The number of the tickets purchased for upper reserve is 146 and lower is 470.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that there were 616 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $6543.50.
The equations will be formed as,
L + U = 616
12.5L + 8U = 6543.5
Solve the above equations,
12.50L + 8 (616-L) = 6543.5
12.5L + 4928 - 8L = 6543.5
12.50L - 8L = 6543.5 - 4428
4.50L = 2118.5
L = 470
U = 616 - 470
U = 146
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Find the equation perpendicular to y=-2x+10 through (10,7)
Answer:
y = [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 2x + 10 ← is in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute (10, 7 ) into the partial equation
7 = 5 + c ⇒ c = 7 - 5 = 2
y = [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line
To start dividing 126 by 23, Miranda used the estimate 120÷20 = 6. How could you tell six is too high?
Answer:
the product of 6 and 23 is more than 126
Step-by-step explanation:
You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.
Trial dividendWhen the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.
__
Additional comment
Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.
draw a continuous region in a given region that is not a type 1 or type 2 region but can be split into one of eachDraw an example of a region that is(a) type I but not type II(b) type II but not type I
Type I regions- ∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx
Type II regions- ∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy
What is the type I and type II regions?Curves of type I can be described for yy in terms of xx and often "lay above and below" one another.
Type II curves, on the other hand, can be defined for xx in terms of yy and are more or less "left and right" of one another.
Type II regions can be divided into horizontal slices, but Type I regions can be divided into vertical slices.
When a location is simultaneously classified as Type I and Type II, you can choose to examine it in any manner.
Type I regions are regions that are bounded by vertical lines x=a and x=b, and curves y=g(x) and y=h(x), where we assume that g(x)<h(x) and a<b. Then we can integrate first over y and then over x:
∫∫R f(x,y)dA = ∫b x=a ∫h(x) y=g(x) f(x,y) dy dx
Type II regions are bounded by horizontal lines y=c and y=d, and curves x=g(y) and x=h(y), where we assume that g(y)<h(y) and c<d. Then we can integrate first over x and then over y:
∫∫R f(x,y)dA = ∫d y=c ∫h(y) x=g(y) f(x,y) dx dy
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Given
G(t) = 9 − 5t,
write
G(−5 + h) − G(−5)
in simplest form.
The value of the function G(-5 + h) - G(-5) in the simplest form -5h.
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
The given function is,
G(t) = 9 - 5t (1)
To find the value of expression G(-5 + h) - G(-5),
First, find the value of G(-5 +h) by substituting t = -5+h in equation (1),
G(-5 + h) = 9 - 5(-5 + h)
= 9 +25 -5h
= 34 - 5h
The value of G(-5)
G(-5) = 9 - 5(-5)
= 9 + 25
= 34
The required value,
G(-5 + h) - G(-5) = 34 - 5h - 34 = -5h.
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You give a test to 100 students and determine the median of the scores. After grading the test you realize that the 10 students with the highest scores did exceptionally well. You decide to award these 10 students a bonus of 5 more points each. The median of the new score distribution will be (less than, greater than or the same as) that of the original score distribution?
Answer:
R'>R
Step-by-step explanation:
To determine the range of the scores, we conduct a test of 100 students. After grading the test, we realized that the 10 students with the highest scores did exceptionally well. We decide to award these 10 students a bonus of 5 more points each. The range of the new score distribution will be greater than that of the original score distribution.
We know the range is defined by R
R = X(n) - X(1), where X(n) is the maximum value of the observed values, and X(1) is the minimum value of those observed values.
Here for this test study, we awarded 10 highest scorers extra 5 points each. Therefore our maximum observed value becomes X(n) + 5. So, our range also becomes
R = X(n) + 5 - X(1)
So, R'>R. Hence, the range of the new score will be greater than that of the original score distribution.
Which of the following choices can be considered binomial random variables? Choose all answers that apply: A Roll a fair die 5 times and let X = the number of rolls that land showing a "4". B Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6). Roll 5 fair dice at once and let Y = the number of dice that land showing a "4"
The following are binomial random variable,
A)A Roll a fair die 5 times and X = the number of rolls that land showing a "4", is a binomial random variable.
B) Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6), is a binomial random variable.
C) Roll 5 fair dice at once and let Y = the number of dice that land showing a "4" , is a binomial random variable.
