Answer:
-3
Step-by-step explanation:
We know that,
( + ) × ( + ) = ( + )
( - ) × ( - ) = ( + )
( + ) × ( - ) = ( - )
Accordingly, let us solve the given fraction.
-7 - ( - 4 )
-7 + 4
-3
A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 centimeters and the lengths of the prisms vary. It costs $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?
The maximum length of each prism is equal to 7.99 centimeter.
How to calculate the maximum length of each prism?First of all, we would determine the maximum surface area of this regular hexagonal prism by using this mathematical expression:
Maximum surface area (quantity) = Cost/unit price
Maximum surface area (quantity) = $11/$0.04
Maximum surface area (quantity) = 275 square centimeter (cm²).
Mathematically, the surface area of a regular hexagonal prism can be calculated by using this formula:
A = 6al + 3√3a²
Where:
A represents the surface area of a regular hexagonal prism.a represents the edge length (apothem) of a regular hexagonal prism.l represents the length of a regular hexagonal prism.Substituting the given parameters into the formula, we have;
275 = 6 × 4l + (3√3 × 4²)
275 = 24l + 48√3
24l = 275 - 48√3
24l = 191.8616
l = 191.8616/24
Length, l = 7.99 centimeter.
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Comparing and Scaling Rates: Investigation 2.3 Homework 1. Keeley buys songs from a music website. She buys 35 songs for $26.25. What is the price per song? a. Complete the table. b. Lucius and Javier discuss how to write an equation relating price and number of songs. Lucius writes the equation n = 0.75C. Javier writes the equation C = 0.75n. Do you agree with Lucius or with Javier? Use the information from parts (a) to explain. 2. For each situation, find a unit rate and write an equation relating the two quantities. a. 3 dozen apples for $4.50 b. 30 bottles of water for $4.80 c. 24 ounces of mozzarella cheese for $2.88 Number of Songs, n 35 50 1 70 Cost, C $26.25 $3 $15
0.75
37.50
cost
dozen
= 4.50/3 = $1.50 / dozen
cost/bottles
2 3. Which of these items is the better buy? a. an 8-pack of glue sticks for $3.99 or 1 glue stick for $.54 b. a 12-pack of tape for $2.50 or 1 roll of tape for $.19 c. a 100-pack of pencils for $4.88 or 1 pencil for $.05 d. a 50-pack of paper clips for $.89 or a 25-pack of paper clips for $.45.
Answer:
Use the information from parts a
Step-by-step explanation:
A web music store offers two versions of a popular song. The size of the standard version is 2.1 megabytes (MB). The size of the high quality version is 4.7 MB. Yesterday, the high quality version was downloaded twice as often as the standard version. The total size downloaded for the two versions was 3335 MB. How many downloads of the standard version were there?Number of standard version downloads: ?
Answer: 529.3 downloads
Explanation:
Standard version size = 2.1 MB
High quality version = 4.7 MB
The high-quality version was downloaded twice as often as the standard version
H = 2 S
The total size downloaded for the two versions = 3335 MB
H + S = 3335
We have the system:
H = 2 S (a)
H + S = 3335 (b)
Put A into B
(2S ) + S = 3335
3S = 3335
S= 3335/3
S= 1,111.67 MB
Divide the total MB of standard versions by the size of each standard version.
1,111.67 / 2.1 = 529.3 downloads
Two angles are complementary. One angle is 4° less than four times the other angle. Find the measures of the angles.
Answer:
one of the angles is 48 degrees the other is 42 degrees
Step-by-step explanation:
Complementary is 90
45 + 45 = 90
48 +42=90
suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 15 days and a standard deviation of 5 days. let x be the number of days for a randomly selected trial. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n( , ) b. if one of the trials is randomly chosen, find the probability that it lasted at least 12 days. c. if one of the trials is randomly chosen, find the probability that it lasted between 17 and 22 days. d. 72% of all of these types of trials are completed within how many days? (please enter a whole number)
a. the distribution of X ~ N(15,5)
b. the probability that it lasted at least 12 days = 0·72575
c. the probability that it lasted between 17 and 22 days = 0.30567
d. 72% of all of these types of trials are completed within 13 days
(a)
The x follow normal distribution with mean standard deviation
X ~ N(15,5)
(b)
probability at least 12 days.
P(X≥12) = 1 - P(X ≤12)
= 1 - P((X - μ)/б ≤ (12-15)/5 ]]
= 1 - P[Z < -0.6]
= 1 - 0·27425
= 0·72575
(c)
Probability at least between 16 & 21 days
P(16 < x < 21) = p( (16-15)/5 < (X - μ)/б - (21-15)/5]
= p (0.2 < Z < 1.2 )
= p[Z < 1.2] - P[Z < 0.2]
= 0.8849 - 0.5792
= 0.30567
(d)
standard normal table z is 0.65
p (Z < 0.65) = 0.74215
using Z score formula
X = Z x б + μ
X = 0.65 x 5 + 15
X = 13
Explain probability ?This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.
