Answer:
The larger number is 100
The smaller number is 60
Step-by-step explanation:
x + (40 + x) = 160
2x + 40 = 160
x + 20 = 80
x = 60
60 + (40 + 60) = 160
160 = 160
A(t) = 17t - 1/2 * t ^ 2 power lawn mowers, 10. Suppose that the factory's cost of manufacturing units is C(x) After hours of operation, an assembly line has assembled C(x) = 2772 + 110x (a)Express the factory's cost as a (composite) function of the number of hours of operation of the assembly line )What is the cost of the first 2 hours of operation?
The function of the number of hours of operation of the assembly line will be 2772 + 110[17t - 1/2t²].
The cost of the first 2 hours of operation will be $6292
How to calculate the functionFrom the information, A(t) = 17t - 1/2t² power lawn mowers, 10 and we suppose that the factory's cost of manufacturing units is C(x) after hours of operation, an assembly line has assembled C(x) = 2772 + 110x.
Therefore, the (composite) function of the number of hours of operation of the assembly line will be:
= 2772 + 110[17t - 1/2t²]
The cost of the first 2 hours of operation will be:
2772 + 110[17t - 1/2t²]
= 2772 + 110[17 × 2 - 1/2 × 2²
= 2772 + 110(34 - 2)
= $6292
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Use the commutative and/or associative properties to simplify (17)(0.25)(4).
The solution is, (17)(0.25)(4) = 17.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
(17)(0.25)(4)
=(17)*1
=17
at first we have to multiply the last two terms i.e. (0.25) and (4), then, we multiply the result 1 with 17, and get the result 17.
Hence, The solution is, (17)(0.25)(4) = 17.
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[tex] {x}^{\frac{2}{3} }{ } = 64 [/tex]
Solve the following equation
The value of x in the given equation using laws of exponents is; x = 512
How to use Laws of Exponents?The different laws of exponents include;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
We have the equation as;
x^(2/3) = 64
We can write 64 as (∛512)²
This can be further expressed as;
512^(2/3)
Thus, we have;
x^(2/3) = 512^(2/3)
Thus, by identity rule;
x = 512
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1. Takis Machine Shop paid a base rate for the state's workers' compensation insurance of $9.40 per $100 paid in wages. Takis has a monthly payroll of $53,896.84. After reevaluating the frequency and severity of accidents at machine shops, the state increased the base rate to $10.40 per $100 paid in wages. Assuming the monthly payroll stays the same, how much more will Takis pay each year for state workers' compensation insurance in dollars. Round to the nearest hundredth of a percent.
2. The Madison County tax assessor determined the market value of a home to be $590,000. The rate of assessment in Madison County is 40% of market value. The tax rate is 42.73 mills. Calculate the real estate tax in dollars. Round to the nearest hundredth of a percent.
3. Vanesa Vasquez contributes $2,500 per year to her Roth IRA, an ordinary annuity, starting at age 35. If she earns 7.4% annual interest compounded annually, what is the fair market value of her Roth IRA at age 65? How much interest will she have earned in dollars? Round to the nearest hundredth of a percent.
4. Marty and Roslyn Seymour purchase a GNMA Mortgage issue bond selling at a premium of 103.7% of its $10,000 face value. The bonds are selling at a premium because they have an annual yield of 8.75%. Find the interest rate as a percent? Round to the nearest hundredth of a percent.
5. Ricardo Ramirez took out a single-payment loan for $2,500 at 7.8% ordinary interest to pay his federal income tax bill. If the maturity value of the loan was $2,548.75, in how many days would Ricardo have to pay back the loan?
Answer: do you need me to answer all or anthor example.
Step-by-step explanation:
I will answer
A population mean is normally distributed with a mean of 56 and a standard deviation of 12.
The mean of the sampling distribution (p) and The standard error of the mean (o) are 56 and 2 respectively.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
According to question:(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.
(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:
o = 12 / √36 = 2
(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.
This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.
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Samuel took a survey of people entering several random ice cream shops to find out who liked vanilla and who liked chocolate ice cream.
biased or unbiased
Answer:
ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.
Step-by-step explanation:
please help me ive been struggling for a little bit
Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.
What is Triangle like?It is the simplest polygon and a key component in many branches of science and mathematics.
A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.
In triangle STU, right angled at T, we have:
[tex]ST = 6UT = \sqrt{(22)}[/tex]
We can use the Pythagorean theorem to find the length of TU:
[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]
Now, we can use the definition of cosine:
cos(S) = adjacent/hypotenuse
In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:
[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]
To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):
cos(S) ≈ 0.78 (rounded to the nearest hundredth)
Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.
