The solutions for all the equations are:
1) x = 4
2) x = ±7
3) x = 5²´³
4) x = ±5³´²
How to solve the equations for x?The first equation is:
x³ = 64
If we apply the cubic root in both sides we will get:
∛x³ = ∛64
x = ∛64 = 4
2) now we have:
x² = 49
If we apply the square root:
√x² = ± √49
(remember the plus minus sign when you use a even degree root)
x = ±7
In this case we have two solutions.
3) x³ =25
Like in the first case:
x = ∛25 = ∛5² = 5²´³
Now we can't simplify this, so we leave it in this way.
4) x² = 125
Remember that 125 = 5³, then:
x² = 5³
x = ±√5³ = ±5³´²
These are all the solutions.
Learn more about cubic roots at:
https://brainly.com/question/20896994
#SPJ1
Use the vertex ( h, k ) and a point on the graph ( x, y ) to find the standard form of the equation of the quadratic function:
Vertex = (0,6)
Point = (2,7)
G( x )= Answer field 1
(x- Answer field 2
)^2 +Answer field 3
The required equation of the quadratic function in standard form is:
f(x) = (1/4) x² + 6.
A parabola is a cross-section cut out of the cone and represented by an equation f(x) = a(x - h)² + k.
The standard form of a quadratic function is given by:
f(x) = a(x - h)² + k
where (h, k) is the vertex of the parabola.
Given the vertex (0, 6) and the point (2, 7), we can find the values of a and k and use them to write the equation in standard form.
Let's use the vertex form of the equation:
f(x) = a(x - h)² + k
Since the vertex is (0, 6), we have h = 0 and k = 6:
f(x) = a(x - 0)² + 6
f(x) = a × x² + 6
Next, we use the point (2, 7) to find the value of a:
f(2) = a × 2² + 6
7 = 4a + 6
7 - 6 = 4a
1 = 4a
a = 1/4
So, the equation of the quadratic function in standard form is:
f(x) = (1/4) x² + 6
Learn more about parabola here:
brainly.com/question/4074088
#SPJ1
Translate into a proportion: What number is 63% of 107? Let n= the number.
Answer:
look at the picture.......................
If a 123 pound man can have 1213 mg of a medicine in a day, how much can a 102 pound woman have?
(round answer to one decimal place)
The woman weighing 123 pound can take 1005.9 mg of medicine
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
If a 123 pound man can have 1213 mg of a medicine in a day. Hence:
Unit rate = 1213 mg / 123 pound = (1213/123) mg per pound
For a 102 pound:
Amount of medicine = (1213/123) mg per pound * 102 pound = 1005.9 mg
The woman can take 1005.9 mg of medicine
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
_______ is the error due to the particular sample selected being an imperfect representation of the population of interest. it may be defined as the variation between the true mean value for the sample and the true mean value of the population.
Random sampling error is the error due to the particular sample selected being an imperfect representation of the population of interest.
What is random sampling error?When an analyst selects a sample that is not a true representation of the entire population of data, they commit a statistical error known as a sampling error. The results of the sample therefore do not fairly represent the results of the entire population.
Sampling is a type of analysis where a small sample of observations are selected from a larger population. The selection process has the potential to result in both sampling errors and non-sampling errors.
According to the definition, random sampling error is the error that results from the particular sample being chosen not accurately representing the population of interest. It could be described as the difference between the true mean value for the sample and the true mean value of the population.
Learn more about error here:
https://brainly.com/question/5290588
#SPJ4
Miko packed 40 bottles of perfume in a box. She sold each bottle of perfume for $30. How much money did she receive from sale of 15 boxes of perfume in all?
Answer: $18 000
Step-by-step explanation:
40 bottles per box
40*15 = 600 bottles total
600 * $30 = $18 000
She made $18 000 in total.
Amount of money she receives from sale of 15 boxes of perfume in all is $18,000.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Given that,
Number of bottles of perfume packed in a box = 40
Cost for each perfume = $30
Cost for 40 perfumes = 40 × $30 = $1200
So cost for a box of perfume = $1200
Cost for 15 boxes of perfume = 15 × $1200
= $18,000
Hence the amount for 15 boxes of perfume is $18,000.
