 16/2.75 = 5.82 = 5 stops (rounding downwards)
We round downwards because the number of stops must be a whole number and it must be lesser than or equal to $21 altogether
22.2: X's Y'S Match each expression in column A with an equivalent expression from column B. Be prepared to explain your reasoning. А 1.1934) Buty 1. 12(x+y) the w 2. 12(x - y) w 2. (9x + 5y)-(3x + 7y) 3. (9x + 5y)-(3x - 7y) 3.6(x - 2y) 4. 9x - 7: + 3x + 5y 4. 9x + 5y + 3x - 7 5. 9x - 7y + 3x - 5y 5.9x + 5y - 3x + 7y 6.9x - 7y - 3x - 5y 6.9x - 3x + 5y - 7y
Answers
Given data:
The given list.
1) The first expression can be written as,
[tex]\begin{gathered} 9x+5y+3x+7y=12x+12y \\ =12(x+y) \end{gathered}[/tex]2) The second expression can be written as,
[tex](9x+5y)-(3x+7y)=9x-3x+5y-7y[/tex]3)The third expression can be written as,
[tex](9x+5y)-(3x-7y)=9x+5y-3x+7y[/tex]4)The fourth expression can be written as,
[tex]9x-7y+3x+5y=9x+5y+3x-7y[/tex]5)The fifth expression can be written as,
[tex]\begin{gathered} 9x-7y+3x-5y=12x-12y \\ =12(x-y) \end{gathered}[/tex]6)The sixth expression can be written as,
[tex]\begin{gathered} 9x-7y-3x-5y=6x-12y \\ =6(x-2y) \end{gathered}[/tex]Thus, the correct match is 1-1, 2-6, 3-5, 4-4, 5-2, 6-3.
Simplify the expression cos x/ cot x.a. cos xb. tan xc. sin xd. cos²x/sin x
Answers
cosx/cotx = cosx *tan x =cosx (sinx/cosx) = sin x
Answer
c. sin x