The length of one side of the box is 10 inches.
How to find the volume of a cube?Suppose that: The side length of the considered cube is L units.
Then, we get the Volume of that cube = L³ cubic units.
The volume of a cube is of the form V = L³, where L is the side length.
Given that the shipping box has a volume of 1,000 cubic inches.
Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:
1000 = L³
Cube root both sides:
L = [tex]\sqrt[3]{1000}[/tex]
Therefore, each side is 10 inches.
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discuss the advantages and disadvantages of using sampling to reduce the number of data objects. would simple random sampling (without replacement) be a good approach to sampling? why or why not? what kind of sampling method that you would like to use? g
The advantage and disadvantages are sampling.
We have to find the advantages and disadvantages of sampling.
The advantage is:
It provides an opportunity to do data analysis with a lower likelihood of carrying an error.
Researchers can analyze the data that is collected with a smaller margin of error thanks to random sampling. This is permitted since the sampling procedure is governed by predetermined boundaries. The fact that the entire procedure is random ensures that the random sample accurately represents the complete population, which enables the data to offer precise insights into particular topic matters.
The disadvantage is:
No extra information is taken into account.
Although unconscious bias is eliminated by random sampling, deliberate bias remains in the process. Researchers can select areas for random sampling in which they think particular outcomes can be attained to confirm their own bias. The random sampling does not take into account any other information, however sometimes the data collector's supplementary information is retained.
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i inserted a picture of the question answers to choices A 5/2B 2/5C -2/5D -5/2
If two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. Given a value, a/b, the negative reciprocal of a/b is - b/a.
From the information given, the slope of the red line is 2/5. This means that the slope of the green line which is perpendicular to the red line is - 5/2
Option D is correct
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Well your answer is down below
Step-by-step explanation:
First as a Inequality −3(2x−5)<5(2−x)
Step 1: Simplify both sides of the inequality.
−6x+15<−5x+10
Step 2: Add 5x to both sides.
−6x+15+5x<−5x+10+5x
−x+15<10
Step 3: Subtract 15 from both sides.
−x+15−15<10−15
−x<−5
Step 4: Divide both sides by -1.
−x−1<−5−1 x>5
So your answer is x>5
hope this helps
~~Wdfads~~
Represent the following sentence as an algebraic expression, where “a number” is the letter x. You do not need to simplify 3 is multiplied by the difference of seven and a number
The given statement can be written algebraically as follow:
3(7 - x)
3 means '3 is multipled by' and the factor (7-x) means 'the difference of seven and a number'
Solve the proportion 4/x = 7/26 X=
given the proportion :
[tex]\frac{4}{x}=\frac{7}{56}[/tex]we will find x as follows:
[tex]\begin{gathered} \frac{7}{56}=\frac{7\cdot1}{7\cdot8}=\frac{1}{8} \\ \\ \frac{4}{x}=\frac{1}{8} \\ \\ x=4\cdot8=32 \end{gathered}[/tex]So, the answer is: x = 32
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3). What is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2?
The function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is;
(5, 3+2) +2 = (5, 5) + 2
Given,
A quadratic function y=f(x)y=f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3)(5,3).
To find the what is the vertex of the function defined as g(x)=f(x+2)+2g(x)=f(x+2)+2
Now,
What is the equation of the parabola?
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
A quadratic function y = f(x) is plotted on a graph and the vertex of the resulting parabola is (5, 3).
Hence, if the function; g(x)=f(x+ 2)+2, it follows that the vertex of the function is; (5, 3+2) +2 = (5, 5) + 2.
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helpppppp math its hard for me
Step-by-step explanation:
You would start off with solving inside, the parenthesis, and you would get -8/27.
Then, your would solve the 1 1/4 - 3/4 and get 1/2.
You then have to multiply -8/27*1/2, which is -4/27.
Lastly, you divide by negative 4.
-4/27 divided by -4.
You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.
Since negative times negative is positive, the answer would be 1/27.
