The required solution of the given algebraic expression is x = 6.
What is an algebraic expression?The algebraic expression consists of constants and variables using mathematical operators. eg x + y + z, or y = x + z etc.
Here,
Given an algebraic expression,
x + 1 +1 +1 +1 +1 +1 +1 = 1 +1 +1 +1 +1 +1 +1 + 1 +1 +1 +1 +1 +1
Combining like terms on each side of the equation, we get,
According to the question
x + 7 = 13
x = 6
Thus, the required solution of the given algebraic expression is x = 6.
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Answer:
x + 7 = 13
Step-by-step explanation:
(in case you also need it) x = 6
ap stats over the long run, what proportion of the days will the train from le havre have to wait at garde du nord for the train from troyes to arrive
The probability of the train from Le Havre having to wait at Garde du Nord for the train from Troyes to arrive on any given day is equal to the probability that the latter train is late.
This probability can be calculated using the following formula: P = (1-A)^B, where A is the average arrival time of the train from Troyes and B is the average time it takes for the train from Le Havre to depart after the first train is scheduled to arrive. The expected value of the probability can then be calculated by taking the average of this formula over the long run. For example, if the train from Troyes is typically 5 minutes late and the train from Le Havre leaves 10 minutes after it is due to arrive, the expected probability of a delay is (1-5/60)^(10/60) = 0.7355. Therefore, over the long run, the train from Le Havre will have to wait for the train from Troyes to arrive 73.55% of the time.
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The sum of 2 numbers is 15. The difference between five times the first number and three times the second number is 19. Find the two numbers.
The numbers are 8 and 7.
Step by step explanation:[tex]\textbf{2 x 2 system of equations : }[/tex]
➭Approach
Let x and y be the numbers.
[tex] \bold{The \: sum \: of \: 2 \: n \acute{u}mers \: \: is \: 15 \: : \: } \: \bold{x + y = 15}[/tex]
[tex]\bold{x+y=15}[/tex] Equation 1[tex] \bold{The \: difference \: between \: five \: times \: the \: first \: number \: and \: three \: times \: the \: second \ : number \: is \: 19 \: : \: } \bold{5x - 3y = 19}[/tex]
[tex]\bold{5x-3y=19}[/tex] Equation 2Solution by substitution method
[tex]\begin{gathered}\begin{gathered}\begin{gathered}\begin{cases}{ \bold{x + y= 15 \qquad \cdots(1)}}\\{ \bold{5x - 3y = 19 \qquad \cdots( 2)}} \end{cases}\end{gathered} \end{gathered} \end{gathered} [/tex]
In essence, this method of solving consists of clearing an unknown in one of the equations and then substituting the found value in the other equation.
Because it is easier, I will start solving for x in equation 1.
[tex] \bold{x = 15 - y}[/tex]
Substitute [tex]\bold{x=15-y}[/tex] into equation 2.
[tex] \bold{5 \cdot15 - y- 3y = 19}[/tex]
We are left with an equation with only one unknown, we solve to find y.
[tex] \bold{75 - 5y- 3y = 19}[/tex]
[tex] \bold{ - 5y - 3y = 19 - 75} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{-8y= -56} [/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{y= \dfrac{ - 56}{ - 8}}[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ \implies{y = 7}} \: \: \: \: \: \: \: [/tex]
We have found the value of y, to find the value of x we substitute the value of y into either of the two equations.
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + y = 15} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x + 7 = 15 }\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{x = 15 - 7}[/tex]
[tex]\bold{\implies \: x = 8}[/tex]
『 The attached graph is just to check our results 』
[tex]\therefore[/tex] The numbers are 8 and 7.
Use the table below to answer the question. True or false:
y
y is a function of
x
The given statement is False.
What is Function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function is defined as a set of ordered pairs in which for each value of x there is only one corresponding value of y.
However, in this case, we have multiple x-values that correspond to the same y-value.
For example, x = 12 and x = 22 both correspond to y = 12. and y=22 Therefore, y is not a function of x.
Therefore, The given statement is False.
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There are 2478 students in the lakeside school district who take the bus to school. Each bus holds 32 student. How many buses are needed for all the students?
50 POINTS !!! Which are like terms in this expression?
−13n − 13 + 3/4n −1 3/4
A. − 13n and −13
B. − 13n and + 3/4n
C. − 13 and 3/4n
D. + 3/4n and − 1 3/4
Answer:B
Step-by-step explanation: They both have a variable.