Learn more about Proportions here :
https://brainly.com/question/29774220
#SPJ2
The number of tickets purchased by an individual for Beckham College's holiday music festival is a uniformly distributed random variable ranging from 5 to 15. Find the mean and standard deviation of this random variable. (Round your answers to 2 decimal places.)
The U.S. Department of Education and the U.S. Office for Civil Rights track sexual violence complaints in U.S. Higher Education. The annual data for 2009-2016 are presented below in table form.
Sexual Violence Complaints in U.S. Higher Ed
Year 2009 2010 2011 2012 2013 2014 2015 2016
Number of Complaints 9 11 19 17 32 106 165 177
Calculate the average rate of change in the number of sexual violence complaints for the specific years requested. Ignore the years in between the ones specified. Notice that the time periods are not of equal length. Round all values to the nearest whole number. You get one submission for each unit.
Sexual Violence Complaints in U.S. Higher Ed
Years 2009-2011 2011-2012 2012-2016
Average Rate of Change in Complaints per per per
The average rate of change for the first period is 3.33 cases per year, for the second period is 1 case per year, and for the third period is 40 cases per year.
How to calculate the average rate?To calculate this, the key is to determine the change in the annual rate and divided it by the number of years:
2009- 2011 =
9 - 19 = 10 / 3 = 3.33 cases per year
2011-2012=
19 - 17 = 2/ 2 = 1 case per year
2012-2016=
17 - 177 = 160 / 4 = 40 cases per year
Notice that the second period shows a decrease, while the first and second ones show an increase.
Learn more about rates in https://brainly.com/question/14731228
#SPJ1
can someone tell me how to do this problem?
Answer:
C-intercept(s): (0,0)
t-intercept(s): (0,0), (6,0), (-4,0)
Step-by-step explanation:
the C-intercept is essentially the y intercept. this occurs when t=0:
C(0) = 4(0)^4 - 8(0)^3 - 96(0)^2 = 0. so the C-intercept is at (0,0).
the t-intercept is the x-intercept, and occurs when C(t) = 0:
4t^4 - 8t^3 - 96t^2 = 0 = [tex]4t^{2} (t-6)(t+4)[/tex]. C(t) = 0 when t = 0, t= 6, and t = -4.
The absolute value of the sum of two Integers does not exceed the sum of the absolute values of these integers. əziou? aydunu le O V x Vy( ]z +y] 5 [+/+ 1y1) (18) + (0) 5126+2EXE O (18) + |3| 5] +31 ANEXE 0 (IAI + 3 + x| -) AXA
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
To learn more about the inequality from the given link
https://brainly.com/question/25275758
#SPJ4
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
The absolute value of the sum of two integers does not exceed the sum of the absolute values of these integers. ∀x, ∀y, |x + y|≤|x| + |y| .
This inequality, sometimes called as the triangle inequality.
To learn more about the inequality from the given link
brainly.com/question/25275758
#SPJ4
The length of a rectangular pool is 4 meters less than twice the width. if the pool's perimeter is 94 meters, what is the width?
Answer:
see below
Step-by-step explanation:
length = x
width = y
x = 2y -4
2*(x+y) =94
x+y = 47
so x = 47-y
so 47-y= 2y -4
so 3y = 51
y = 17
x=30
in a class of 24 students, 23 of them took an exam in class and 1 student took a make-up exam the following day. the professor graded the first batch of 23 exams and found an average score of 78 points with a standard deviation of 6.4 points. the student who took the make-up the following day scored 62 points on the exam
The average score for the class on the exam was 78 points with a standard deviation of 6.4 points. The student who took the make-up exam scored 79.25points.
1. Calculate the mean of the first 23 exams:
Mean = 78 points
2. Calculate the standard deviation of the first 23 exams:
Standard Deviation = 6.4 points
3. Calculate the mean of the entire class:
Mean = (78 x 23) + 62 = 1840 + 62 = 1902
Total = 24
Mean = 1902 / 24 = 79.25 points
The average exam score for the class of 24 students was 78 points with a standard deviation of 6.4 points. This means that most students in the class scored between 71.6 and 84.4 points on the exam. The student who took the make-up exam the following day scored 79.25points. This score is significantly lower than the average score of the class, suggesting that the student may have not done as well on the exam compared to the other students. It is also possible that the student faced additional challenges that the other students did not have to face, such as taking the exam on a different day. Regardless, the student's score was significantly lower than the average score of the class.