Answer:
1/27
Hope this helped! :)
Factor Completely.. Please help with this I am really behind..
The factors of the quadratic equation 5x^2 + 44x - 9 are (5x - 1) and (x + 9)
What is factorization?In Mathematics, factorization or factoring is defined as the breaking or decomposition of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.
In the given question, we can factorize 5x^2 + 44x - 9 by finding two factors that when they multiply will give us the original polynomial.
The factor for this polynomial or quadratic equation are (5x - 1)(x + 9).
This can be summarized as the factorization of 5x^2 + 44x - 9 is (5x -1)((x+ 9)
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if the textbook committee makes a histogram of the sample data and it is single-peaked with no outliers, are the conditions of randomness and normality of the population met for this test?
Yes, conditions of randomness and normality of the population met for this test.
The textbook committee made a histogram of the sample data, and it was single peaked with no outliers. The conditions of randomness and normality of the population met for this test, the reason is that it was a random sample, and the plot of the sample data has no outliers.
So, yes, conditions of randomness and normality of the population met for this test.
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I need help 9th grade math
Answer:
A. y - 2 = 2/3 (x - 0)
Step-by-step explanation:
Can someone please help! And thank you!
Answer:
x = 20
Step-by-step explanation:
X = 20 Because the values are Corresponding Angles This means that they are congruent
2,048 rounded to the nearest tenth?
answer to the question that you have
2,048.0
2050 because
1-9 = ones place
10-99 = tenth place
100-999 = hundrends place
1000 - 999999 - thousands place
and you round to the nearest 0 if it is 5 or up and if it is 1 to 4 it stays the same
Use the equation one sixth plus s equals 21 over 30 to answer the questions.
Part A: Determine two numbers that the solution to the equation is between. Support your answer using the correct vocabulary. (2 points)
Part B: Solve for the variable. Show your work. (2 points)
(Its due in 45 minutes so help answer it plsss)
s is 4/15 of the equation one sixth plus s equals 21 over 30.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
one sixth plus s equals 21 over 30
This can be written as
one sixth can be written as 1/6.
21 over 30 can be written as 21/30.
so the equation is 1/6+s=21/30.
Let us separate the variable s to find the value of s.
s=21/30-1/6
The LCM of 30 and 6 is 30
s=21-5/30
s=16/30=4/15
Hence s is 4/15 of the equation one sixth plus s equals 21 over 30.
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Rewrite all 3 fractions with the least common denominator between them.
Answer:
To rewrite the given fraction with the least common denominator between them
The given fractions are,
[tex]\frac{1}{3},\frac{5}{10},\frac{7}{30}[/tex]we get, LCM of 3,10,30 is 30
The equivalent fractions for the above factions as common denominator 30 is as follows,
For 1/3,
Multiply and divide by 10, we get,
[tex]=\frac{1}{3}\times\frac{10}{10}=\frac{10}{30}[/tex]Using this we get,
[tex]\frac{1}{3}=\frac{10}{30}[/tex]For 5/10,
Multiply and divide by 3, we get,
[tex]\frac{5}{10}=\frac{5}{10}\times\frac{3}{3}=\frac{15}{30}[/tex]Using this we get,
[tex]\frac{5}{10}=\frac{15}{30}[/tex]For 7/30,
Since the denominator 30, we get same fraction,
[tex]\frac{7}{30}=\frac{7}{30}[/tex]Answer is:
[tex]\frac{1}{3}=\frac{10}{30}[/tex][tex]\frac{5}{10}=\frac{15}{30}[/tex][tex]\frac{7}{30}=\frac{7}{30}[/tex]we have a coin which, with equal odds, is either weighted so that heads has .75 probability, or weighted so that heads has .25 probability. we flip the coin twice and observe two heads. what is the conditional probability that the coin is weighted toward heads with .75 probability?
The Conditional Probability that the coin is weighted towards heads is 0.25/0.75 . Conditional probability is the result of Bayes’ Theorem .
A coin is tossed twice . So, total outcomes are { HH , TH , HT, TT} that is 4 .