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which of the following equation have roots 4 and -4
x² -16=0
1) Since we have two roots and any quadratic equation can be rewritten as once we have the roots:
[tex]a(x-x_1)(x-x_2)=0[/tex]So let's find one equation whose roots are 4 and -4, with coefficient a=1
(x-4)(x+4)=0
x² -16=0
2) So the equation x² -16= 0 has roots x_1=4 and x_2= -4 S={-4,4}
What is the area of the rectangle with verticals at A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)? Use the distance formula to find the length of segment AB (the base), and Segment BC (the height) Hint A=bh
The area of the rectangle would be 4.90 units which is shown in the given graph.
What is the area of rectangle?The area of a rectangle is defined as the product of the length and width.
The rectangle is given which has:
verticals at A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)
The length of segment AB = √ (-3 - (-4))² + (1 - 0)² = √ (1 + 1) = √2
The length of segment BC = √ (-3 - 0)² + (1 - (-2))² = √ (9 + 3) = √12
The area of the rectangle = length of segment AB x length of segment BC
The area of the rectangle = √2 x √12
The area of the rectangle = √24
The area of the rectangle = 4.90 units
Thus, the area of the rectangle would be 4.90 units
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Can someone help me with my practice? I am having trouble with this question.
We are to solve an inequality and give the answer in graph form.
The inequality is:
[tex]6-5+n\ge\text{ 18}[/tex]Let's solve for n in order to be able to answer the question.
we start by trying to isolate n on one side of the inequality symbol. So first combine 6-5 = 1 and re-write the inequality:
[tex]1+n\ge18[/tex][tex]\begin{gathered} n\ge18-1=17 \\ n\ge17 \end{gathered}[/tex]Now, subtract 1 from both sides, and you get the final answer:
n must be larger than or equal to 17. WHich agrees with the first answer option provided by the problem.
The domain of the given function is ____ (use integers of fractions for any numbers in the expression.)f(z) = 5z²- 6z+2 —————- 6z² +5
Given:
[tex]f(z)=\frac{5z^2-6z+2}{6z^2+5}[/tex]Required:
To find the domain of the given function.
Explanation:
Now consider
[tex][/tex]Determine if the table shows a proportional relationship. x 42.5 29.2 69.4 y 21.25 14.6 34.7 Yes, it is proportional because the ratios for y over x are all equivalent to one half. Yes, it is proportional because the ratios for y over x are all equivalent to one third. No, it is not proportional because 21.25 over 42.5 is not equal to 29.2 over 14.6. No, it is not proportional because 42.5 over 21.25 is not equal to 34.7 over 69.4.
Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
What is proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. A straight line represents a proportional relationship. Mathematically -
y = kx + c
(y - c)/x = k [k is constant]
or
y = kx
k = y/x [k is constant]
Given is the following data -
[x] 42.5 29.2 69.4
[y] 21.25 14.6 34.7
In order to find if the given coordinates represent proportional relationship, plot these coordinates on graph. If the by joining the coordinate points, we get a straight line, then it represents a proportional relationship. Graph is attached with the answer. It can be seen that its graph is a straight line and hence represents a proportional relationship.
Now, the ratio of [y] by [x] -
m = (21.25 - 14.6)/(42.5 - 29.2) = 6.65/13.3 - 0.5 = 1/2
Therefore, we can say that, Yes, it is proportional because the graph of these coordinates is a straight line and the ratios for [y] over [x] are all equivalent to one half.
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Answer: Yes, it is proportional because the ratios for y over x are all equivalent to one half.
Step-by-step explanation:
I did the test. :)
Part of the graph of the function f(x) = (x + 4)(x - 6) isshown below.Which statements about the function are true? Selecttwo optionsThe vertex of the function is at (1,-25).6The vertex of the function is at (1,-24).The graph is increasing only on the interval -4
The vertex of the function is (1, -25) Correct
Because
f(x) = (x + 4)(x - 6)
Substitution
-25 = (1 + 4)(1 - 6)
Simplification
-25 = (5)(-5)
Result
-25 = -25 As both sides of the equation are equal this option is true
5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis
Factor 24cd − 36c^2d.
Answer:
12cd(2-3c)
Step-by-step explanation:
check:
12cd( 2 - 3c)
12cd(2) - 12cd(3c)
24cd - 36[tex]c^{2}[/tex]d
A pie weighs 500g. jamie cuts it into 4 slices. the largest slice weighs the same as the other 3 combined. what is the weight of the largest piece of pie?
