Let 'x' represent number of marbles
Let 'y' represent number of table tennis balls
Amelia had a total of 1,260 marbles and table tennis balls,
The mathematical representation is,
[tex]x+y=1260\ldots\ldots\text{.}.1[/tex]She had 40 fewer marbles than table tennis balls.
The mathematical representation is,
[tex]x=y-40\ldots\ldots\ldots2[/tex]Substitute x = y - 40 from equation 2 into equation 1 to solve for y
[tex]\begin{gathered} y-40+y=1260 \\ y+y=1260+40 \\ 2y=1300 \\ \frac{2y}{2}=\frac{1300}{2} \\ y=650\text{ table tennis balls} \end{gathered}[/tex]Hence, she has 650 marbles.
There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. How many litersthere are roughly in a gallon?to. 2b. 3C. 4d. 5Is your estimate greater or less than the exact number of liters in a gallon? Explainhow do you know.
Answer
Option C is correct.
There are roughly 4 liters in 1 gallon
And the estimate (4 liters in 1 gallon) is greaster then the exact number of liters in a gallon (3.79 liters in 1 gallon).
Explanation
We are given some parameters
33.8 fluid ounces = 1 liter
128 fluid ounces = 1 gallon
We are then told to find the amount of liters that are roughly in a gallon.
To do this, we will put the parameters that are equivalent as fractions on each other
[tex]\begin{gathered} \frac{33.8\text{ fluid ounces}}{1\text{ liter}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \end{gathered}[/tex]We can write the first relation as an inverse and we will still have the same thing
[tex]\begin{gathered} \frac{1\text{ liter}}{33.8\text{ fluid ounces}}=1 \\ \frac{128\text{ fluid ounces}}{1\text{ gallon}}=1 \\ \text{ Since, 1 }\times1=1 \\ We\text{ can find the relation betw}een\text{ liter and gallon by saying} \\ \frac{1\text{ liter}}{33.8\text{ fluid ounces}}\times\frac{128\text{ fluid ounces}}{1\text{ gallon}} \\ \frac{128}{33.8}\frac{\text{liter}}{\text{gallon}} \\ =\frac{3.79\text{ liters}}{1\text{ gallon}} \end{gathered}[/tex]3.79 liters = 1 gallon
A right approximation will be that
1 gallon = 4 liters
We can then see that the estimate is greater than the exact number of liters in a gallon.
Hope this Helps!!!
List all numbers from the given set that area. natural numbersb. whole numbersd. rational numberse. irrational numbersc. integersf. real numbers{0.1. VT6.0. -2. 15. -3, 98. }a natural numbers =(Use a comma to separate answers as needed. Do not simplify.)b. whole numbers =(Use a comma to separate answers as needed. Do not simplify.)c. integers =(Use a comma to separate answers as needed. Do not simplify)d. rational numbers =(Use a comma to separate answers as needed. Do not simplify.)e irrational numbers =(Use a comma to separate answers as needed. Do not simplify.)f. real numbers =(Use a comma to separate answers as needed. Do not simplify.)
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.
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]help me asap please on this math question
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
To know more about Direct variation here
https://brainly.com/question/18087321
#SPJ1
polinomials (x + 3)2
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
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.
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]consider parallelogram JKLM below.use the information given in the figure to find m
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°
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
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
Given the table below, write a linear equation that defines the dependent variable, c, in terms of the independent variable, a.
For a linear equation, the first step is to find the slope.
Based on the table, I see that every time "t" increases by 1, then "k" increases by 4.
Since we're told k is the dependent variable, the slope will be
[tex]\dfrac{\text{change in }k}{\text{change in }t}} = \dfrac{4}{1} = 4[/tex]
The slope is always [tex]\dfrac{\text{change in dependent variable}}{\text{change in independent variable}}[/tex].
Once you have the slope, you need the vertical (We'd normally call this this y-intercept, but there's no "y" here. You could call it the "k" intercept in this example.)
From the table, we again see that t=0 has k=2, so that 2 is the value we need.
This gives us our equation: k = 4t + 2.
(This all is really just the slope-intercept form with x's now being called "t" and y's now being called "k".)