Probability= favourable outcomes / total outcomes
Probability of getting two heads = ¼ = 0.25
Favourable outcomes are { HH , HT, TH}
Probability of getting at least one head = ¾ = 0.75
Conditional probability is measure of the probability of an event occurring, given that another event has already occurred.
Formula , P(A|B) = P(A and B)/ P(B)
Here, p(A|B) is conditional probability of A given B
P(B) is probability of event B occur
P(A and B) is probability of both events A and B occur
We have to find conditional probability that coin is weighted towards heads and it is = Probability of getting both heads / probability of getting at least one head
= ¼ / ¾ = 0.25 / 0.75
Which is required result .
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Solve the inequality for x. Show each step of the solution.
12(x+3)>4x-8
Answer:x>-11/2
search it for a better understanding of the understanding the question
Answer:
x > -11/2
Step-by-step explanation:
Given inequation,
→ 12(x + 3) > 4x - 8
Now the value of x will be,
→ 12(x + 3) > 4x - 8
→ 12x + 36 > 4x - 8
→ 12x - 4x > -8 - 36
→ 8x > -44
→ [ x > -11/2 ]
Hence, value of x is -11/2.
39+(20.4) can u help me with this answer I don't know how to do it
You have the following expression:
39 + (-20.4)
In order to simplify the previous expression, you first eliminate the parenthesis. To do that, you take into account that the sign before the parenthesis must multiply the sign inisde. In this case, you have a positive sign + before the parenthesis, and inside you have a minus -. When the parenthesis is eliminated, these signs are multiplied (here you use the multiplication rule for signs). Thus, you have that - x + = - (positive multiplied by negative is equal to negative). And the expression becomes:
39 + (-20.4)
= 39 - 20.4
= 18.6
Hence, the simplified expression is 18.6
I just need a little help
Which table represents a function?
Answer:
A would be the correct answer because to find a function when you draw a line on the graph, the line cannot cross each other. Even if the line is verticle, it is still crossing each other.
Step-by-step explanation:
Distribute:
-8(9 - 4x)
Answer:
32x – 72
OR
–72 + 32x
Step-by-step explanation:
To use the Distributive Property, just simply follow my steps:
Write the equation:
–8(9 – 4x)
To distribute, multiply the numbers inside the parenthesis by the number outside of the parenthesis SEPARATELY. It should look like this:
(–8 • 9)(–8 • –4x)
(–72)(32x)
Since the 32 is positive, the equation could be written either way:
–72 + 32x
OR
32x – 72
If you want the equation to be fully solved...
Set the equation equal to zero:
32x – 72 = 0
Isolate the variable. Subtract 72 from both sides:
32x – 72 + 72 = 0 + 72
32x = 0 + 72
32x = 72
Divide:
32x/32 = 72/32
x = 9/4 (Improper Fraction Form)
OR
x = 2 (and) 1/4 (Mixed Number Form)
Convert 9/4 to a decimal:
x = 9/4
x = 2.25
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Please help me I don’t know it
Answer:
angle 4 and 5 are interior angles, and 3 and 6 as well
what is the type of angle are <1 and <14??????????
1° and 14° are acute angles.
An acute angle is one that is less than 90°, or one that is between 0° and 90°.
The opposite of an acute angle is an obtuse angle. In other terms, an obtuse angle is one that is larger than 90° and less than 180°. It is the angle that is between 90° and 180°.
90° is the standard for a right angle. Any angle that is less than 90° is called acute, and any angle that is larger than 90° is called obtuse.
∠1 and ∠14 are less than 90° therefore, they are acute angles.
Correct question :
What type of angle are 1° and 14°?