A random binomial variable should satisfy the following conditions:
1. The number of trials are defined or fixed.
2. Each trial is independent of others.
3. The probability of success is same in all trials.
4. There should be only two outcomes in each trial.
Lets we evaluate the options based on the above conditions:
(A) Rolling fair dice 5 times have 5 trials, each rolling is independent, probability of 4 is 1/6 in all cases and the dice will either land 4 or will not land 4. So, X will have values from 0 to 5, 0 when dice doesn't land 4 even once in 5 rolls and 5 when dice land 4 in all rolls. This variable satisfies the condition to be a random binomial variable. So, X is a random binomial variable.
(B)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice with even number to all 5 dices with even number. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Z is a random binomial variable as it satisfies all the conditions.
(C)For rolling 5 dices at once, the number of trials is 1 and fixed and the outcomes are 0 dice land with 4 to all 5 dices land with 4. If the dices are rolled multiple times each trial will be independent of each other and the probability of success will be same for each trial. So the variable Y is a random binomial variable as it satisfies all the conditions.
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Construct a confidence interval for p₁ -P2 at the given level of confidence.
x₁ = 355, n₁ = 536, x₂ =438, n₂ = 598, 99% confidence
The researchers are confident the difference between the two population proportions, p₁ - P₂, is between
(Use ascending order. Type an integer or decimal rounded to three decimal places as needed.)
Using confidence interval concepts, it is found that the correct options are:A. With 99% confidence, the mean width of all widgets is between 14.3 and 30.4.
Find the solution ?There is a 99% chance that the mean of the population is between 14.3 and 30.4.
The interpretation of a x% confidence interval is that we are x% sure that the population mean is in the interval.
In this problem, 99% confidence interval for widget width is between 14.3 and 30.4, hence we are 99% sure that the population mean, that is, the mean width of all widgets is between 14.3 and 30.4, hence options A and C are correct.
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Solve the equation b/16 = -4 for b
-64
-4
4
64
Answer: -64
Step-by-step explanation:
To solve this equation, you need to isolate the b term on one side of the equation. You can do this by dividing both sides of the equation by 16. This will give you:
b/16 = (-4)
You can then divide both sides of the equation by -4 to get:
b/16 = -4
b/16 * -4 = -4 * -4
b = -64
Therefore, the solution to the equation is b = -64.
Reese is taller than Gage. If r represents Reeses's height and g represents Gage's height, write an inequality that shows the relationship between thier heights
The inequality that shows the relationship between thier heights is g < r or r > g
How to determine the inequality that shows the relationship between thier heightsFrom the question, we have the following parameters that can be used in our computation:
Reese is taller than Gage.
Also, from the question; we have
Reeses's height = r
Gage's height = g
Because Reese is taller than Gage, then it means that
The value of r is greater than the value of g
So, we have the following inequality expression
r > g
Also, we have
g < r
Hence, the inequality is g < r
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Let T(n) denote the nth term of a sequence t. if T(1) = 3, and T(n+1) = T(n) +5 for n>1, what are the first four terms of the sequence
Based on the given analysis where T(1) = 3, and T(n+1) = T(n) +5 for n>1, the first four terms of the sequence are 3, 7, 8, 9
What is the first four terms of the sequence?First term, T(1) = 3
nth term, T(n+1) = T(n) +5 for n>1
Second term, T2 = T(n) +5
= 2 + 5
= 7
Third term, T3 = T(n) +5
= 3 + 5
= 8
Fourth term, T3 = T(n) +5
= 4 + 5
= 9
Therefore, the first four terms of the sequence are 3, 7, 8, 9
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A spinner is divided into four sections, each in a different color, as shown below. A spinner is divided into 4 unequal parts. Each part is labeled with a color. From largest to smallest: Blue takes up almost half of the spinner. Red takes up a little more than a quarter of the spinner. Green takes up a little less than a quarter of the spinner. Yellow takes up about half of a quarter of the spinner. After the spinner is spun, the arrow points to one of the colors. Which statement about possible outcomes is true?
The true statement regarding the probabilities on the spinner is given as follows:
The probability that the spinner will point to yellow is less than 1/4.
What is a probability?The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.
Hence, for the spinner given in this problem, the probabilities are given by the fraction occupied by each area, as shown by the image given at the end of the answer.
From the text, these fractions, representing the probabilities, are given as follows:
Blue: around 1/2.Red: around 1/4.Green: around 1/4.Yellow: around 1/8.Missing InformationThe problem is given by the image shown at the end of the answer.
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How much would you need to deposit in an account now in order to have $5,000.00 in the account in 1633 days?