The weight of the largest piece of pie is 250 gram.
How to calculate the weight?Let the weights of others be illustrated as x.
Therefore, the weight of the largest weight is the addition of the others weight. This will be:
= x + x + x = 3x
Therefore, the weights will be:
3x + x + x + x = 500
6x = 500.
Divide
x = 500 / 6
x = 83.33.
The larger weight will be:
= 3x
= 3 × 83.33
= 250
The pie weights 250g.
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Parallel lines investigation
From the given figure the value of x is 6 and the measure of angle 3 is 57°.
From the given figure, m∠4=(20x+3)° and m∠6=(9x+3)°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
22). From the given figure
m∠4+m∠6=180° (Coointerior angles sum is equal to 180°)
(20x+3)°+(9x+3)°=180°
⇒ 29x+6=180
⇒ 29x=174
⇒ x=6
m∠4=(20x+3)°=123°
m∠3+m∠4=180° (Adjacent angles sum is equal to 180°)
m∠3+123=180
m∠3=57°
23). From the given figure
m∠3=m∠6 (Alternate interior angles are congruent)
x+10 = 4x-20
⇒ 3x=30
⇒ x=10
Now, m∠6=4x-20
=20
m∠6+m∠8=180° (Adjacent angles sum is equal to 180°)
20+m∠8=180°
⇒ m∠8=160
Therefore, from the given figure the value of x is 6 and the measure of angle 3 is 57°.
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4. Round the number 5,997 to the nearest hundred.
Answer:
6,000
Step-by-step explanation:
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.ingles TestGiven mZA = m D = 90° and AABC ADFE. If AB = 5 inches and BC = 13 inches, determine DE.POSSIBLE
We will apply the principle of similar triangles to solve this question
Given that
[tex]\begin{gathered} AB=5 \\ BC=13 \end{gathered}[/tex]Method: Find side AC
We will use the Pythagoras theorem to evaluate AC
[tex]\text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2[/tex][tex]13^2=5^2+AC^2[/tex][tex]\begin{gathered} AC^2=13^2-5^2 \\ AC^2=169-25 \\ AC^2=144 \\ AC=\sqrt[]{144} \\ AC=12 \\ \end{gathered}[/tex]T
which of the following additional statements would you need to prove these two triangles are by SAS similarity?
∠I ≅∠L
1) Given that the triangles are similar, then we can write:
[tex]\begin{gathered} \frac{KL}{HI}=\frac{JL}{GI} \\ \frac{18}{12}=\frac{27}{18}\text{ =}\frac{3}{2} \end{gathered}[/tex]Notice that the sides are proportional to k=3/2.
2) Since we need to prove that these triangles are similar under SAS -Side, Angle Side, examining the picture we can state that one of their corresponding angles are congruent so
[tex]\begin{gathered} \angle I\cong\angle L \\ \end{gathered}[/tex]3) Having one of these angles as congruent would fit to prove that these triangles are similar by SAS similarity.
Answer:
∠I ≅∠L
Step-by-step explanation:
Christel House DORS is taking a field trip. Some students will travel in cars, which can carry 5 students, and others will travel in vans, which can carry 15 students. The equation 5(2)+15v=100 describes the relationship between the number of vans needed, v, and the number of students going on the trip. Which statement below is true?
Given,
5(2)+15v=00
where v is the number of vans.
Solving,
15v=90
v=6
Thus the correct answer is 6 vans are needed to transport students.
If a rectangle has a length of 6cm and a width of 4cm what is it's area
Answer:
area = l×b
= 6×4
. = 24 cm²
Step-by-step explanation:
this is the answer
Richard and teo have a combine age of 38 Richard is 11 years okder than twice teo age how old are Richard and teo?
Answer: Richard is 29 and Teo is 9.
Step-by-step explanation: Use Substitution
Please answer the following questions. What is the slope of the line? How much does the distance increase for each hour since Alan crossed the bridge?
SOLUTION
The slope of the line can be gotten using the formula
[tex]\begin{gathered} \text{Slope =}\frac{change\text{ in distance}}{\text{change in time }}\text{ = }\frac{d2-d1}{t2-t1} \\ \text{Taking two points on along the line we have } \\ \text{Slope = }\frac{350-100}{7-2} \\ \\ \text{Slope =}\frac{250}{50} \\ \\ \text{Slope = 50} \end{gathered}[/tex]The slope is 50. This means the distance increased by 50 miles for every hour.
what do all the captain codes of ethnics have in common ?A.they all identify four or ethnic or principles of accounting B.they all spend hundreds of pages covering confidentiality C.they all go into great detail on the responsibilities of accountants D. they all separate accounting principles into three categories (just answer)
An accountant’s ethical code of conduct represents the moral values, principles, and rules that accountants should have.