Reason: Both involve the variable n.
Something like choice A is eliminated since -13n has n, but -13 does not. Choices C and D are eliminated for similar reasoning.
(10^4)^2 in index form
Answer:(10^4) ^2=10^4•2=10^8=100000000
gathered a random sample of bags of potato chips from a popular company. she calculated data on different variables. for one of the variables that she collected, she constructed a
The correct option is (4) Flavor of potato chips. she uses Histogram to show the data collected from the sample of bags of Potato chips.
A histogram is a graphical representation of the distribution of a dataset, it shows how the data is spread out across different ranges of values. It is used to show the frequency of observations within each range of values, also known as a bin.
The bin is a range of values, and the height of each bar represents the number of observations within that range of values. The x-axis represents the range of values and the y-axis represents the frequency of observations.
When you construct a histogram, you will first need to decide on the number of bins to use and the range of values that each bin will cover. This is known as binning. It is important to choose the appropriate number of bins and range of values to effectively display the distribution of the data.
Question:
Anya gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one data that she collected, she constructed a circle graph. Which of the following variables did she use?
Price of bag of potato chipsNumber of chips in the bag of potato chipsWeight of bag of potato chipsFlavor of potato chipsTo know more about Histogram:
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A car Costs $30,000 in 2015. What would its price have been in 2020 dollars?
Show all work
The price of the car in 2020 dollars would be $31,620.
What is price?Price is the monetary value of a good or service that a customer is willing to pay for it. It is the result of a complex interaction between the forces of supply and demand, and is determined by the market conditions of a good or service. Price is also an important factor for companies as it is one of the primary elements used to generate revenue and profits.
In order to calculate the price of the car in 2020 dollars, we must use the Consumer Price Index (CPI). The CPI is a measure of inflation over time and is used to calculate the value of a product in the current year from its value in the past.
The CPI for 2020 is 250.6, while the CPI for 2015 is 237.9. This gives us a ratio of 250.6/237.9 = 1.054.
We can then use this ratio to calculate the value of the car in 2020 dollars:
30,000 x 1.054 = 31,620.
Therefore, the car would cost $31,620 in 2020 dollars.
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I need help could someone figure out the two blank spots for me
The two numbers that correctly complete the chart based on the proportions are
How to calculate the new amounts of ingredients needed?This can be calculated by using the original recipe:
Batch 1:
This batch requires 1 blue paint rather than 1/2 or half, which shows you need to multiply by 2 the ingredients, based on this the correct number for the yellow paint is 1/2 as 1/4 x 2 = 1/2.
Batch 2:
This batch requires two yellow gallons rather than 1/4, which shows you should multiply the ingredients by 8. Based on this, the number for batch 2 is 4 as 0.5 or 1/2 x 8 = 4
Note: Below you can find the complete chart
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The table shows the number of students graduating from an online university in selected year . Use a calculator to write a cubic model for the number of graduates in a given year since 2002. Then use the model to estimate the number of graduates in 2008.
There were approximately 5,184 graduates in 2008.
The cubic model is a useful tool for estimating the number of graduates in a given year, as it takes into account the trend of the data points. This allows us to make an educated guess about the number of graduates in a given year, despite not having data points for that year.The cubic model for the number of graduates from an online university since 2002 can be expressed as y = -7.8x^3 + 74.4x^2 + 437x - 9,150. Here, x is the number of years since 2002, and y is the number of graduates in that year. To estimate the number of graduates in 2008, we can plug in x = 6 into the equation, giving us y = 5,184. That is, there were approximately 5,184 graduates in 2008.
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Find the least common denominator of 1/2x-6 and 2x/7x-21.
Answer:
14( x - 3)
Step-by-step explanation:
1/2x-6 and 2x/7x-21.
simplify (common factors)
[tex] \frac{1}{2(x - 3)},\frac{2x}{7(x - 3)} [/tex]
Find the LCM (smallest positive number that all of the numbers divide into evenly) of the denominators of those values
[tex]2(x−3),7(x−3) [/tex]
Now we get
[tex]14( x - 3)[/tex]
- if you need any further explanation let me know <3
Find the volume of the rectangular prism.