Assume the account earns 42% simple interest.
You would need to deposit ___
in your account now.
You would need to deposit $2,500 in order to have $5,000.00 in the account in 1633 days.
1st method: This can be found by using the simple interest formula I=PRT. In this case, I=5000, P=2500, R=.42, and T=1633. Solving for I gives you the answer.
2nd Method: If you deposit $2,500 in an account now, you will have $5,000 in the account in 1633 days. $2,500 * 1.42 = $3,550 $3,550 + $2,500 = $6,050 $6,050 / 2 = $3,025
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Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels, how much butter does she need? Round your answer to the nearest hundredth.
The required butter she needed is given as 1.67 cups of butter.
As given in the question, Jennie is making popcorn. The recipe calls for 1/2 cup of butter, 3 tablespoons of kernels, and 1 teaspoon of salt. If she uses 10 tablespoons of kernels,
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
here,
Let the nutter need be x cups,
now,
Taking the ratio o butter to kernels
[1 / 2] / 3 = x / 10
x = 10 / 6
x = 1.67
Thus, As of the given proportion, she requires 1.67 cups of butter.
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A new gaming chair costs $309.99. You have already saved $144.99 and earn $27.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
27.5w − 144.99 = 309.99; w = 17
27.5 + 144.99w = 309.99; w = 6
27.5w − 309.99 = 144.99; w = 17
27.5w + 144.99 = 309.99; w = 6
The linear equation we need to solve is:
$27.50*w = $309.99 - $144.99
And the solution is w = 6.
How to write and solve the equation?
We know that the cost of the gaming chair is $309.99.
To buy this, you already have saved $144.99, and save another $27.50 per week, then the amount you have after w weeks is:
f(w) = $144.99 + $27.50*w
So the linear equation we need to solve is:
$144.99 + $27.50*w = $309.99
To solve this we need to isolate w.
$144.99 + $27.50*w = $309.99
$27.50*w = $309.99 - $144.99
w = ($309.99 - $144.99)/$27.50 = 6
So they can buy the chair after 6 weeks.
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Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly, and requiring monthly payments. At this time, interest rates on 15-year loans have dropped to 2.1% APR, compounded monthly, and you wish to refinance what you still owe with a new loan at this new rate. (a) How much (in dollars) will you be refinancing? Round your answer to the nearest dollar. (b) How much (in dollars) will your new monthly payment be after refinancing? Round your answer to the nearest cent.
Five years ago, you acquired a 30-year loan of $130,750, charging 6.6% annual interest, compounded monthly,
a) You will be refinancing $122536.
b) New monthly payment be after refinancing is
$794.1858 or 79 418.58 cents.
We have given that
Initial loan amount = $ 130,750
Number of year of loan = 30 year
Nomber of month of loan "n" = 30x12= 360
Annual interest rate = 6.6%
monthly rate "r" = 6.6% /12 =
monthly payment on the loan is
PMT= loan× r / [1 - (1+r)⁻ⁿ]
= $ 130750 X 12/(1 - (1+ 6.6%/12)⁻³⁶⁰)
= $719,125/(1- (1+0.0055) ⁻³⁶⁰
= $835.046
Monthly payment, $835.046 on initial loan.
Now after 5 years refinishing is done . So, amount and remaining balance is for 30-5 = 25 years and 25×12 = 300 months . The present value of unpaid monthly payment is
= PMT× ( (1 - (1+r)⁻ⁿ)/r)
= $835.046( 1 - (1+6.6%/12)⁻³⁰⁰/ 6.6%/12]
= $835.046× 196.74179
= $122536
Hence, amount refinanced is $122536.
b) New monthly payment will be on loan =$122536
Annual rate = 2.1%
monthly rate, r' = 2.1%/12
Number of years for refinancing = 15 years
Number of months , n' = 15× 12 = 180
Using the formula new monthly payment is
PMT = new loan× r'/ [1 - (1+r')⁻ⁿ´ ]
= $122536× 2.1%/12[ 1 - (1+2.1%/12)⁻¹⁸⁰]
= $214.43826/0.2700104
= $794.1858
Hence, new monthly payment is $794.1858.
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Zendaya's math teacher finds that there's roughly a linear relationship between the amount of time students spend on their homework and their weekly quiz scores. This relationship can be represented by the equation y=7.6x+60y=7.6x+60, where yy represents the expected quiz score and xx represents hours spent on homework that week. What is the meaning of the xx-value when y=100y=100?
