Area of the given rectangle as per given perimeter and width is equal to 60m².
As given in the question,
Perimeter of the given rectangle = 64m
Width of the given rectangle 'w' = 2m
Let us consider 'l' be the length of the rectangle
Perimeter of the rectangle = 2 ( l + w )
Substitute the values
64 = 2 ( l + 2)
⇒32 = l + 2
⇒l = 32 - 2
⇒l = 30m
Area of the given rectangle = l × w
= 30 × 2
= 60m²
Therefore, the area of the given rectangle as per given dimensions is equal to 60m².
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Is this a function? Explain, why or why not!
X
-2
-4
-6
Y
1
1
1
Edit View Insert Format Tools Table
By using the concept of function, it can be seen that the given table represents a function.
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here the values under x represents the domain and the values under y represents the Range.
From the table it can be seen that
Every point of the domain maps to unique point on the range.
So this is a function.
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Can someone help me with this math quick plsss
Answer: nope
Step-by-step explanation:
the length of the hypotenuse of a right triangle in 23in.one leg measures 16in.find the length of the other leg. round your answer to two decimal places
Answer:
16.52
Step-by-step explanation:
hyp²= opp²+adj²
let opp =16in
hyp= 23in
adj²=23²-16²
=529 -256
= 273
adj =√273
= 16.52
Ashley added ice cubes to her iced tea. The change in temperature of her tea was - 15F. If she added 5 ice cubes, what integer represents the change in tea per ice cube?
Answer:
To find the change in temperature per ice cube, you need to divide the total change in temperature by the number of ice cubes. In this case, you would divide -15F by 5 ice cubes to get -3F per ice cube. The negative sign indicates that the temperature of the tea decreased.
Step-by-step explanation:
You have 1,312 grams of radioactive kind of lanthanum. If its half-life is 93 minutes, how much will be left after 279 minutes?
If its half-life is 93 minutes, then the amount left after 279 minutes will be equal to 164 grams.
What is Half-life?In radioactivity, the half-life is the amount of time needed for half of a radioactive sample's atomic nuclei to spontaneously decay (convert into different nuclear species by emitter particles and energy) or, alternatively, the amount of time needed for the radioactive material's disintegration rate to drop by half.
As per the given information given in the question,
Initial amount, N₀ = 1312 grams
Time elapsed, t = 279 min
Half-life, [tex]t^1^/^2[/tex] = 93
Then, use the formula of half-life:
N(t) = N₀[tex](\frac{1}{2})^t^/^(^t^)^1^/^2[/tex]
Substitute the values in above equation,
N(t) = 1312[tex](\frac{1}{2})^2^7^9^/^9^3[/tex]
N(t) = 1312(1/2)³
= 1312 × 0.125
N(t) = 164 grams.
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Answer: 164 grams
Step-by-step explanation: I got the answer right on my ixl
A freezer in a lab i et o that the temperature change at a rate of -1. 6C every hour. What i the change in the temperature after 4 1/4 hour? Show your work
The change in the temperature after 4 1/4 hour is -6.8 C.
Given :
A freezer in a lab is set so that the temperature changes at a rate of –1.6 C every hour.
Temperature :
Temperature is the degree of hotness or coldness of an object.
The degrees must contain any units like kelvin , centigrade etc .
Change in temperature after 4 1/4 hours = change rate for hour * number of hours.
= -1.6 C * 4 1/4
= -1.6 C * 4.25
= -16 / 10 C * 425 / 100
= -16 * 425 / 10 * 100 C
= -6800 / 1000 C
= -68 / 10 C
= -6.8 C
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James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall
charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget.
James and Bethany can invite at most people to the reception.
(Round down to the nearest whole person.),
Step-by-step explanation:
James and Bethany Morrison are celebrating their 10th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $32 per person, find the greatest number of people that they may invite and still stay within their budget. James and Bethany can invite at most people to the reception. (Round down to the nearest whole person).
3,500 = 32p + 50
subtract 50 from both sides:
3,450 = 32p
divide both sides by 32:
p = 107.8125
because you cannot invite part of a person, round down to 107 people.
Answer:
107
Step-by-step explanation:
You have $3,450 to work with and you divide that by 32, which is the cost per person, and you come up with 107.8... You can round up to 108, but you risk(because you are) being over budget.
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 50 nails and each large box has 350 nails. The contractor bought 3 more small boxes than large boxes, which altogether had 2950 nails. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
The number of small boxes and large boxes for the given linear equation condition purchased is 10 and 7 respectively.
What is a linear equation?
Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
According to the question, a builder needs to purchase nails in order to construct a house.
Both small and large boxes of nails are provided. There are 50 nails in each small box and 350 in each large box.
The contractor purchased 3 more small boxes than large boxes, hence it is assumed that he purchased an 'x' number of large boxes.