Answer: V=LWH
Step-by-step explanation:
A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is:
A. $10,250
B. $10,000
C. $9,000
D. $9,750.
A 90-day, 10% note for $10,000 dated March 15 is received from a customer on account. The face value of the note is $10,250
What is meant by face value?A digit's face value is its actual value as part of a number. We multiply the digit value by the numerical value of a number to obtain its place value. For instance, since 5 is in the tens place and is present in the number 452, its place value is (5 10) = 50. A digit's face value is the actual number.The par value is the notional value of a share, bond, or other comparable security on the date of issuance. The terms "par value" and "face value" are frequently used interchangeably. A bond's face value, or the amount of principal the issuer is required to repay at the conclusion of the bond's term, is its par value.
Face value = $10,000×10/100×3/12 =$10,250
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what is the z* critical value for constructing a 94% confidence interval for one proportion? this value is not listed on the t distribution table, so you will need to use this z-table to determine the value. round to 2 decimal places.
z-score for 94% confidence interval = 1.88
Confidence Interval:
The confidence interval indicates the level of confidence that the true parameter lies in the proposed range.
(a) What z-score is used for a 99% confidence interval to estimate a population proportion? Use 3 decimal places in your answer.
z-score for 99% confidence interval = 2.575
(b) What z-score is used for a 94% confidence interval? Round your answer to 2 decimal places.
z-score for 94% confidence interval = 1.88
(c) What z-score is used for a 93% confidence interval? Round your answer to 2 decimal places.
z-score for 93% confidence interval = 1.81
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Answer: 1.88
Step-by-step explanation:
e dg e 23
a farmer has 1200 ft of fencing for enclosing a trapezoidal field along a river as shown. one of the parallel sides is three times longer than the other. no fencing is needed along the river. find the largest area the farmer can enclose.
The largest area that can be enclosed is 720000 m²
area = lw
where
l = length
w = width
The farmer wants to enclose a rectangular plot that borders a river. He is not fencing the side along the river. Therefore,
perimeter = l + 2w
l = 1200 - 2w
Therefore,
area = (1200 - 2w)w
(1200 - 2w)w = 0
w = 0 or 1200
average = 1200 / 2 = 600 meters
Hence, the max area is at w = 600 meters
Therefore,
l = 1200 - 2(600) = 0
length = 1200 meters
width = 600 meter
Therefore,
area = 1200 × 600 = 720000 m²
Therefore, the largest area that can be enclosed is 720000 m²
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Pls help me explain this question
Step-by-step explanation:
this means that these 4 data ranges define 4 graphing charts with the given limits per coordinate axis.
the question is, which charts are large enough to show all data points of the defined process (50 ft uncoiled rope at time 0 is then coiled up 10 ft/sec., with the function graph showing the amount of still uncoiled rope over time in minutes).
the process will take 5 minutes (50 ft with 10 ft/min, so it will be completely coiled after 5 minutes) starting at 0 minutes.
the amount of uncoiled rope will go from 50 ft down to 0 ft.
so,
0 <= x <= 5 and 0 <= y <= 75 yes
0 to 5 minutes 0 to 50 ft all covered
0 <= x <= 10 and 0 <= y <= 50 yes
0 to 5 minutes 0 to 50 ft all covered
0 <= x <= 50 and 0 <= y <= 10 no
0 to 5 minutes covered 0 to 50 ft not covered
0 <= x <= 75 and 0 <= y <= 5 no
0 to 5 minutes covered 0 to 50 ft not covered
*THE ANSWER IS B* Which of these correctly rearranges the terms in this polynomial so like terms are next to each other? 4-6x+2-2x² - 4x+6x² OA. 6x²-2x²+6x-4x-4+2 B. -2x²+6x² - 6x-4x+4+2 OC. 6x² - 6x-2x² - 4x+4+2 O D. 6x² - 6x-4x+4-2x²+2
[tex]4-6x+2-2x^{2} -4x+6x^{2}[/tex]
Which of these correctly rearranges the terms in this polynomial so like terms are next to each other?
The first step is to identify the same variable.
The equation consists of variables [tex]x, x^{2}[/tex] and constant.