Learn more about average here
https://brainly.com/question/24057012
#SPJ4
Adam invests $1,051 in a savings account with a fixed annual interest rate that is compounded continuously. After 8 years, the account balance reaches $1,698.49. What is the interest rate of the account?
The account has an annual interest rate of 6.80%, compounded continuously.
What is interst rate?Interest is the cost associated with the boring money or to return on for lending money it is typically expressed as a percent of the principal amount borrowed or lent and usually the paid periodically over the life of loan interest can also be on from investment such as saving account bonds and the other financial instrument.
The interest rate of the account can be calculated as follows:
Rate = ln(1,698.49/1,051)/(8×ln(1))
Rate = 0.0680 or 6.80%
This means that the account has an annual interest rate of 6.80%, compounded continuously.
To know more about intrest rate click-
https://brainly.com/question/16134508
#SPJ1
What is the algebraic expression of 2 ( x + 7 ) +10
Answer:
2(x+12)
Step-by-step explanation:
Internet
Find the measurement of the following angels and please show work, Im doing corrections aa due at the end of today I will give crown if you try ur best and giving 15 points please please help
Answer:
x=90° (given)
54°+90°+z=180°
144°+z=180°
z=180°-144°
z=30°
Edudig Digger
£35950
Samir buys this digger and expects to use it for 1250 hours each year.
The digger will decrease in value at a yearly rate of 18% of its value at the end of the previous
year.
Use this information to calculate the decrease in value of Samir's digger when it has been
used for 10000 hours.
Answer: To calculate the decrease in value of Samir's digger after 10000 hours, we need to determine its value at the end of each year, taking into account the yearly depreciation of 18%.
Here's the calculation for the first year:
Value at the end of Year 1 = £35950 - (£35950 * 18%) = £29576
And for the second year:
Value at the end of Year 2 = £29576 - (£29576 * 18%) = £24480.48
And so on, until we reach 10000 hours. To determine the exact value after 10000 hours, we would need to perform the calculation for each year until we reach the total number of hours used. However, this calculation would involve multiple steps and can become quite complex. A simpler way to estimate the decrease in value would be to use the concept of present value.
Business acumen is the ability to make decisions based on principles of business that will most likely
lead to positive outcomes.
Which course of action would be the least effective in helping you to develop business acumen?
A) Find an internship in your field.
B) Ask a professional in your field to mentor you.
C) Interview experienced people in your field.
D) Ask trusted friends their opinions of your field.
Business acumen, often referred to as business savviness, business sense, and business knowledge, is the keenness and rapidity with which one perceives and responds to a business issue in a way that is most likely to produce a favorable result.
What are the 4 disciplines of business acumen?The success of an organization depends heavily on the four pillars of business acumen: planning, operations, finance, and strategy. Business savvy individuals use their abilities and leadership to foster success in each field.Business acumen, often referred to as business savviness, business sense, and business knowledge, is the keenness and rapidity with which one perceives and responds to a business issue in a way that is most likely to produce a favorable result. Understanding business difficulties is a sign of someone with business acumen. It is the accumulation of information on how things are done and why, both generally and within the context of the organization. It is a crucial quality for leadership and manifests in both one's inquiries and their choices.A combination of knowledge, technical skills, and soft skills called "business acumen" is utilized to improve an organization and its workforce.To learn more about Business acumen refer to:
https://brainly.com/question/29517196
#SPJ1
At a local preschool there is a ratio of 3 boys to every 4 girls if there are 245 total preschoolers enrolled then how many boys are there
Answer:
105
Step-by-step explanation:
B:G=3:4
Add 3 and 4 to get 7
then divide 245 by 7 to get 35.
after you will need to times 35 by the ratio of boys which is 3.
35 ×3 =105.
So your answers is 105 boys.
Answer: 105 preschoolers are boys
The first thing we must do is add up our total to get a starting fraction. 3+4 is 7. Which means 3/7 of our students are boy and 4/7 of our students are girls.