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what could be a ratio between the lengths of the two legs of a 30-60-90 triangle
Answer:
Below
Step-by-step explanation:
One leg would be hyp * cos 30 and one would be hyp cos 60
hyp cos 30 : hyp cos 60
cos 30 : cos 60
= ratio sqrt (3) /2 : 1/2 or sqrt 3 : 1
question 4 i need help with
Answer:
$3.00
Step-by-step explanation:
The drinks for the first family were 4, and the drinks for the second were 3. They were 2 numbers apart in price and so that means that they costed around $1. Minus a drink on the first to get $17.00. Now tell how far apart it is.
Calculate the range and interquartile range for the following set of scores from a continuous variable: 5, 1, 6, 5, 4, 6, 7, 12. Identify the score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile. Why is the interquartile range a better description of variability in the data than the S range?
The range and interquartile range is 11 and 2 respectively. The score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile is 7 and 4 respectively.
To calculate the range, we subtract the smallest value from the largest value:
Range = Largest Value - Smallest Value = 12 - 1 = 11
To calculate the interquartile range, we first need to find the first and third quartiles. We can do this by ordering the scores from lowest to highest and finding the median of the lower half and upper half of the scores, respectively:
1, 4, 5, 5, 6, 6, 7, 12
The median of the lower half (Q1) is the middle value of the numbers 1, 4, 5, and 5, which is 4.5 (the average of the two middle values).
The median of the upper half (Q3) is the middle value of the numbers 6, 6, 7, and 12, which is 6.5.
Interquartile Range = Q3 - Q1 = 6.5 - 4.5 = 2
To find the score that corresponds to the 75th percentile, we first need to find the index corresponding to the 75th percentile. We can do this by multiplying 0.75 by the total number of scores, which is 8. This gives us an index of 6, meaning the 75th percentile score is the 6th score in the ordered list:
1, 4, 5, 5, 6, 6, 7, 12
The score that corresponds to the 75th percentile is 7.
To find the score that corresponds to the 25th percentile, we can follow the same procedure. The index corresponding to the 25th percentile is 0.25 times the total number of scores, or 2. The 2nd score in the ordered list is 4.
The interquartile range is a better description of variability in the data than the range because the range is heavily influenced by outliers. In this case, the range is 11, which is largely driven by the outlier score of 12. The interquartile range, on the other hand, only considers the middle 50% of the scores and is therefore less affected by outliers. It gives a more accurate measure of the spread of the scores around the median.
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Problem 1. Compute the complex norm |z|= √zz for the following complex numbers z:
1. z = −i
2. z = (2 + i)2
3. z = (3 −4i)3
4. z = (3 + 4i)3
Recall that the complex norm (or modulus) of a complex number z = a + bi is defined as the nonnegative square root of the product of the complex number and its conjugate, i.e., |z| = √(z × z*), where z* is the complex conjugate of z.
Using this definition, we can calculate the complex norm of each of the given complex numbers as follows:
[tex]z = -i\\z* = i (conjugate of -i)\\|z| = √(z z*) = √(-i i) = √1 = 1Therefore, |z| = 1.[/tex][tex]z = (2 + i)^2\\z* = (2 - i)^2 (conjugate of (2 + i)^2)\\|z| = √(z z*) = √((2 + i)^2 (2 - i)^2) = √((2^2 + 2i + i^2) (2^2 - 2i + i^2))= √((4 + 4i - 1) (4 - 4i - 1)) = √(9 * 9) = 9Therefore, |z| = 9.[/tex][tex]z = (3 - 4i)^3\\z* = (3 + 4i)^3 (conjugate of (3 - 4i)^3)\\|z| = √(z z*) = √((3 - 4i)^3 (3 + 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex][tex]z = (3 + 4i)^3\\z* = (3 - 4i)^3 (conjugate of (3 + 4i)^3)\\|z| = √(z z*) = √((3 + 4i)^3 (3 - 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex]What is complex number?A complex number is a number that can be expressed in the form [tex]a + bi[/tex], where a and b are real numbers, and i is the imaginary unit defined by [tex]i^{2} = -1[/tex]. The real part of the complex number is a, and the imaginary part is bi.
Complex numbers can be added, subtracted, multiplied, and divided in a manner similar to real numbers. They can also be graphed on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part.
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is 68/33 rational or irrational
Answer:
Given value is Rational. The value is 2.06
Step-by-step explanation:
Answer: Rational.
