In response to the stated question, we may state that Hence, the 95% CI function for u is (16.72, 19.48), rounded to two decimal places in increasing order.
what is function?In mathematics, a function is a connection between two sets of numbers in which each member of the first set (known as the domain) corresponds to a single element in the second set (called the range). In other words, a function takes inputs from one set and produces outputs from another. Inputs are commonly represented by the variable x, whereas outputs are represented by the variable y. A function can be described using an equation or a graph. The equation y = 2x + 1 represents a linear function in which each value of x yields a distinct value of y.v
We use the following formula to create a confidence interval around the population mean u:
CI = x ± z*(s/√n)
where x represents the sample mean, s represents the sample standard deviation, n represents the sample size, z represents the z-score associated with the desired degree of confidence, and CI represents the confidence interval.
Because the degree of confidence is 95%, we must calculate the z-score that corresponds to the standard normal distribution's middle 95%. This is roughly 1.96 and may be determined with a z-table or calculator.
CI = 18.1 ± 1.96*(4.1/√34)
CI = 18.1 ± 1.96*(0.704)
CI = 18.1 ± 1.38
Hence, the 95% CI for u is (16.72, 19.48), rounded to two decimal places in increasing order.
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P, Q, R, S, T and U are different digits.
PQR + STU = 407
Step-by-step explanation:
There are many possible solutions to this problem, but one possible set of values for P, Q, R, S, T, and U is:
P = 2
Q = 5
R = 1
S = 8
T = 9
U = 9
With these values, we have:
PQR = 251
STU = 156
And the sum of PQR and STU is indeed 407.
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If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (_____, _____) such that f'(c)>_______
If "f" is differentiable and f(1) < f(2), then there is a number "c", in the interval (1, 2) such that f'(c)> 0.
How do we know?Applying the Mean Value Theorem for derivatives, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one number c in the interval (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
In the scenario above, we have that f is differentiable, and that f(1) < f(2).
choosing a = 1 and b = 2.
Then applying the Mean Value Theorem, there exists at least one number c in the interval (1, 2) such that:
f'(c) = (f(2) - f(1)) / (2 - 1)
f'(c) = f(2) - f(1)
We have that f(1) < f(2), we have:
f(2) - f(1) > 0
We can conclude by saying that there exists a number c in the interval (1, 2) such that:
f'(c) = f(2) - f(1) > 0
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If A B C are three matric such that AB=AC such that A=C then A is
Answer:
invertible
Step-by-step explanation:
If A is invertible then ∣A∣ =0
The roots of a quadratic equation a x +b x +c =0 are (2+i √2)/3 and (2−i √2)/3 . Find the values of b and c if a = −1.
[tex]\begin{cases} x=\frac{2+i\sqrt{2}}{3}\implies 3x=2+i\sqrt{2}\implies 3x-2-i\sqrt{2}=0\\\\ x=\frac{2-i\sqrt{2}}{3}\implies 3x=2-i\sqrt{2}\implies 3x-2+i\sqrt{2}=0 \end{cases} \\\\\\ \stackrel{ \textit{original polynomial} }{a(3x-2-i\sqrt{2})(3x-2+i\sqrt{2})=\stackrel{ 0 }{y}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{ \textit{difference of squares} }{[(3x-2)-(i\sqrt{2})][(3x-2)+(i\sqrt{2})]}\implies (3x-2)^2-(i\sqrt{2})^2 \\\\\\ (9x^2-12x+4)-(2i^2)\implies 9x^2-12x+4-(2(-1)) \\\\\\ 9x^2-12x+4+2\implies 9x^2-12x+6 \\\\[-0.35em] ~\dotfill\\\\ a(9x^2-12x+6)=y\hspace{5em}\stackrel{\textit{now let's make}}{a=-\frac{1}{9}} \\\\\\ -\cfrac{1}{9}(9x^2-12x+6)=y\implies \boxed{-x^2+\cfrac{4}{3}x-\cfrac{2}{3}=y}[/tex]
Without an appointment, the average waiting time in minutes at the doctor's office has the probability density function f(t)=1/38, where 0≤t≤38
Step 1 of 2:
What is the probability that you will wait at least 26 minutes? Enter your answer as an exact expression or rounded to 3 decimal places.
Step 2 of 2:
What is the average waiting time?
The probability of waiting at least 26 minutes is 0.316. The average waiting time is 19 minutes.