For the quiz score of 100, the time will be equal to 5.26 hours.
What is an expression?Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols. They can also denote the operation order and other properties of the logical syntax.
The numerical variables and operations denoted by the addition, subtraction, multiplication, and division signs are combined in the mathematical expression.
Given that the relationship can be represented by the equation y=7.6x+60. Here x is the time and y is the score of the quiz.
At the score of the quiz of 100, the value of x will be calculated as,
y = 7.6x+60
100 = 7.6x + 60
40 = 7.6x
x = 40 / 7.6
x = 5.26 hours
The meaning of the value of x = 5.26 hours is that for scoring 100 on the quiz the time will be 5.26 hours.
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Help ASAP FIRST ONE TO GIVE CORRECT ANSWER GET BRAINLYEST ANSWER Artists use different techniques to make their prints unique.
Which print displays the artist's use of the woodcut technique?
Answer:Printmaking is the process of creating artworks by the process of printing. It can be done on paper, brick, wood, and even metal.A lithographic is a planetographic process where the design is drawn into a flat stone and is prepared by use of metal. As per the paintings shows the artwork shows us the rhinosaruers. The painting is made from water and oil.Hence the painting B shows us the use of lithography.
Here are the dimensions of two designs for a sandbox for the primary playground. Each sandbox is a rectangular prism. One design is 3 m by 3 m by 30 cm.
A second design is 3.25 m by 3.25 m by 25 cm.
a) Sketcheachsandbox.Includeitsdimensions.
b) Compare the designs. For each design, calculate the area
of material needed to build it and the volume of sand
it will hold.
c) Whichsandboxshouldbebuilt?Justifyyouranswer.
The volume of the first and second designs are 2.7 m³ and 2.64 m³ so, the second design will hold more sand.
What is volume?
The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
One design is 3 m by 3 m by 30 cm,
A second design is 3.25 m by 3.25 m by 25 cm,
Calculate the volume for the first design as shown below,
Volume of first design = 3 × 3 × 30/ 100 (1 m = 100 cm),
The volume of the first design = 270 / 100
The volume of the first design = 2.7 m³
Calculate the volume of the second design as shown below,
The volume of the second design = 3.25 × 3.25 × 25 / 100
The volume of the second design = 264.06 / 100
The volume of the second design = 2.64 m³
The difference in the volume of both designs = The volume of the first design - The volume of the second design
The difference in the volume of both designs = 2.7 - 2.64
The difference in the volume of both designs =0.06 m³
Thus, the first design will hold more volume of sand.
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The graph of the linear function passes through points (2, 44) and (5, 80). What is the equation of the function? PLEASE HELP!! I WILL MARK BRAINLIEST!!!
Answer:
y=12x+20
Step-by-step explanation:
Your question and a graph of picture are different. So I just considered your question.
m= (80-44)/(5-2) = 36/3=12
(y- y_1)=m(x-x_1)
(y-44)= 12(x-2)
y-44=12x-24
y= 12x-24+44
y=12x+20
a snail travels 5 meters in 20 minutes. He travels the same amount of time per meter. How long will it take him to travel 11 meters?
Answer:
Step-by-step explanation:rate = minute/meter => 20/5
so, 5/1 for rate
so for 11 meter, (5m/1min)(11)
The answer is 55 minutes
on monday therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Therease should take her 7th dose on Friday at 9:00AM
What is time ?
Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.
The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.
If Theresa took her first dose at 9:00 AM on Monday,
Simply add 12 hours every time up to the 7th dose,
First dose ----> 9:00 AM on Monday,
Second dose ----> 9:00 PM on Monday,
Third dose ----> 9:00 AM on Tuesday,
Fourth dose ----> 9:00 PM on Tuesday,
Fifth dose ----> 9:00 AM on Thursday,
Sixth dose ----> 9:00 PM on Thursday,
Seventh dose ----> 9:00 AM on Friday,
Hence, Theresa should take her 7th dose at 9:00 AM on Friday.
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Can you please help me
Answer:
the first option
Step-by-step explanation:
in an "and" statement both parts need to be true, so that the overall condition is true.
is x = 6 a valid solution ?
no, it violates both, x <= -8 and x <= 4
is a value between -8 and 4 a valid solution like x = -2 ?
no, it violates x <= -8, even though it is true for x <= 4.
only values that are smaller or equal to -8 (like -9) are true for both.
and therefore the first answer option is correct.