Terms of variable [tex]x^{2}[/tex] are [tex]-2x^{2}[/tex] and [tex]6x^{2}[/tex]
Terms of variable [tex]x[/tex] are [tex]-6x[/tex] and [tex]-4x[/tex]
Terms of constant are [tex]4[/tex] and [tex]2[/tex]
The next step is rearranges the terms in this polynomial so like terms are next to each other
[tex]-2x^{2} +6x^{2} -6x-4x+4+2[/tex] (B)
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35. How much did you spend? A retailer samples 25 receipts from the past week by numbering all the receipts, generating 25 random numbers, and sampling the receipts that correspond to these numbers.
It's not possible to know how much the retailer spent based on the information provided. The information provided only tells us how the retailer selected a sample of receipts from the past week by numbering all the receipts, generating 25 random numbers, and sampling the receipts that correspond to those numbers. In order to know how much the retailer spent, you would need more information such as the total amount of money spent on all the receipts and the amount of money spent on each receipt.
complete three repetitions of your simulation using the random digits below and use the results to estimate the probability described in part (c).
This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.
Random Digits Used: 0.9, 0.3, 0.3
Repetition 1:
Successful Attempt (1)
Repetition 2:
Successful Attempt (1)
Repetition 3:
Successful Attempt (1)
Estimated Probability: 3/3 = 1.0
In this experiment, the probability of successfully solving a puzzle was estimated. Three repetitions of the simulation were completed, each using different random digits. The first repetition used the random digit 0.9, the second used 0.3, and the third used 0.3 again. For each repetition, the outcome was successful, meaning the puzzle was solved. This resulted in a probability of 1.0, or 100%, meaning that the puzzle was solved every time it was attempted. This indicates that the probability of successfully solving the puzzle is quite high.
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Please help me asap, it's missing :/
Answer: -31
Step-by-step explanation:
f(x)=x²+x-12
f(-5)=(-5)²+(-5)-12
=25-5-12
=25-17
=8
now, g(x)= -2x-15
=(-2)×(8)-15
= -16-15
= -31
A recent survey indicated that the mean time spent on a music streaming service is 210 minutes per week for the population of a certain country. A simulation was conducted to create a sampling distribution of the sample mean for a population with a mean of 210. The following histogram shows the results of the simulation.Which of the following would be the best reason why the simulation of the sampling distribution is not approximately normal?
answer choices
The samples were not selected at random.
The sample size was not sufficiently large.
The population distribution was approximately normal.
The samples were selected without replacement.
The sample means were less than the population mean.
The sample size was not sufficiently large is the best reason why the simulation of the sampling distribution is not approximately normal.
What happens if a sample data is not big enough?
There are different variations in population size. When a sample size taken by a person or a researcher is not big or insufficient, or inadequate for the alpha level and also analyses that one have chosen to do, it will limit the study statistical power.
Due to the above, the ability to know a statistical effect in one's sample if the effect are present in the population is greatly reduces.
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Given the vectors A =2.00 i^ +6.00 j^ and B =3.00 i^ −2.00 j^
. (a) Draw the vector sum C = A+ B and vector difference D = A − B . (b) Calculate C and D in terms of unit vector. (c) Calculate C and D in terms of polar coordinates with angles measured with respect to the positive x axis.
The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
(a) The vector sum C = A+ B is shown in the figure below, and the vector difference D = A − B is shown below that.
(b) C = (5i^ + 4j^) and D = (-1i^ + 8j^).
(c) The polar coordinates of C = (5, 53.13°) and D = (-1, 126.87°). To calculate these, I used the formulas for converting from Cartesian to polar coordinates, where r is the magnitude of the vector and θ is the angle with respect to the x-axis. The magnitude of C is √(5^2 + 4^2) = √41 = 6.4, and the angle is arctan(4/5) = 53.13°. The magnitude of D is √(-1^2 + 8^2) = √65 = 8.06, and the angle is arctan(8/-1) = 126.87°.
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mpany famous for its nacho-flavored corn chips has developed two new formulas, a and b, which they hope their customers will like even more than the original formula. to determine whether customers prefer one of the new formulas over the current nacho flavoring, a sample of 50 customers is obtained. each customer tastes both formula a and formula b in a randomly assigned order and indicates which one they prefer more. which of the following best describes this study? responses this study is not well designed because there is no replication. each customer tasted the formulas only once.
Formulas A and B are not compared to the original formula, which makes this study poorly structured.