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Colin has 29,820 in a saving account that earn 7% interest per year how much will he have in four years
EXPLANATION
Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:
[tex]Simple\text{ Interest = P}\cdot r\cdot t[/tex]Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,
Plugging in the numbers into the expression:
[tex]\text{Interest}=29,820\cdot0.07\cdot4[/tex]Multiplying numbers:
[tex]\text{Interest}=8,349[/tex]Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169
In conclusion, Colin will have $38,169 after 4 years
Mai is riding her bicycle she rides at a speed
ANSWER
[tex]3.2hours[/tex]EXPLANATION
Given;
[tex]\begin{gathered} speed=\frac{8km}{hr} \\ distance=25.6km \end{gathered}[/tex]Recall;
[tex]\begin{gathered} time=\frac{distance}{speed} \\ =\frac{25.6}{8} \\ 3.2 \end{gathered}[/tex]Therefore, the time taken is 3.2hours.
PLS ANSWER FAST!!! A triangle has coordinates R(2,−1),S(3,3), and T(4,6). The triangle is dilated by a scale factor of 1.5 with the origin as the center of dilation. What is the x-coordinate of R′ in the dilated triangle?
The x-coordinate of point R′ after dilation is 3
How to determine the x-coordinate of R′ after dilation?The given parameters are:
R(2,−1),S(3,3), and T(4,6).
The scale factor of dilation is given as
Scale factor = 1.5
Mathematically, this transformation can be represented as
(x, y) = 1.5(x, y)
When represented as a function, we have
Image = 1.5 * Point
For point R, we have
R = (2, -1)
Substitute the equation Point = (2, -1) in the equation Image = 1.5 * Point
So, we have the following equation
R' = 1.5 * (2, -1)
Evaluate the product
R' = (3, -1.5)
Remove the y-coordinate
R'x = 3
Hence, the image of the x cooridnates is 3
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2. Use powers to rewrite these problems:
Example: 5 x 5 = 5^2
a. 4 * 4 * 4 * y * y * y
b. 7 * 7 * 7
c. 3 * 3 * 3 * x * x * x
Answer:
[tex] {4}^{3} {y}^{2} \\ {7}^{3} \\ {3}^{3} {x}^{3} [/tex]
Mrs. Doctor made a pot of hot chocolate in the teacher’s lounge. She wants to put 2/3 cup of hot chocolate into mugs to share with the other teachers. The pot holds 10 cups. How many mugs will Mrs. Doctor be able to fill?
Using the mathematical operation of division, Mrs. Doctor can fill 15 mugs using 10 cups.
What is the division operation?The division operation is one of the basic mathematical operations.
The division operation involves using the divisor to divide the dividend, which results in a quotient.
For instance, since the pot holds 10 cups and the distribution is 2/3 cups for each mug, we can divide 10 cups by 2/3 cups to get 15 mugs.
The quantity of hot chocolate for each mug = 2/3 cups
The total number of cups that the pot holds = 10 cups
The number of mugs that can be filled from 10 cups = 15 (10 ÷ 2/3)
Thus, we can divide 10 cups by 2/3 cups to get the number of mugs Mrs. Doctor can fill.
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in a basketball game Tatiana May 23 baskets each of the baskets was worth either two or three points and Tatiana scored a total of 53 points let x represent the number of two-point baskets she made and why represent the number of three-point baskets she made.part a write a system of equations represent the situation.part b would you use graphing or substitution to solve the system and determine the number of 2.3 point baskets Tatiana made? explain.part c use the method you chose in part b to solve the system and find out how many two point and 3-point baskets Tatiana made.
Part A
start by naming the variables you will be using in the system of equation
x= number of two-point baskets
y= number of three-point baskets
since she did 23 baskets the first equation representing the number of baskets she made will be
[tex]x+y=23[/tex]the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.
[tex]2x+3y=53[/tex]Part B
Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.
However both methods could be used.
Part C
[tex]\begin{gathered} x+y=23 \\ 2x+3y=53 \end{gathered}[/tex]One of the rows in the table has an error and does not have the same ratio as the other rows. Which explains how to correct the error in the table?
Conversion Chart
Feet
Centimeters
Row 1
3
91.44
Row 2
6
172.88
Row 3
7
213.36
Row 4
9
274.32
Row 1 should show 3 feet is equivalent to 92.44 centimeters.