Step-by-step explanation:
An irrational number is one that terminates forever, and cannot be expressed as a fraction. 68/33 is a fraction, therefore it's rational. Irrational can be values like pi, which do not have a ratio form (e.g. fraction).
One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
The circumference of a circle is 81.64 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer
Answer:13
Step-by-step explanation:
r = circumference/2pi
81.64/6.28 = 13
The radius of the garden is 13 units.
question is in the picture
The formula of the area of the trapezium as subject to x is,
x = 2A/h - y.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The area of the trapezium,
A = (1/2)h(x + y)
To make x the subject of the equation:
2A/h = (x + y)
2A/h - y = x
x = 2A/h - y
Therefore, the formula is x = 2A/h - y.
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Select the correct answer. Which is a warning sign that someone needs the help of a mental health professional? a. Feeling shy when asked to walk onstage b. Overeating to increase bodily strength c. Inablity to sleep properly for weeks.
Inability to sleep properly for weeks is a warning sign that someone needs the help of a mental health professional. Correct option is C.
Difficulty sleeping, or insomnia, can be a warning sign that someone needs the help of a mental health professional. Insomnia can be caused by a number of mental health conditions, such as anxiety, depression, or post-traumatic stress disorder (PTSD), as well as other factors such as stress, poor sleep habits, or physical health problems.
Feeling shy when asked to walk onstage and overeating to increase bodily strength may be signs of anxiety or other emotional or psychological issues, but they are not necessarily warning signs that someone needs the help of a mental health professional.
However, if these behaviors are causing significant distress or interfering with daily life, it may be a good idea to seek the help of a mental health professional.
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Please helpppp
if y+3/y-3 = 6
What is the value of y?
f(x) =3(x-2) (x+4)
f(x) = (3x+12) (x-2)
f(x) =3(x+4) (x+2)
f(x) = 3 (x-4) (x+2)
Answer:
Step-by-step explanation:
The answer is d. f(x) = 3 (x-4) (x+2).
A function is given.
g(x) =
4
x + 5
; x = 0, x = h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
A function is given net change and the average rate of change between the given values of the variable.
A. = - [tex]\frac{4h}{7h + 49}[/tex]
B. = - [tex]\frac{4}{7h + 49}[/tex]
What exactly is a sample average rate?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
According to given information:a) The net change is just the difference between g(h) and g(0). This is found below.
g(h) - g(0) = [tex]\frac{4}{h + 7}[/tex] - [tex]\frac{4}{0 + 7}[/tex]
= [tex]\frac{28 - 4h -28}{7h + 49}[/tex]
= - [tex]\frac{4h}{7h + 49}[/tex]
b) The average rate of change is the net change divided by the length of the interval. This is:
[tex]\frac{g(h) - g(0)}{h - 0}[/tex] = - [tex]\frac{{4h}/{7h + 49}}{h - 0}[/tex]
= - [tex]\frac{4}{7h + 49}[/tex]
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The pto is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 200 tickets sold. The winter gets a prize worth $76.
Answer:
Step-by-step explanation:
The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.
Let's first calculate the total revenue:
Number of tickets sold = 200
Price per ticket = $4
Total revenue = 200 * $4 = $800
Next, let's calculate the cost of the tickets:
Number of tickets sold = 200
Price per ticket = $4
Total cost = 200 * $4 = $800
Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:
Profit = Total revenue - Total cost
Profit = $800 - $800 = $0
So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.
Sara can type 90 words in
4 minutes. About how many words
would you expect her to type in
10 minutes at this rate?
[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]
what is the substitution for -3x+5y=21
Answer:
5
_ y - 7
3
the five is floating for some reason its supposed to be under the line
Written as a simplified polynomial in standard form, what is the result when
(x − 2)² is subtracted from 4x?
Step-by-step explanation:
(x-2)(x-2)-4x
x²-2x-2x +4-4x
x²-4x-4x +4
x²-8x+4
Answer:
4x - (x - 2)² = 4x - x² + 4 = 3x + 4
Step-by-step explanation:
Write the equation is slope intercept form given
f(0) = -3 and f(1) = 2
The equation is slope-intercept form is equal to y = 5x - 3.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Based on the information provided, we can logically deduce the following data points on the line:
Points on x-axis = (0, 1).Points on y-axis = (-3, 2).At point (0, -3), a linear equation of this line can be calculated in slope-intercept form as follows:
y - (-3) = (2 + 3)/(1 - 0)(x - 0)
y + 3 = 5x
y = 5x - 3.