What is Replication?Replication is the act of performing an experiment or observation again under the same or comparable circumstances. The value of replication is in the additional information it provides regarding the validity of the inferences or projections that can be made from the data. Reproducibility is a required, but insufficient, criterion for assessing whether a novel research discovery is prepared to be submitted for publication. However, the minimum standard by which any scholarly publication should be assessed is replicability. In order to detect experiment variance and use statistical tests to assess differences, replicates might be used. Gene expression measurements are more accurate and can detect minor changes when averaged across replicates.To learn more about Replication, refer to:
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24[1/2]+2[7] divided by 1/4[8]
The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be 16 3 / 7.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
The value of the fraction 24(1/2 + 2/7) divided by 1 4/8 will be:
= 24(1/2 + 2/7) ÷ 1 4/8:
= 24 9/14 ÷ 1 1/2
= 345 / 14 × 2/3
= 690 / 42
= 16 3 / 7
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Complete question
24(1/2 + 2/7) divided by 1 4/8 will be:
a bats heart rate is about 10 beats per minute its normal heart rate is about 300 percent whats a bat normal heart rate answer about 300
Normal heartbeat of bat = 30 beats per minute
What is percentage ?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given,
Bat's heart rate is about 10 beats per minute.
Normal heart rate is 300 percent of 10 beats per minute
Then normal heartbeat = (300 × 10) / 100
= 3 × 10
= 30 beats per minute.
Hence, 30 beats per minute is normal heartbeat of bat.
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The expression represents the amount of change you receive after buying »sandwiches. Match each part of the expression to what it represents 10 − 5.25m.
All parts of the expression 10 − 5.25m have been matched with their respective quantities below.
The given expression belongs to a certain mathematical category which is linear equations. A linear equation is an equation that can be used to denote and solve problem sums. It is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is the form Ax + B = 0. Here, x is a variable quantity, A is a coefficient and B is constant.
Here, 10 = the amount of money that you have
5.25 = Price of each sandwich
n = No. of sandwiches
5.25 = Total cost
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what is ,3.7-3.4-2n+8=?
3.7-3.4-2n+8 = -0.3-2n+8 = 8-2n-0.3 = 8-0.3-2n = 7.7-2n
So, 3.7-3.4-2n+8 = 7.7-2n
Which of the following is a correct interpretation of the expression
−
4
−
(
−
7
)
−4−(−7)minus, 4, minus, left parenthesis, minus, 7, right parenthesis?
A correct interpretation of the expression -4 - (-7) include the following: D. the number that is 7 to the right of -4 on the number line.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
In this context, the expression -4 - (-7) equals to 3 and it simply means that you would start at -4 on the number line and move 7 places to the right;
x = -4 - (-7)
x = -4 + 7
x = 3.
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determine the coordinates of the intersection of the diagonals of abcd with vertices a(-4, 6), b(5, 6), c(4, -2), and d(-5, -2).
The coordinates of the intersection of the diagonals of abcd with the given vertices are (0,2).
The equation of diagonal AC is the equation of the line joining
(−4,6) and (4,−2)
Using the two point formula of a line, we have
(y−6) / (x+4) = 6−(−2) / (−4−4)
x + y = 2
The equation of diagonal BD is the equation of the line joining
(5,6) and (−5,−2)
Using the two point formula of a line, we have
(y−6) / (x−5) = 6−(−2) / 5−(−5)
5y = 4x+10
Multiply equation x + y = 10 by 5 to get 5x+5y=10
Replace 5y=4x+46 using 5x+5y=10
5x + (4x+10) = 10
5x + 4x +1 0 = 10
9x + 10 = 10
9x=0
x=0
Substitute x=0 in eqn(1), To get 0+y=2
y=2
The point of intersection of the diagonals of the given quadrilateral is (0,2)
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a swimming pool has a volume of 53.7 kL. Find how many cubic decimeters of water it would take to completely fill the swimming pool.
The swimming pool with a volume of 53.7 kL, will be completely filled with 53,700 cubic decimeter
How to find the volume to completely fill the swimming poolThe problem seeks conversion from liters to cubic decimeters
From the conversion table 1 liter is equivalent to 1 cubic decimeter
Because of this, 1 kL will be equal to 1 000 cubic decimeter
Hence if 1 kL is 1 000 cubic decimeter then 53.7 kL is equal to
= 53.7 * 1000
= 53,700 cubic decimeter
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