Next we must multiply our total students "245" into the number of boys and girls.
3/7 x 245 is 105. 4/7 x 245 is 140.
105+140 is 245, which means our numbers are correct.
And finally that leads us with our answer.
105 of the students are boys.
I hope this helped & Good Luck <3!!
Five rectangular picture frames are shown below.
Which 2 of the picture frames are similar shapes?
Answer:
A and E
Step-by-step explanation:
Ratio of A=20/30=2/3
Ratio of B=28/50=14/25
Ratio of C=35/50=7/10
Ratio of D=14/26=7/13
Ratio of E=32/48=2/3
therefore A and E are similar shapes
HELP ASAP.Next time, the rabbit from the previous problem started at 10 where on the number line can he be after the same three jumps?
This is the previous problem: A rabbit started at point 0 and made 3 jumps a jump of 4 units then a jump of 2 units and then a jump of 1 unit we do not know the direction of either jump where on the line could the rabbit be.
Since the rabbit from the previous problem started at 10, it would be at 17 units on the number line after the same three jumps.
What is a number line?In Mathematics, a number line is a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.
From the previous problem, the total distance covered by the rabbit is given by:
Total distance = 4 units + 2 units + 1 unit
Total distance = 7 units.
Since the second point is at 10 units and the open circle arrow points to the right of the number line, the rabbit would cover 7 more distance from this point:
Total distance = 10 units + 7 units
Total distance = 17 units.
Read more on number line here: brainly.com/question/16482555
#SPJ1
A shop tech earns a base pay of $18.48 per hour, plus "time-and-a-half for overtime (time exceeding 40 hours). If he works 44.5 hours during a particular week, what
is his gross pay?
The gross pay is $
Answer: Gross pay = $733.04
Step-by-step explanation:
Andrew collects stamps. he collected a total of 150 stamps. is 84% of the stamps he collected were foreign, how many other stamps did he collect?
Answer:
24
Step-by-step explanation:
If 84% of the stamps he collected were foreign, that means he collected 150 * 0.84 = 126 foreign stamps.
So, he collected 150 - 126 = 24 stamps that were not foreign.
Subsets
What is the symbol for subset?
Step-by-step explanation:
I honestly don't know how to put it sideways but the symbol for subset is "⊂" with a line right under it. (So like the quotation marks but have the line underneath the sideways U.
"⊂
_"
I need help with this. Please explain
I=PRT
P=5,600
R=0.2
T=4
Step-by-step explanation:
The formula "I=PRT" is the simple interest formula, where:
I = interest
P = principle (the initial amount of money)
R = interest rate (as a decimal)
T = time (in years)
Given the values of P, R, and T:
P = 5,600
R = 0.2
T = 4
We can plug these values into the formula to find the interest:
I = P * R * T = 5,600 * 0.2 * 4 = 4,480
So, the interest earned on a principle of $5,600 at an interest rate of 0.2 (or 20%) for 4 years would be $4,480.
in a sequence diagram, a represents the time during which an object above it is able to interact with the other objects in the use case
In a sequence diagram, the vertical line labeled 'a' represents the amount of time during which an object is active and can interact with the other objects in the use case. This can include sending messages, waiting for a response, or any other type of interaction.
In a sequence diagram, the vertical line labeled 'a' is used to represent the amount of time during which an object is active and capable of interacting with the other objects in the use case. This time frame is usually shown as a timeline to give the viewer an idea of how long the object is active. The time ‘a’ could include any kind of interaction between the objects, such as sending messages, waiting for a response, or any other type of interaction. The ‘a’ time frame also indicates when an object is no longer interacting with the other objects in the use case. This timeline can be used to identify points where a user or system may need to wait for a response or where a user or system is no longer able to interact with the other objects in the use case. In essence, the ‘a’ timeline helps to demonstrate how long the use case is active, how long an object is interacting with other objects in the use case, and when the use case has ended.
Learn more about amount here
https://brainly.com/question/28970975
#SPJ4
Nolan buys a $12,000, 13-week treasury bill at 5%. What’s his effective rate? Round your answer to the nearest hundredth of a percent.