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14,125 ÷ 18 = ? With a remainder
Answer:
784 R 13
Hope this helps!
Step-by-step explanation:
Determine the Domain and Range for the graph below. Write your answer in interval notation and as an inequality.
Domain written in Interval Notation:
Domain written as an Inequality:
Range written in Interval Notation:
Range written as an Inequality:
Points on the graph are:
(0,1) (1,2) (2,3) (3,4) (4,5)
(-1,0) (-2,-1) (-3,-2) (-4,-3)
The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5] ; (2) Domain [-1,-4], Range =[0,-3]
Domain and Range of a set of Ordered pairsThe domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.
The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.
From the points on the graph given:
(0,1) (1,2) (2,3) (3,4) (4,5)
Domain: (0, 1, 2, 3, 4)
In interval notation: = [0,4]Range: (1, 2, 3, 4, 5)
In interval notation: = [1, 5](-1,0) (-2,-1) (-3,-2) (-4,-3)
Domain: ( -1, -2, -3, -4)
In interval notation: = [-1, -4]Range: (0, -1, -2, -3)
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In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?
A) 1:3
B) 2:3
C) 6:13
D) 4:15
Answer:
B) 2:3
Step-by-step explanation:
If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.
RatioThe ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.
mercury : copper = 1 : 5 = 2 : 10
Then ...
mercury : tin : copper = 2 : 3 : 10
You need 2 parts mercury to 3 parts tin.
mercury : tin = 2:3 . . . . . . choice B
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Shen is riding in a bike race that goes through a valley and a nearby mountain range.
The table gives the altitude (in feet above sea level) for the five checkpoints in the race.
Use the table to answer the questions.
Checkpoint Altitude
(feet above sea level)
1 3,459
2 1,499
3 668
4 -202
5 -99
(a) The top of a hill rises 66 feet above Checkpoint 4.
What is the altitude of the top of the hill?
(b) How much higher is Checkpoint 1 than Checkpoint 5?
1) Note that the altitude of the top of the hill is -136 feet above sea level.
2) Note that Checkpoint 1 is 3,558 feet higher than Checkpoint 5.
What is the rationale for the above response?Altitude or height is a distance measurement between a reference datum and a point or object, generally in the vertical or "up" direction. The precise definition and reference datum vary depending on the circumstance.
1) Checkpoint 4 has an altitude of -202 feet above sea level. The top of the hill rises 66 feet above Checkpoint 4. Therefore, the altitude of the top of the hill is:
-202 + 66 = -136 feet
So, the altitude of the top of the hill is -136 feet above sea level.
2) To find the difference in altitude between Checkpoint 1 and Checkpoint 5, we need to subtract the altitude of Checkpoint 5 from the altitude of Checkpoint 1.
Altitude difference = Altitude of Checkpoint 1 - Altitude of Checkpoint 5
Substituting the values given in the table, we get:
Altitude difference (AD) = 3,459 - (-99)
AD = 3,459 + 99
Thus, AD = 3,558
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3. The number of pages
in my book is less
than 96 and greater
than 90.
Who could I be?
2
I have 3 letters in my
'name.
Who am I?
4.
The number of pages in the book is given by the inequality 90 < A < 96 , where A is the number of pages
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let the number of pages in the book be A
And , it is more than 90 and less than 96
So , the value of A is { 91 , 92 , 93 , 94 , 95 }
On simplifying , we get
90 < A < 96 , where A is the number of pages
Hence , the inequality is 90 < A < 96
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Mark and John work the same amount of hours babysitting and tutoring. Mark gets paid $6 per hour for babysitting and $15 an hour tutoring. He makes $150 in one week. John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114. How many hours were spent babysitting and tutoring?
The requried hours spent babysitting and tutoring are 5 and 8 hours respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the hours spent babysitting and tutoring be x and y respectively,
According to the quesiton,
Mark gets paid $6 per hour for babysitting and $15 an hour for tutoring. He makes $150 in one week.
6x + 15y = 150 - - - -(1)
John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114.
10x + 8y = 114 - - - - -(2)
Solving above equations 1 and 2 by elimination method we get x = 5 and y = 8
Thus, the requried hours spent for babysitting and tutoring are 5 and 8 hours respectively.
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Pat deposits $ 600 in a savings account at a simple interest rate of 6% per year for 5
years. how much will pat have earned in interest by the end of 5 years
Answer:
will earn in interest $ 180