Step 1:
The probability of waiting at least 26 minutes can be calculated by finding the area under the probability density function from 26 to 38:
P(waiting at least 26 minutes) = ∫26^38 (1/38) dt = [t/38] from 26 to 38
= (38/38) - (26/38) = 12/38 = 0.316
So the probability of waiting at least 26 minutes is 0.316 or approximately 0.316 rounded to 3 decimal places.
Step 2:
The average waiting time can be calculated by finding the expected value of the probability density function:
E(waiting time) = ∫0³⁸ t f(t) dt = ∫0³⁸ (t/38) dt
= [(t²)/(238)] from 0 to 38
= (38²)/(238) = 19
Therefore, the average waiting time is 19 minutes.
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Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading less than 0.35°C.
Round your answer to 4 decimal places
The probability of obtaining a reading less than 0.35° C is approximately 35%.
What exactly is probability, and what is its formula?Accοrding tο the prοbability fοrmula, the likelihοοd οf an event οccurring is equal tο the ratiο οf the number οf favοurable οutcοmes tο the tοtal number οf οutcοmes. Prοbability οf an event οccurring P(E) = The number οf favοurable οutcοmes divided by the tοtal number οf οutcοmes.
The readings at freezing οn a set οf thermοmeters are nοrmally distributed, with a mean (x) οf 0°C and a standard deviatiοn (μ) οf 1.00°C. We want tο knοw hοw likely it is that we will get a reading that is less than 0.35°C.
To solve this problem, we must use the z-score formula to standardise the value:
[tex]$Z = \frac{x - \mu}{\sigma}[/tex]
Z = standard score
x = observed value
[tex]\mu[/tex] = mean of the sample
[tex]\sigma[/tex] = standard deviation of the sample
Here
x = 0.35° C
[tex]\mu[/tex] = 0° C
[tex]\sigma[/tex] = 1.00°C
Using the values on the formula:
[tex]$Z = \frac{0.35 - 0}{1}[/tex]
Z = 0.35
The probability of obtaining a reading less than 0.35° C is approximately 35%.
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I will mark you brainiest!
If the triangles above are reflections of each other, then ∠D ≅ to:
A) ∠F.
B) ∠E.
C) ∠C.
D) ∠A.
E) ∠B.
Answer:
D I believe
Step-by-step explanation:
se spherical coordinates to evaluate the triple integral where is the region bounded by the spheres and .
The value of the triple integral[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex] by using spherical coordinates [tex]2\pi(e^{-1}-e^{-9})[/tex].
Given that the triple integral is-
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
E is the region bounded by the spheres which are,
[tex]x^2+y^2+z^2=1\\\\x^2+y^2+z^2=9[/tex]
In spherical coordinates we have,
x = r cosθ sin ∅
y = r sinθ sin∅
z = r cos∅
dV = r²sin∅ dr dθ d∅
E contains two spheres of radius 1 and 3 () respectively, the bounds will be like this,
1 ≤ r ≤ 3
0 ≤ θ ≤ 2π
0 ≤ ∅ ≤ π
Then
[tex]\int \int\int _{E } \frac{e^{-(x^2+y^2+z^2)}}{\sqrt{(x^2+y^2+z^2}}\sqrt{dV}[/tex]
[tex]\int\int\int _{E} \frac{e^{-r^2}}{r}r^2Sin\phi drd\phi d\theta\\\\2\pi \int_{0}^{\pi} \int_1^3 re^{-r^2} dr d\phi\\\\2\pi \int_1^3 re^{-r^2} dr\\\\2\pi(e^{-1}-e^{-9})[/tex]
The complete question is-
Use spherical coordinates to evaluate the triple integral ∭ee−(x2 y2 z2)x2 y2 z2−−−−−−−−−−√dv, where e is the region bounded by the spheres x2 y2 z2=1 and x2 y2 z2=9.
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Parts A-D. What is the value of the sample mean as a percent? What is its interpretation? Compute the sample variance and sample standard deviation as a percent as measures of rotelle for the quarterly return for this stock.