100 points for this one
Answer:
C) x < - 11 or x > 8---------------------------------------
First, solve the inequality:
|2x + 3| > 192x + 3 > 19 or 2x + 3 < - 192x > 16 or 2x < - 22x > 8 or x < - 11This is option C (you have chosen it correctly).
Now, graph it:
Mark points - 11 and 8 on the number line with open circle, then shade to the left from point - 11 and to the right from point 8.Answer:
x < -11 or x > 8
Step-by-step explanation:
Given absolute value inequality:
[tex]|2x+3| > 19[/tex]
[tex]\boxed{\begin{minipage}{7.1 cm}\underline{Absolute rule}\\\\If\;\;$|u| > a,\;a > 0$\;\;then\;\;$u < -a$\;\;or\;\;$u > a$\\ \end{minipage}}[/tex]
Apply the absolute rule:
[tex]\underline{\sf Case\;1}\\\begin{aligned}2x+3& < -19\\2x& < -22\\x& < -11\end{aligned}[/tex] [tex]\underline{\sf Case\;2}\\\begin{aligned}2x+3& > 19\\2x& > 16\\x& > 8\end{aligned}[/tex]
To graph the solution:
Place open circles at -11 and 8.Shade to the left of the open circle at -11.Shade to the right of the open circle at 8.(20points) Let A be a symmetric positive define matrix with Cholesky decomposition A = LLT = RTR. Prove that the lower triangular matrix L(or that the upper triangular matrix R) in the factorization is unique.
In the factorization, the bottom triangular matrix L is the only one.
What is Cholesky decomposition?The exponent of a number indicates how many times it has been multiplied by itself.
Exponent-related issues can be solved using either exponent laws or exponent characteristics. When a number is repeated numerous times by itself, writing the product without the use of exponents becomes very difficult. Major exponentiation rules are also thought of as having these characteristics.
Given that A is a positively defined symmetric matrix with a Cholesky decomposition,
A = L[tex]L^{T}[/tex] = [tex]R^{T} R[/tex]
Let A be our positive define symmetric matrix,
suppose A has Cholesky decomposition,
A = L₁L₂ = L₁L₂ , for L₁, L₂ lower triangular matrix with positive diagonal entries,
thus (A x ,x) = (Lx, Lx) = (Lx, Lx)
pick x = eₓ the last coordinate vector,
then (Aₓ, x) = Axx = || L₁x||² = || L₂x||²
Given that L1, and L2 are lower triangular, which necessitates that their lower right entry be the same,
The Kth entry is currently the last row.
given by (L₁, eₓ, eₓ) = 1/√Axx (L₁eₓ, L₂eₓ) = 1/ Aₓ = (Aeₓ, eₓ)
so the last row of L₁, L₂ be the same,
we reduce our A to new (n - 1)x(n - 1) submatrix,
which will likewise be true, and then repeat the process to discover each row's unique value.
Thus, the inductive process shows that L1 = L2.
As a result, the factorization's bottom triangular matrix L is exclusive.
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Rewrite the expression as a single logarithm
Please help will give brainlist only if correct!
The correct option is (d) i.e. log [ √x × (x-1)^3 / ∛ (x+1)^2 ] is as the single logarithm.
What is logarithm?
Logarithm is a mathematical operation which is used to determine the exponential power of a number. It is the inverse operation of exponentiation. Logarithm is commonly used in calculus, algebra, and other areas of mathematics. It can also be used to solve problems involving exponents, roots, and powers. Logarithm is denoted by the symbol log, and is read as "log to the base". The base is the number which the logarithm is taken to. For example, log2 10 is the logarithm to the base 2 of 10. This is equivalent to saying "2 to the power of what equals 10?" The answer is that 2 raised to the power of 3 (2^3) would equal 10.
Given, log x / 2 + 3 [ log(x-1) - 2/9 log(x+1) ]
= log √x + 3 log(x-1) - 2/3 log (x+1) {∵ log x^a = a log x }
= log √x + log (x-1)^3 - log (x+1)^2/3
= log √x + log [(x-1)^3 / (x+1)^2/3] {∵ log a - log b = log a/b }
= log [√x × (x-1)^3 / (x+1)^2/3 ]
= log [ √x × (x-1)^3 / ∛ (x+1)^2 ]
Hence, (d) is the correct option.
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Damian works after school. Each day he earns a set amount, plus an hourly wage. The function f(x)=12 x+10 models the amount he earns each day for working x hours. How much does Damian earn on Friday if he works for 2.75 hours?