He purchased (x+3) small boxes.
So, 50(x+3) + 350(x) = 2950.
50x + 150 + 350x = 2950.
400x = 2950 - 150.
400x = 2800.
x = 7.
∴ The no. of large boxes he purchased is 7.
∴ The no. of small boxes he purchased is 10.
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Find the slope of the line that passes through (-21, -47) and (-15,-44).
The slope of the line is 1/2 or 0.5
What is slope of a line ?The slope of a line characterizes the direction of a line.
To find the slope of a line when the coordinates of the two points are given you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .
Thus if
A ( x1, y1) and B( x2, y2)
The slope of the line is y2 - y1 / x2-x1
Calculations
Given ;
A ( -21, -47)
B(-15, -44)
slope = 3/6
=1/2 or 0.5
The slope of the line is 1/2 or 0.5
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4. What is one point of intersection between the graphs of the functions
f(x) = (x+6)(x+2) and g(x) = x + 6?
A. (0,6)
B. (-1,5)
C. (-2,0)
D. (-4,-4)
the point of intersection of the given function will be (-1,5).
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
the functions f(x) = (x+6)(x+2) and g(x) = x + 6
Equating them with each other
(x+6)(x+2) = x + 6
x+2 = 1
x = -1
f(-1) = 5
So the point of intersection of the given function will be (-1,5).
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Create a perpendicular bisector of AB and label the intersection point of the lines E. To verify your result, measure AE and EB and the angles between the bisector and AB. Take a screenshot of your work, and paste it below.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.
Make an opposite bisector of the Stomach muscle and mark the convergence point of line E. To check your outcome, measure AE and EB and the points between the bisector and Stomach muscle.
The line CD is the bisector line that divides the line segment AB into two equal parts that are AE = EB.
The diagram is given below.
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COLVE IT PLSS HELP WILL GIVE BRAINLIEST IF THE ANSWER IS RIGHT!
Answer:
degree 5monomialStep-by-step explanation:
You want to know if 5x²y²z +10x²y²z is monomial, binomial, or trinomial, and what its degree is.
DegreeThe degree of a term is the sum of the degrees of the variables in the term:
degree = 2 + 2 + 1 = 5
TermsTwo terms are shown. However, the terms are like terms, so can be combined into one term:
15x²y²z
This tells us the expression is a monomial.
__
Additional comment
The terms of a binomial must be unlike. That is, they don't count as separate terms if they can be combined.
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Solve for all possible values of x.
√9x-9 = x + 1
Omg help someone i don’t get this
Answer:
x = 2 , x = 5
Step-by-step explanation:
assuming you mean
[tex]\sqrt{9x-9}[/tex] = x + 1 ( square both sides to clear the radical )
([tex]\sqrt{9x-9}[/tex] )² = (x + 1)² ← expand using FOIL
9x - 9 = x² + 2x + 1 ( subtract 9x from both sides )
- 9 = x² - 7x + 1 ( add 9 to both sides )
0 = x² - 7x + 10 ← factor the quadratic
consider the factors of the constant term (+ 10) which sum to give the coefficient of the x- term (- 7)
the factors are - 2 and - 5 , since
- 2 × - 5 = + 10 and - 2 - 5 = - 7 , then
(x - 2)(x - 5) = 0
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 5 = 0 ⇒ x = 5
As a check
substitute these values into the equation and if both sides are equal then they are the solutions.
x = 2
left side = [tex]\sqrt{9(2)- 9}[/tex] = [tex]\sqrt{18-9}[/tex] = [tex]\sqrt{9}[/tex] = 3
right side = 2 + 1 = 3
left side = right side , so x = 2 is a solution
x = 5
left side = [tex]\sqrt{9(5)-9}[/tex] = [tex]\sqrt{45-9}[/tex] = [tex]\sqrt{36}[/tex] = 6
right side = 5 + 1 = 6
left side = right side, so x = 5 is a solution
A man walked a certain distance at a constant rate. If he had gone 1/2 mile per hour faster, he would have walked the distance in four-fifths the time; if he had gone 1/2 mile per hour slower, he would have been 2 1/2 hours longer on the road. How far did he walk?
Answer:
15
Step-by-step explanation:
15
He walked 15
Christina also invests $10,000, but instead chooses to invest into a passively managed index fund that is linked to the S&P 500, with an expense ratio of 0. 2%. Her investment also earns a 7% rate of return.
a)How much did she make in one year on her investment with the 7% rate of return?
b)How much does she pay in fees for her passively managed index fund?
c)At the end of the year, what’s the total value (AFTER FEES) of Christina’s mutual fund?
a. The return on investment is $700.
b. The payment should be $20.
c. The total value is $10,680.