The sample mean is 2.1, the sample variance is 212.5% and the standard deviation is 14.57%
What is the sample mean?a. The sample mean can be computed as the average of the quarterly percent total returns:
[tex](11.2 - 20.5 + 13.2 + 12.6 + 9.5 - 5.8 - 17.7 + 14.3) / 8 = 2.1[/tex]
So the sample mean is 2.1%, which can be interpreted as the average quarterly percent total return for the stock over the sample period.
b. The sample variance can be computed using the formula:
[tex]s^2 = sum((x - mean)^2) / (n - 1)[/tex]
where x is each quarterly percent total return, mean is the sample mean, and n is the sample size. Plugging in the values, we get:
[tex]s^2 = (11.2 - 2.1)^2 + (-20.5 - 2.1)^2 + (13.2 - 2.1)^2 + (12.6 - 2.1)^2 + (9.5 - 2.1)^2 + (-5.8 - 2.1)^2 + (-17.7 - 2.1)^2 + (14.3 - 2.1)^2 / (8 - 1) = 212.15[/tex]
So the sample variance is 212.15%. The sample standard deviation can be computed as the square root of the sample variance:
[tex]s = \sqrt(s^2) = \sqrt(212.15) = 14.57[/tex]
So the sample standard deviation is 14.57%.
c. To construct a 95% confidence interval for the population variance, we can use the chi-square distribution with degrees of freedom n - 1 = 7. The upper and lower bounds of the confidence interval can be found using the chi-square distribution table or calculator, as follows:
upper bound = (n - 1) * s^2 / chi-square(0.025, n - 1) = 306.05
lower bound = (n - 1) * s^2 / chi-square(0.975, n - 1) = 91.91
So the 95% confidence interval for the population variance is (91.91, 306.05).
d. To construct a 95% confidence interval for the standard deviation (as percent), we can use the formula:
lower bound = s * √((n - 1) / chi-square(0.975, n - 1))
upper bound = s * √((n - 1) / chi-square(0.025, n - 1))
Plugging in the values, we get:
lower bound = 6.4685%
upper bound = 20.1422%
So the 95% confidence interval for the standard deviation (as percent) is (6.4685%, 20.1422%).
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the c on the left has blank1 - word answer please type your answer to submit electron geometry and a bond angle of
The CH3-CIOI-CNI molecule contains three carbon atoms with different electron geometries and bond angles. The CH3 and CIOI carbon atoms have tetrahedral geometry with a bond angle of approximately 109.5 degrees, while the CNI carbon atom has a trigonal planar geometry with a bond angle of approximately 120 degrees.
Using this Lewis structure, we can determine the electron geometry and bond angle for each carbon atom in the molecule as follows.
The carbon atom in the CH3 group has four electron domains (three bonding pairs and one non-bonding pair). The electron geometry around this carbon atom is tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CIOI group has four electron domains (two bonding pairs and two non-bonding pairs). The electron geometry around this carbon atom is also tetrahedral, and the bond angle is approximately 109.5 degrees.
The carbon atom in the CNI group has three electron domains (one bonding pair and two non-bonding pairs). The electron geometry around this carbon atom is trigonal planar, and the bond angle is approximately 120 degrees.
Therefore, the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI are:
CH3 carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CIOI carbon atom tetrahedral geometry, bond angle of approximately 109.5 degrees
CNI carbon atom trigonal planar geometry, bond angle of approximately 120 degrees
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_____The given question is incomplete, the complete question is given below:
Determine the electron geometry and bond angle for each carbon atom in the structure CH3-CIOI-CNI
Use the power of a power property to simplify the numeric expression.
(91/4)^7/2
Using the power property to simplify the expression (9¹⁺⁴)⁷⁺², we have 9^7/8
Given the expression
(9¹⁺⁴)⁷⁺²
To simplify this expression using the power of a power property, we need to multiply the exponents:
(9¹⁺⁴)⁷⁺² = 9(¹⁺⁴ ˣ ⁷⁺²)
Simplifying the exponents in the parentheses:
(9¹⁺⁴)⁷⁺² = 9⁷⁺⁸ or 9^7/8
Therefore, (9¹⁺⁴)⁷⁺² simplifies to 9^(7/8).
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The point on the parabola y=x^2 that is closest to the point (1,0) is (_______,_______). The distance between the two points is ________.
you can use Newtons's Method or Bisection to help but you don't have to.
Answer:Approximately
(0.58975,0.34781)
Step-by-step explanation:
If (x,y) is a point on the parabola, then the distance between (x,y) and (1,0) is:
√(x−1)2+(y−0)2=√x4+x2−2x+1
To minimize this, we want to minimize
f(x)=x4+x2−2x+1
The minimum will occur at a zero of:
f'(x)=4x3+2x−2=2(2x3+x−1)
graph{2x^3+x-1 [-10, 10, -5, 5]}
Using Cardano's method, find
x=3√14+√8736+3√14−√8736≅0.58975
y=x2≅0.34781
According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.