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
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
10<=6-2x<14 solve the inequality
Having that
10 ≤ 6 - 2x < 14
It meets two statements:
10 ≤ 6 - 2x and 6 - 2x < 14
We are solving each of them separately. We have to remember that we can add or substract any amount both sides of the inequalities and multiply or divide by a positive number both sides.
First statement: 10 ≤ 6 - 2xOn one hand, we want to solve:
10 ≤ 6 - 2x
then
10 ≤ 6 - 2x
↓ adding 2x both sides
10 + 2x ≤ 6
↓ substracting 10 both sides
2x ≤ 6 -10
↓ 6 - 10 = -4
2x ≤ -4
↓ dividing by 2 both sides
2x/2 ≤ -4/2
↓ -4/2 = -2
x ≤ -2
We have that x ≤ -2
Second statement: 6 - 2x < 14For the other hand, we want to solve
6 - 2x < 14
then
6 - 2x < 14
↓ adding 2x both sides
6 < 14 + 2x
↓ substracting 14 both sides
6 - 14 < 2x
↓ 6 - 14 = -8
-8 < 2x
↓ dividing by 2 both sides
-8/2 < 2x/2
↓ -8/2 = -4
-4 < x
We have that -4 < x
Therefore, joining both conclusions, we have that -4 < x and x ≤ -2, then
Answer: -4 < x ≤ -2Complete 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
f(x) = -x^2 + 2x + 5
x -1 0 1 2 3
f(x) 2 5 6 5 2
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?
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]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
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
-5|x+4|-7 describe the transformation.
Answer:3
Step-by-step explanation:
so you take 41 and divide by 2 and get 5. then take -51 and times by 6 which is 24.then you take seven and multipy by 3 and get 20. so you are left with 5, 24, and 20. Multiply all of them and get 3!!
What number is 2% of 35
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
Y 3+ 2+ 1+ -4 -3 -2 -1 1 2 3 -1- -2 -3+ -4 47 What is the slope of the line?
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]Simplify the expression cos x/ cot x.a. cos xb. tan xc. sin xd. cos²x/sin x
cosx/cotx = cosx *tan x =cosx (sinx/cosx) = sin x
Answer
c. sin x
#6) long division a. Let P(x) = 8x^3 + 27 and D(x) = 2x + 3
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]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
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
A __ is a polynomial with one term.
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
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
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.
To learn more about multiplication refer here
https://brainly.com/question/869839
#SPJ9
Find the value of b. * 4 b 6 Y 9 5.8 W
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
A 104° sector of a circle has an area of 56 square centimeters. Tothe nearest centimeter, what is the diameter of the circle?
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]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
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.
What is the measure of
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.
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?
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.
The box plot shows the average monthly high temperatures in New York City for 12 months. What is the difference between the range and interquartile range of the temperatures data?
The difference between the range and interquartile range of the temperatures data is equal to 16.
What is a range?Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range = 84 - 38
Range = 46.
What is an interquartile range?Mathematically, interquartile range (IQR) is the difference between first quartile (Q₁) and third quartile (Q₃):
IQR = Q₃ - Q₁
Based on the given box and whisker plot (see attachment), we can logically deduce the following quartile ranges:
Third quartile, Q₃ = 48
First quartile, Q₁ = 78
Now, we can calculate the interquartile range (IQR) is given by:
Interquartile range, IQR = Q₃ - Q₁
Interquartile range, IQR = 78 - 48
Interquartile range, IQR = 30
For the difference, we have:
Difference = Range - IQR
Difference = 46 - 30
Difference = 16
Read more on interquartile range here: brainly.com/question/17083142
#SPJ1
a laptop was originally sold for %975 the laptop is now on sale for $828.75 what is the percent markdown
The percent markdown is of the 15% of the price.
What is the percent markdown?We know that the original price is $975, and at the moment is sold by $828.75.
If we define the markdown (as a decimal) as r, then we can write the equation:
$828.75 = $975*(1 - r)
Solving this for r, we get:
($828.75 - $975)/(-$975) = r = 0.15
To write this as a percentage, we just need to multiply this by 100%.
0.15*100 = 15%
Laern more about percentages:
https://brainly.com/question/843074
#SPJ1
What is the complement of a 54 1/2 degree angle
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