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Row 3 should show 7 feet is equivalent to 223.36 centimeters.
Row 4 should show 9 feet is equivalent to 284.32 centimeters.
The correct option regarding the error in the proportional relationship is given as follows:
Row 2 should show 6 feet is equivalent to 182.88 centimeters.
Direct proportional relationshipA direct proportional relationship is a function in which the output variable y is calculated by the multiplication of the input variable x and the constant of proportionality k, as follows:
y = kx.
In the context of this problem, the input and the output are given as follows:
Input: Length in feet.Output: Length in centimeters.The constant is calculated dividing the output by the input of each of the lengths, hence:
Row 1: k = 91.44/3 = 30.48.Row 2: k = 172.88/6 = 28.81.Row 3: k = 213.36/7 = 30.48.Row 4: k = 274.32/9 = 30.48.Due to the different ratio, the mistake is in Row 2, and the correct value should be of:
6 x 30.48 =182.88 centimeters.
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Use the information on the diagonal to find: a. the length ACb. the length ABc. the perimeter of quadrilateral ABCDd. the area of quadrilateral ABCD
A) To find the length AC, we must use the trigonometric ratio
[tex]\cos \text{ 31 =}\frac{adjacent}{hypothenuse}[/tex]adjacent = 5cm
hypothenuse = AC
[tex]\begin{gathered} \cos 31\text{ = }\frac{5}{AC} \\ AC\text{ = }\frac{5}{\cos 31} \\ AC\text{ =}5.8332\operatorname{cm} \end{gathered}[/tex]B) To find the length AB, we will use the value of AC just obtained to get it
since triangle ABC is a right-angled triangle, we will use Pythagoras theorem
so that
|AC|^2 = |AB|^2 +|BC|^2
AC = 5.8332cm
BC = 4cm
|AB|^2 = |AC|^2 - |BC|^2
[tex]\begin{gathered} AB\text{ = }\sqrt[]{5.8332^2-4^2} \\ AB\text{ = }\sqrt[]{18.0262224} \\ AB\text{ = 4.245729883cm} \end{gathered}[/tex]C) The perimeter of the quadrilateral can be found by adding the length of all the sides around its edges.
Perimeter = AD +CD + BC + AB
We do not have CD and we must find CD
[tex]\begin{gathered} CD\text{ = }\sqrt[]{|AC|^2-|AD|^2} \\ CD\text{ =}\sqrt[]{5.8332^2-5^2} \\ CD\text{ =}\sqrt[]{9.02622224} \\ CD\text{ = 3.004366195cm} \end{gathered}[/tex]Perimeter of ABCD = 5 + 3.004366195 + 4 +4.245729883 = 16.25009708cm
D) To find the area of the quadrilateral we must find the area of triangle ADC and triangle ABC.
Area of triangle ADC = 1/2 x base x height= 1/2 x 3.004366195 x 5 = 7.510915488 square centimeter
Area of triangle ABC = 1/2 X base x height = 1/2 x 4 x 4.245729883 =8.491459766 square centimeter
Area of quadrilateral ABCD = 7.510915488 + 8.491459766 = 16.00237525 square centimeter
24. OPEN-ENDED Complete the table so that when t is the
independent variable, the relation is a function, and when
t is the dependent variable, the relation is not a function.
The following table shows how the relation is a function when t is the independent variable and not a function when t is the dependent variable:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
A vertical line drawn from the independent variable axis (x-axis) meets the function graph only once because a function is a relationship between an input and an output in which each input has just one output.
The independent variable is the input, while the dependent variable is the output.
Filling out the table in such a way that when t is the independent variable, the relationship is a function, and when t is the dependent variable, the relation is not a function, results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
Given that each value of the independent variable t has a corresponding value of the velocity v, the aforementioned is a function.
However, when t is the dependent variable, the independent variable value of 1 produces two outputs of 1 and 5, which results in the following table:
t 0 1 2 3 4 5
v 0 1 2 3 4 5
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