$=________
The amount earned by Damian on Friday, if The function f(x) = 12 x + 10, and he works for 2.75 hours, is $43.
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
Given:
The function f(x) = 12 x + 10, where x is working hours,
Calculate the amount by putting the value of x = 2.75 in the function as shown below,
f(x) = 12 × 2.75 + 10
f(x) = 33 + 10
f(x) = $43
Thus, the amount earned is $43.
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Find the length of BD. Use that length of BC. Round to the nearest tenth
By means of trigonometric functions, the length of side BC is approximately equal to 11.6 centimeters.
How to determine a missing length in a system of triangles by trigonometric functions
In this problem we find a geometric system formed by two right triangles, from which we need to determine the exact measure of side BC. This can be done by means of trigonometric functions, that represents relationships between two sides of a right triangle:
sin θ = y / r
cos θ = x / r
tan θ = y / x
cot θ = x / y
sec θ = r / x
csc θ = r / y
Where:
r - Hypotenusex - Leg adjacent to the angle.y - Leg opposite to the angle.First, obtain the length of side BD:
cos θ = BD / AB
BD = AB · cos θ
BD = 5 · cos 30°
BD = 5√3 / 2 cm
Second, calculate the length of side BC:
sin θ = BD / BC
BC = BD / sin θ
BC = 5√3 / 2 / sin 22°
BC ≈ 11.6 cm
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What is the discontinuity and zero of the function f of x equals x squared plus 5 times x minus 6 all over quantity x plus 6 end quantity question mark
a
Discontinuity at (−6, −7), zero at (−1, 0)
b
Discontinuity at (6, 5), zero at (−1, 0)
c
Discontinuity at (−6, −7), zero at (1, 0)
d
Discontinuity at (6, 5), zero at (1, 0)
The discontinuity of our given function is at point (-6, -7).
The zero of our given function is, (1, 0).
What is discontinuity and zero of the function?
A discontinuous function is a graph function that is not connected to any other functions. If the left-hand limit of f(x) and the right-hand limit of f(x) both exist but are not equal, then the function f(x) is said to have a discontinuity of the first kind at x = a.
The x-intercept(s) of the function's graph represent the real zero of the function.
Consider the given function,
[tex]f(x) = \frac{x^2+5x-6}{x+6}[/tex]
We know that a function is discontinuous, when its denominator is equal to zero.
To find the discontinuity for our given function, we will equate denominator to 0 as:
x + 6 = 0
x = -6
Now simplify the given function.
[tex]f(x) = \frac{x^2+5x - 6}{x+6}\\ f(x) = \frac{x^2 +6x - x - 6}{x+6}\\ f(x) = \frac{x(x+6)-1(x+6)}{x+6}\\ f(x) = \frac{(x-1)(x+6)}{x+6} \\f(x) = x-1[/tex]
Take y = x - 1
Since the denominator term is cancelled out, so our give function has a removable discontinuity.
Now, we will find value of y by substituting x = -6
⇒ y = -6 - 1
y = -7
Therefore, the discontinuity of our given function is at point (-6, -7).
Now, we will find zero of our given function by substituting f(x) = 0,as zero of the function is the point, where graph intersects x-axis and value of y is 0 at x-axis:
⇒ 0 = x - 1
x - 1 = 0
x = 1
Therefore, the zero of our given function is, (1, 0).
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In a network of 39 computers, 4 have a copy of a particularly critical file to sustain an organization's regular operations. Suppose that 8 computers at random fail. What is the probability that all 4 computers with the critical file fail in this incident? (Round to four decimal places.)
Mariah has a total of $15,000 invested in two accounts. The total amount of interest she earns from the accounts in the first year is $1540. If one account pays 8% per year and the other pays 12% per year, how much did she invest in each account?
The amount invested in the account that earns 8% interest is $6500
The amount invested in the account that earns 12% interest is $8500
How much did she invest in each account?a + b = $15,000 equation 1
0.08a + 0.12b = $1540 equation 2
Where:
a = amount invested in the account that earns 8% interest
b = amount invested in the account that earns 12% interest
The elimination method would be used to determine the required values:
Multiply equation 1 by 0.08
0.08a + 0.08b = 1200 equation 3
Subtract equation 3 from equation 2
0.04b = 340
Divide both sides of the equation by 0.04
b = 340 / 0.04
b = $8500
a + 8500 = 15,000
a = $15,000 - $8,500
a = $6500
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