The ethical codes of conduct of AICPA and IFAC are the two main codes most countries adopt to guide their members on how to deal with accounting information from an ethical perspective.
The fundamental principles within the Code – integrity, objectivity, professional competence and due care, confidentiality, and professional behavior – establish the standard of behavior expected of a professional accountant (PA) and it reflects the profession’s recognition of its public interest responsibility.
The common thing in all accounting codes of conduct is that "they all go into great detail on the responsibilities of accountants."
Therefore, the correct option is OPTION
6. There were a total of 139 points scored in the basketballgame. The Falcons scored (9x+22) and the Mavericks scored(16x - 8). What was the Falcons score for the game?
The total score in the basket game = 139
Falcons score = 9x + 22
Maverick score = 16x - 8
Therefore,
139 = 9x + 22 + 16x - 8
collect like term
139 - 22 + 8 = 9x + 16x
125 = 25x
divide both sides by 25
x = 125/25
x = 5
Falcons score = 9x + 22
Falcons score = 9(5) + 22
Falcons score = 45 + 22
Falcons score = 67
Which of the following is not true? 1/2 m is equal to 500 mm1000 mg is equal to 1 g1 mg is equal to 1 ml
To solve the question we would need to state some facts.
1) In measurements, there are one thousand millimeters in a meter.
[tex]\therefore\frac{1}{2}\text{metre}=500\text{milimetres}[/tex]2) Also one thousand milligrams equals one gram
3) However one milligram is not equal to one milliliter
Answer: 1mg is equal to 1ml is not true
Which is the order from least to greatest of the following: 4/3, 0.8, 1/5, 30%?
Answer:
1/5, 30%, 0.8, 4/3
if 5 people can finish 3 cups of rice,
how many cups of rice will 35 people
eat at the same rate
Answer:
21 cups
Step-by-step explanation:
This question tests on the the concept of Unit Conversion.
Unit ConversionUnit Conversions involving converting values into per unit values.
Example: 15 apples in 3 days = (15 ÷ 3) apples per day = 5 apples per day
ApplicationFor this Question, we are given:
5 people per 3 cups of rice.
We are asked to find the number of cups of rice that 35 people can finish.
5 people = 3 cups
(5 ÷ 5) people = (3 ÷ 5) cups
1 person = 0.6 cups
(1 × 35) people = (0.6 × 35) cups
35 people = 21 cups
the following data are from a simple random sample. 5 8 10 7 10 14 a. what is the point estimate of the population mean? b. what is the point estimate of the population standard deviation?
The point estimate of the population mean is 9
The point estimate of the population standard deviation is 2.83
Part a
Point estimate of population mean:
Given the sample data is 5,8,10,7,10,14
Number of samples, n is 6
Population mean=[tex]\frac{\sum x }{n}[/tex]
=(5+8+10+7+10+14)/6
=54/6
=9
Point estimate of mean=9
Part b
Point estimate of population standard deviation:
Mean=9
Data (x) (x-mean)^2
5 16
8 1
10 1
7 4
10 1
14 25
Total 48
Standard deviation=√(x-mean)^2/n
=√48/6
=√8
=2.83
Hence, the point estimate of population standard deviation is 2.83
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5 people can claim joint ownership of an item and intend to divide it by the method of sealed bids. The winner offers a bid of $8,000, how much will that bidder need to put into a kitty for the other bidders to be compensated?
Step-by-step explanation:
there is one item and it cannot be split.
the winning bid was $8,000.
that means the fair share for each one of the 5 participants is
8000/5 = $1,600
the winner is getting one item with a value greater than his fair share.
so, he has to pay the difference into the kitty :
8000 - 1600 = $6,400
What are the vertex and range of y = |x + 3| + 2?
a (−3, 2); 2 ≤ y < ∞
b (−3, 2); −∞ < y < ∞
c (0, 5); 2 ≤ y < ∞
d (0, 5); −∞ < y < ∞
The vertex of the equation is (-3, 2). And the range will be the set of all real numbers equal to or larger than 2, written as:
y ≥ 2.
What is the vertex and range of the absolute value function?
For an absolute value function of the form:
y = |x - a| + b
The vertex is a the point (a, b).
And the range (the set of the possible values of y that we can get with the function) will be the set of all real values equal or larger than b.
In this case, the absolute value function is:
y = |x + 3| + 2
Comparing it with the general one, we can see that the vertex is (-3, 2)
And then the range is y ≥ 2.
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