Calculation of the return on investment, payment and total value:
a. Since the return on investment is 7%
And, the invested amount is $10,000
So, the return on investment should be
= 7% of $10,000
= $700
b. Since the expense ratio is 0.2%
So, here the payment be like
= 0.2% of $10,000
= $20
c. The total value should be
= $10000-$20 +$700
= $10680
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Please help with the question below
Answer:
A = -5
Step-by-step explanation:
PLEASE HELP Clinical trials involved treating flu symptoms with a new medicine. Among 724 patients treated with the medicine, 72 experienced a side effect of nausea. The claim is that the rate of nausea is greater than the 6% rate experienced by flu patients given a placebo. Find a test statistic of the proportion.
z = 4.47
z = –1.41
z = 4.53
z = 1.41
The test statistic of the proportion is given as follows:
z = 4.47.
How to calculate the test statistic for the proportion?The equation that gives the test statistic for a proportion is given as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the expected proportion from the population, or the test proportion.n is the sample size.In the context of this problem, the values of these parameters are given as follows:
[tex]p = 0.06, n = 724, \overline{p} = \frac{72}{724} = 0.0994[/tex]
Hence the test statistic for the proportion is calculated as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.0994 - 0.06}{\sqrt{\frac{0.06(0.94)}{724}}}[/tex]
z = 4.47.
Meaning that the first option is correct.
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Derivative of log(tanhx)
Derivative of log(tanhx) = 2cossec(2x)
Let us assume y = log (tan hx)
On differentiating both sides ,
[tex] \frac{dy}{dx \: } = \frac{d \: log(tanhx)}{dx} [/tex]
[tex] \frac{dy}{dx} = \frac{d log( \tan(hx) ) }{d \tan(hx).d \tan(hx) } \times dx[/tex]
[tex] \frac{dy}{dx} = \frac{1}{ \tan(hx) \times \sec( {h}^{2x} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{ \cos(hx) }{ \sin(hx) } \times \frac{1 }{ \cos(h {}^{2} ) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{2 \sin(hx). \cos(hx) } [/tex]
[tex] \frac{dy}{dx} = \frac{2}{ \sin(h)(2x) } [/tex]
dy/dx = 2 cos sec (2x)
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Apply the 45°-45°-90° Triangle Theorem to find the length of the hypotenuse of the triangle
If the length of each leg of the triangle is 15√2 in, what is the length of the hypotenuse(c)?
Answer:
30
Step-by-step explanation:
The 45-45-90 Triangle Theorem states that in the isosceles 45-45-90 triangle, if we designate each leg as [tex]a[/tex], the base, or hypotenuse is [tex]a\sqrt{2}[/tex] . Since we know the leg is [tex]15\sqrt{2}[/tex], the hypotenuse would be:
[tex]15\sqrt{2} * \sqrt{2} =\\15 * 2=\\30[/tex]
WILL GIVE YOU 85 POINTS IF YOU ANSWER THIS QUESTION ASAP
the accompanying table shows the number of math problems completed correctly by students on a recent test. what is the average number of problems completed correctly by all students?
Answer:
B) 69.6
Step-by-step explanation:
Eric ha already ran 5 mile and i continuing to run at a pace of 1 mile per hour. Je ha only
The required hours will they have ran the same number of miles is 3.
What is distance and speed?Speed distance time is the equation used to make sense of the connection between speed, distance and time. That is speed = distance ÷ time. Or on the other hand to put it one more way distance isolated by speed will give you the time. Given you know two of the sources of info you can resolve the third.
According to question:Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour.Erick distance:: 5 + 1x
Similarly for jess,
Jess distance:: 2 + 2x
To cover same number of miles, above two equations will be equate;
5 + x = 2 + 2x
x = 3 hrs
Thus, requierd number of hours is 3.
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Correct question:
Eric has already ran 5 miles and is continuing to run at a pace of 1 mile per hour. Jess has only run 2 miles and is continuing to run at a pace of 2 miles per hour. In how many hours will they have ran the same number of miles?
What i the volume of the following rectangular prim? Volume ==equal unit^3 3 cubed
Since the side length is three units, the specified rectangular prism's volume will be 27 units.
What is volume?Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity. The capacity of an object is measured by its volume. For instance, a cup's capacity is stated to be 100 ml if it can hold 100 ml of water in its brim. The quantity of space occupied by a three-dimensional object can also be used to describe volume.
Here,
Length of side=3 units
Volume=(side)³
=3³ unit
=27 unit³
The length of side is 3 unit, so the volume of the given rectangular prism will be 27 unit.
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I REALLY NEED HELP WITH THIS QUESTION!!!!
Jim took clothes to the cleaners three times last month. First, he brought 2 shirts and 2 pairs of slacks and paid $17.96. Then he brought 6 shirts, 3 pairs of slacks, and 2 sports coats, and paid $49.89. Finally, he brought 5 shirts and 1 sports coat and paid $21.94. How much was he charged for each shirt, each pair of slacks, and each sports coat?