(a) What is the probability that a household in Maryland has an annual income of $90,000 or more? (Round your answer to four decimal places.)
(b) What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)
The required probability that a household in Maryland with annual income of ,
$90,000 or more is equal to 0.3377.
$50,000 or less is equal to 0.2218.
Annual household income in Maryland follows a normal distribution ,
Median = $75,847
Standard deviation = $33,800
Probability of household in Maryland has an annual income of $90,000 or more.
Let X be the random variable representing the annual household income in Maryland.
Then,
find P(X ≥ $90,000).
Standardize the variable X using the formula,
Z = (X - μ) / σ
where μ is the mean (or median, in this case)
And σ is the standard deviation.
Substituting the given values, we get,
Z = (90,000 - 75,847) / 33,800
⇒ Z = 0.4187
Using a standard normal distribution table
greater than 0.4187 as 0.3377.
P(X ≥ $90,000)
= P(Z ≥ 0.4187)
= 0.3377
Probability that a household in Maryland has an annual income of $90,000 or more is 0.3377(rounded to four decimal places).
Probability that a household in Maryland has an annual income of $50,000 or less.
P(X ≤ $50,000).
Standardizing X, we get,
Z = (50,000 - 75,847) / 33,800
⇒ Z = -0.7674
Using a standard normal distribution table
Probability that a standard normal variable is less than -0.7674 as 0.2218. This implies,
P(X ≤ $50,000)
= P(Z ≤ -0.7674)
= 0.2218
Probability that a household in Maryland has an annual income of $50,000 or less is 0.2218.
Therefore, the probability with annual income of $90,000 or more and $50,000 or less is equal to 0.3377 and 0.2218 respectively.
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Solve please geometry, solve for x
Answer: The answer is D
Step-by-step explanation:
Pythagorean theorem: a²+b²=c²
x²+x²=14²
2x²=196
Evaluate...
x=7√2
Is the function represented by the following table linear, quadratic or exponential?
The function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
What is function in mathematics?Function in mathematics is a relation between two sets, where one set is the input and the other set is the output. Functions are an important tool in mathematics and can be used to describe and model real-world phenomena. Functions take inputs, manipulate them and produce outputs. They can be used to represent relationships between two or more variables, or to represent a complex process. Functions allow us to break down complex problems into smaller, more manageable pieces and to study how changes in one variable affect other variables.
The function represented by the table is linear. It can be determined by the fact that the y-values change by the same amount every time the x-values increase by one unit. In this case, the y-values decrease by 2 each time the x-values increase by one unit. This is an example of a linear function.
Linear functions have the shape of a straight line and are characterized by having a constant rate of change. The constant rate of change is represented by the slope of the line, which in this case is -2. This means that for every one unit increase in the x-values, the y-values decrease by two.
A quadratic function is the opposite of a linear function, as it has a rate of change that is not constant. Quadratic functions are characterized by their parabolic shape and their rate of change increases as x-values increase. Exponential functions are characterized by their curved shape and increase exponentially as x-values increase.
In conclusion, the function represented by the table is linear, as it has a constant rate of change and is represented by a straight line.
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are the ratios 2:1 and 20:10 equivalent
Yes, there is an analogous ratio between 2:1 and 20:10.
What ratio is similar to 2 to 1?We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.
By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.
As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.
The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:
20 ÷ 10 : 10 ÷ 10
= 2 : 1
As a result, both ratios have the same reduced form, 2:1, making them equal.
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.2 In the diagram below, given that XY = 3cm, XZY = 30° and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. Show Calculations
Sin 30 =3/x
1/2=3/x
x=6
To the nearest hundredth, what is the volume of the sphere? (Use 3.14 for pie.)
Therefore, the volume of the sphere to the nearest hundredth is 724,775.70 cubic millimeters.
What is volume?Volume is a measurement of the amount of space occupied by a three-dimensional object. It is often expressed in units such as cubic meters (m³), cubic centimeters (cm³), cubic feet (ft³), or gallons (gal), depending on the context. The volume of a solid object can be calculated by multiplying its length, width, and height or using a specific formula depending on the shape of the object. For example, the volume of a rectangular box can be calculated as length x width x height, while the volume of a cylinder can be calculated as π x radius² x height. In general, volume is an important concept in many fields, including physics, chemistry, engineering, and architecture. It is often used to describe the capacity of containers, the displacement of fluids, and the amount of material used in construction or manufacturing.