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
what is interest ?Divide the original by the lending rates, the duration of time, and other factors to arrive at simple interest. Simple gain = principal + interested + hours is the marketing formula. This system makes it simpler to calculate interest. The most popular technique to figure out this is as a portion of the principal sum. He can only pay his share of the 100% interest, for example, if he borrow $100 from a friend he agrees to repay him with 5% interest. $100 (0.05) = $5. When you borrow more money, you should pay interest, and when you give it out, you must make payments. Interest is often determined as an indicator of the overall of the loan total. The interest on the loan is this percentage.
given
Simple interest = $12,000 × 0.05 × 13/52 = $150
Simple discount note = ($12,000 - $150) × 13/52 = $2962.5
Effective rate of interest = $150 / $2962.5
Effective rate of interest = 0.0506 or 5.06%
As a result, the actual interest rate is 5.06% since Nolan purchases a $12,000 13-week treasury bill at 5%.
To know more about interest visit:
https://brainly.com/question/28792777
#SPJ1
Which answer is equal to cot(x)?
The cotangent of an angle is obtained dividing the cosine of the angle by the sine of the angle, that is:
cot(x) = cos(x)/sin(x).
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.The cotangent function is the inverse of the tangent function, that is:
cot(x) = 1/tan(x)
cot(x) = 1/(sin(x)/cos(x))
cot(x) = cos(x)/sin(x).
More can be learned about trigonometric ratios at brainly.com/question/24349828
#SPJ1
A sugar solution was made by mixing 11qt. of a 70% sugar solution and 4 qt. of a 85% sugar solution. Find the concentration of the new mixture.
Answer:
Step-by-step explanation:
To find the concentration of the new mixture, we need to find the total amount of sugar in the mixture, and then divide it by the total volume of the mixture.
Let's first find the amount of sugar in each of the two original solutions:
70% solution: 11 qt. * 70% = 7.7 qt. of sugar
85% solution: 4 qt. * 85% = 3.4 qt. of sugar
Now we add the volume of the two original solutions to find the total volume of the new mixture:
Total volume: 11 qt. + 4 qt. = 15 qt.
And add the amount of sugar in the two original solutions to find the total amount of sugar in the new mixture:
Total sugar: 7.7 qt. + 3.4 qt. = 11.1 qt.
Finally, we divide the total amount of sugar by the total volume to find the concentration of the new mixture:
Concentration: 11.1 qt. / 15 qt. = 0.7407 (rounded to four decimal places).
So the new mixture is approximately 74.07% sugar.
arallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed by lines r and s are 1, 2, 3, 4; formed by lines r and t are 5, 6, 7, 8. Which angles are alternate interior angles? Angle3 and Angle5 Angle1 and Angle7 Angle3 and Angle7 Angle4 and Angle5
The angles are alternate interior angles
<4 and <6
<3 and <5.
What are Parallel line?The fundamental characteristics listed below make it simple to recognise parallel lines.
Straight lines that are always the same distance apart from one another are called parallel lines.No matter how far apart they are from one another, parallel lines can never intersect.Given:
As, from the property of parallel line we have the following properties
Alternate Interior angleCorresponding AngleCo- interior angle.So, from the figure the pair angles shows alternate interior angle
<4 and <6
<3 and <5.
Learn more about Parallel line here:https://brainly.com/question/16701300
#SPJ1
If 1 mile equals 1,760 yards, then how many miles are in 11,088 yards? 0.6 miles 1.8 miles 6.3 miles 110 miles
Answer:
6.3 miles
Step-by-step explanation:
We are given 11088 yards.
Use the conversion factor 1 mile equals 1,760 yards.
11088 yards * 1 mile/ 1,760 yards
11088 / 1760 miles
6.3 miles
A chef had to fill up ⅘ of a container with mashed potatoes. He ended up using 2 4/6 pounds of mashed potatoes. How many pounds would he use if he had to fill up the entire container?
question: A chef had to fill up ⅘ of a container with mashed potatoes. He ended up using 2 4/6 pounds of mashed potatoes. How many pounds would he use if he had to fill up the entire container?
Step-by-step explanation: I don't know, u figure it out lol