Each shirt = $2.99, each pair of slacks = $5.99, and each sports coat = $6.99.
What is total ?Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16.
Let shirts equal SH, Slacks equal S, and sports coats equal SC.
2SH+2S equals 17.96.
6SH+3S+2SC=49.89
5SH+1SC=21.94
We'll use them to address
6SH+3S+2SC=49.89
-6SH-6S=--53.88, multiplying by -3 to eliminate SH.
-3S+2SC=-3.99
-30SH-6SC=-131.64, multiplying the third by -6 to eliminate SH
30SH+15S+10SC=249.45,multiplying by 5 to eliminate SH.
15S + 4SC = 117.81
Now 15S + 4SC = 117.81 and -3S+2SC=-3.99
S = $5.99
As a result, we may calculate SH as $2.99 and use the value of S and SH we get SC = $6.99
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Select the correct answer. The sum of two consecutive numbers is 157. This equation, where n is the first number, represents the situation: 2n + 1 = 157. What is the first number? A. 77 B. 78 C. 79 D. 80
Answer:
2n + 1 = 157
2n = 157 - 1
2n = 156
n = 156/2
n = 78
Step-by-step explanation:
hope this helps
The number of songs Oliver has downloaded this year, divided by 12, is equal to 6 less than 30. What is an equation that represents this situation, and how many songs has Oliver downloaded?
Answer: 288
Step-by-step explanation: the number of songs downloaded this year will be x
x/12=30-6
= x/12=24
12*24= 288
x=288
help this nobody my friend
Answer:
t=2/f-5
Step-by-step explanation:
Multiply both sides by "t"subtract 5t from both sidesfactor out "t" from the expressiondivide both sides by "f-5"On average, Jonathan drink 2/3 of a 10-ounce gla of water in 2 4/5 hour. How much water doe he drink, in glae per hour?
In linear equation,(10/21) glasses of water does she drink, in glae per hour.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
3/4 of hour she drinks (2/3) of a glass
So, in 1 hour she drinks (2/3)×(5/14) of a glass
So, in 1 hour she drinks (10/21) glasses of water.
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Find the measure of the exterior angle. A triangle, with an exterior angle marked as 2 a degrees. Two of its other interior angles are labeled as a plus 10 degrees and 44 degrees.
The measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.
What are supplementary angles?If the sums of two angles equal 180 degrees, they are said to be supplementary.
However, two angles do not need to be near one another in order to be complementary.
If two angles' measures sum up to 180 degrees, they are said to be supplementary.
A triangle's outside angle complements the neighboring inner angle.
The adjacent internal angle will therefore likewise be 90 degrees if the exterior angle is.
Therefore, the measure of an exterior angle of a triangle is equal to the measure of its neighboring interior angle if both measure 90 degrees, according to the theory of supplementary angles.
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Correct question:
Can the measure of an exterior angle of a triangle ever equal the measure of its adjacent interior angle? Explain in 2-3 sentences.
at a 25% off sale you buy a game for 45$ what was the original price
Answer:
$60
Step-by-step explanation:
Let x = the original cost
x - .25x = 45
.75x = 45 Divide both sides by .75
x = 60
for an electron in the state of hydrogen, what is the probability of being in a spherical shell of thickness at distance (a) (b) and (c) from the proton?
Thus, the probability of the electron being in a spherical shell at distance (a) from the proton is e^(-a/a0), at distance (b) is e^(-b/a0), and at distance (c) is e^(-c/a0).
What is meant by probability?Probability is a metric for determining the possibility or chance of an event happening. It is a mathematical concept that measures the unpredictability of an occurrence and is frequently stated as a decimal or fraction. For example, if the probability of flipping a coin and obtaining heads is 0.5, there is a 50% chance of flipping heads. The number of favorable outcomes to the total number of potential outcomes is used to compute probability. In other words, it is the number of ways an event may occur divided by the total number of conceivable outcomes. Probability is used to make predictions and take wise decisions in a variety of disciplines, including mathematics, science, finance, and engineering.
How to solve?
If we assume the electron is in a hydrogen 1s orbital, the probability density function is given by the square of the 1s wavefunction, which is:
p(r) = (1/πa0^3) e^(-r/a0)
P(r, r+δr) = ∫p(r')dV = ∫p(r')4πr'^2dr'
For the given distances (a), (b), and (c), the probabilities are:
P(a) = ∫p(r')4πr'^2dr' = (1/πa0^3) ∫e^(-r'/a0)4πr'^2dr' = (1/πa0^3) * 4π * a0^3 * e^(-a/a0) = e^(-a/a0)
P(b) = e^(-b/a0)
P(c) = e^(-c/a0)
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