Here,
The formula for the volume of a sphere is given as V = (4/3)πr³, where r is the radius of the sphere and π is approximately 3.14.
Substituting the given value of the radius, we get:
V = (4/3) x 3.14 x 48³
V ≈ 724,775.68 cubic millimeters
Rounding this value to the nearest hundredth, we get:
V ≈ 724,775.68 ≈ 724,775.70 cubic millimeters (rounded to two decimal places)
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Let the Universal Set, S, have 158 elements. A and B are subsets of S. Set A contains 67 elements and Set B contains 65 elements. If Sets A and B have 9 elements in common, how many elements are in neither A nor B?
There are 92 elements in A but not in B.
What are sets?In mathematics, a set is a well-defined collection of objects or elements. Sets are denoted by uppercase symbols, and the number of elements in a finite set is denoted as the cardinality of the set enclosed in curly braces {…}.
Empty or zero quantity:
Items not included. example:
A = {} is a null set.
Finite sets:
The number is limited. example:
A = {1,2,3,4}
Infinite set:
There are myriad elements. example:
A = {x:
x is the set of all integers}
Same sentence:
Two sets with the same members. example:
A = {1,2,5} and B = {2,5,1}:
Set A = Set B
Subset:
A set 'A' is said to be a subset of B if every element of A is also an element of B. example:
If A={1,2} and B={1,2,3,4} then A ⊆ B
Universal set:
A set that consists of all the elements of other sets that exist in the Venn diagram. example:
A={1,2}, B={2,3}, where the universal set is U = {1,2,3}
n(A ∪ B) = n(A – B) + n(A ∩ B) + n(B – A)
Hence, There are 92 elements in A but not in B.
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 131°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 131°F? Use the discriminant of a quadratic equation to decide.
answer options
1. No
2. Yes
From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.
Will the temperature of the part ever reach or exceed 135°F?The given equation that models the temperature of the machine is;
T = -0.005x² + 0.45x + 125
Let check if there's a value that exists for T = 135
Putting T = 135 in the given equation,
135 = -0.005x² + 0.45x + 125
We can simplify this to;
0.005x² - 0.45x + 10 = 0
From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b² - 4ac
= (-0.45)² - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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Find the measures of angles 1 through 5 in the figure shown !
Answer:
55 degrees angles on a rights angle triangle. 1 and 3 they are equal cause they are vertical opp angles 55 degrees
Uri paid a landscaping company to mow his lawn. The company charged $74 for the service plus
5% tax. After tax, Uri also included a 10% tip with his payment. How much did he pay in all?
Uri paid a total of $85.47 for the landscaping service including tax and tip.
What is tax?Taxes are compulsory payments made by a government organisation, whether local, regional, or federal, to people or businesses. Tax revenues are used to fund a variety of government initiatives, such as Social Security and Medicare as well as public infrastructure and services like roads and schools. Taxes are borne by whoever bears the cost of the tax in economics, whether this is the entity being taxed, such as a business, or the final users of the items produced by the firm. Taxes should be taken into consideration from an accounting standpoint, including payroll taxes, federal and state income taxes, and sales taxes.
Given that company charged $74 for the service plus 5% tax.
The tax is 5%, that is:
Tax = 5% of $74 = 0.05 x $74 = $3.70
Cost after tax = $74 + $3.70 = $77.70
Now, tip is 10%:
Tip = 10% of $77.70 = 0.10 x $77.70 = $7.77
Total cost = $77.70 + $7.77 = $85.47
Hence, Uri paid a total of $85.47 for the landscaping service including tax and tip.
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The breadth of a rectangular playground is 5m shorter than its length. If its perimeter is 130m,find ids length and breadth.
Answer:
Length is 35 m and breadth is 30 mStep-by-step explanation:
Given,
The breadth of a rectangular playground is 5m shorter than its length.Perimeter is 130 mLet length be x and breadth (x - 5).
Perimeter of rectangle is calculated by :
[tex] \: \: \boxed{ \pmb{ \sf{Perimeter_{(rectangle)} = 2(l + b)}}} \\ [/tex]
On substituting the values we get :
[tex]\dashrightarrow \: \: 130 = 2(x + x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 130 = 2(2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \dfrac{130}{2} = (2x - 5) \\ [/tex]
[tex]\dashrightarrow \: \: 65 = 2x - 5 \\ [/tex]
[tex]\dashrightarrow \: \: 65 + 5 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: 70 = 2x \\ [/tex]
[tex]\dashrightarrow \: \: \frac{70}{2} = x \\ [/tex]
[tex]\dashrightarrow \: \: 35 = x \\ [/tex]
Hence,
Length = x = 35 m.Breadth = x -5 = (35 -5) = 30 mThe Nutty Professor sells cashews for $6.80 per pound and Brazil nuts for $4.20 per pound. How much of each type should be used to make a 35 pound mixture that sells for $5.31 per pound?
The Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts tο make a 35 pοund mixture that sells fοr $5.31 per pοund.
Assume the Nutty Prοfessοr makes a 35-pοund mixture with x pοunds οf cashews and (35 - x) pοunds οf Brazil nuts.
The cashews cοst $6.80 per pοund, sο the tοtal cοst οf x pοunds οf cashews is $6.8x dοllars.
Similarly, Brazil nuts cοst $4.20 per pοund, sο (35 - x) pοunds οf Brazil nuts cοst 4.2(35 - x) dοllars.
The tοtal cοst οf the mixture equals the sum οf the cashew and Brazil nut cοsts, which is:
6.8x + 4.2(35 - x) (35 - x)
When we simplify, we get:
6.8x + 147 - 4.2x
2.6x + 147
The mixture sells fοr $5.31 per pοund, sο the tοtal revenue frοm selling 35 pοunds οf the mixture is:
35(5.31) = 185.85
When we divide the tοtal cοst οf the mixture by the tοtal revenue, we get:
2.6x + 147 = 185.85
Subtractiοn οf 147 frοm bοth sides yields:
2.6x = 38.85
When we divide by 2.6, we get:
x ≈ 14.94
Tο make a 35-pοund mixture that sells fοr $5.31 per pοund, the Nutty Prοfessοr shοuld use apprοximately 14.94 pοunds οf cashews and 35 - 14.94 = 20.06 pοunds οf Brazil nuts.
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A mountain is 13,318 ft above sea level and the valley is 390 ft below sea level What is the difference in elevation between the mountain and the valley
Answer: 13,708 ft
Step-by-step explanation:
To find the difference in elevation between the mountain and the valley, we need to subtract the elevation of the valley from the elevation of the mountain:
13,318 ft (mountain) - (-390 ft) (valley) = 13,318 ft + 390 ft = 13,708 ft
Therefore, the difference in elevation between the mountain and the valley is 13,708 ft.
Answer: The difference is 13,708 ft.
Given that a mountain is 13,318 feet above sea level. So the elevation of the mountain is [tex]= +13,318 \ \text{ft}[/tex].
Given that a valley is 390 feet below sea level.
So the elevation of the valley is [tex]= -390 \ \text{ft}[/tex].
So the difference between them is [tex]= 13,318 - (-390) = 13,318 + 390 = 13,708 \ \text{ft}.[/tex]
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Give the interval(s) on which the function is continuous.
g(t) = 1/√16-t^2
The function g(t) is defined as:
g(t) = 1/√(16-t^2)
The function is continuous for all values of t that satisfy the following conditions:
The denominator is non-zero:
The denominator of the function is √(16-t^2). Therefore, the function is undefined when 16-t^2 < 0, or when t is outside the interval [-4,4].
There are no vertical asymptotes:
The function does not have any vertical asymptotes, because the denominator is always positive.
Thus, the function g(t) is continuous on the interval [-4,4].
Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
What is the slope of the line in the following graph?
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
Which expressions are equivalent to 8(3/4y -2)+6(-1/2+4)+1
Answer: 6y + 6
Step-by-step explanation:
To simplify the expression 8(3/4y -2) + 6(-1/2+4) + 1, we can follow the order of operations (PEMDAS):
First, we simplify the expression within parentheses, working from the inside out:
6(-1/2+4) = 6(7/2) = 21
Next, we distribute the coefficient of 8 to the terms within the first set of parentheses:
8(3/4y -2) = 6y - 16
Finally, we combine the simplified terms:
8(3/4y -2) + 6(-1/2+4) + 1 = 6y - 16 + 21 + 1 = 6y + 6
Therefore, the expression 8(3/4y -2) + 6(-1/2+4) + 1 is equivalent to 6y + 6.