get rid of y. that's all you have to do.
A square and a rectangle have the same perimeter. The square has an area of 81 sq. inches and the rectangle has a width of 5 in. What is the area of the rectangle?
Answer:
Area of rectangle = [tex]\mbox{\large \boxed{\textrm{65 sq. inches}}}[/tex]
Step-by-step explanation:
Let square side = [tex]a[/tex]
Area of square [tex]A = a^2[/tex]
Given [tex]A = 81[/tex] and equating it to [tex]a^2[/tex]
[tex]a^2[/tex] [tex]= 81\;in^2[/tex]
[tex]a = \sqrt{81} = 9\;in[/tex]
Perimeter of square = [tex]4a = 4\cdot 9 = 36 \;in[/tex]
If [tex]l[/tex] = length of the rectangle and [tex]w[/tex] = width
Perimeter P of rectangle = [tex]2(l + w)\\[/tex]
Given perimeter of rectangle = perimeter of square we get
[tex]2(l + w) = 36\\\\l + w = 36/2\\\\l + w = 18[/tex]
Given
[tex]w = 5\\\\l + 5 = 18\\\\l = 18 - 5 = 13\\\\[/tex]
[tex]\\\\\textrm{Area of rectangle } = l \times w\\\\= 13 \times 5 \\\\= 65 \;sq.\;inches[/tex]
Evaluate the expression x² + 3x for x = 4.

To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify and we get 28.
What is expression ?
An expression is a combination of values, variables, and operators that represent a specific computation or operation. Expressions can be used to perform various operations such as arithmetic, logical, relational, and more. The value of an expression is determined by evaluating the expression, which involves simplifying and reducing it to a single value. In programming, expressions are a fundamental building block, and are used to write algorithms and control the flow of execution of a program.
To evaluate the expression x² + 3x for x = 4, we simply substitute 4 for x and simplify:
x² + 3x = 4² + 3 * 4 = 16 + 12 = 28
So, when x = 4, the expression x² + 3x = 28.
Hence, after evalution of the expression we get the result 28.
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the average number of dropout for a school dsitrict has been 305 per year with a standard eveiation of 50. what is the probility that the number of dropouts next year will be: g
The probability that the number of dropouts next year will be exactly 305 is virtually zero, the probability of less than 305 is 68%, greater than 305 is 32%, and within one standard deviation of 305 is 95%.
Probability of dropouts next year being exactly 305: 0
Probability of dropouts next year being less than 305: 0.68
Probability of dropouts next year being greater than 305: 0.32
Probability of dropouts next year being within one standard deviation of 305: 0.95
The probability that the number of dropouts next year will be exactly 305 is virtually zero. This is because the standard deviation of 50 suggests that the number of dropouts is likely to be different from 305.
The probability that the number of dropouts next year will be less than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be less than 305 is approximately 0.68, or 68%.The probability that the number of dropouts next year will be greater than 305 can be calculated using the normal distribution. The probability that the number of dropouts will be greater than 305 is approximately 0.32, or 32%.The probability that the number of dropouts next year will be within one standard deviation of 305 (i.e. between 255 and 355) can be calculated using the normal distribution. The probability that the number of dropouts will be within one standard deviation of 305 is approximately 0.95, or 95%.
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There are purple, white and blue counters in a bag in the ratio 16:18:3
There are 78 more purple counters than blue counters.
How many white counters are there?
Answer:
Step-by-step explanation:
Step-by-step explanation:
Let's call the number of purple counters "x". This means that the number of blue counters is x - 78, and the number of white counters is 18x.
According to the ratio, the sum of the number of purple and blue counters is 16x + (x - 78) = 17x - 78.
And the sum of all counters is 16x + 18x + 3x = 37x.
Knowing that the sum of all counters is the same, we can set the two sums equal to each other:
37x = 17x - 78 + 37x
So, we have:
74x = 17x - 78 + 37x
57x = -78
x = -78/57
Since x can't be negative, we have to reject this solution.
However, the number of white counters can be found by multiplying 18 by the number of purple counters:
18 * x = 18 * (x/57) = (18/57) * x = (18/57) * 78 = 72
Therefore, there are 72 white counters in the bag.
4. Astronomers have discovered a new constellation made up of Star A, Star B, and Star C that forms
a right triangle. The angle at Star A is 90 degrees. Star A and Star B are 50 lightyears apart, while
Star A and Star C are 120 lightyears apart. How many lightyears apart are Star B and Star C?
Answer: The distance between Star B and Star C can be found using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the hypotenuse (the longest side). In this case, the lengths of the two shorter sides are the distances from Star A to Star B (50 lightyears) and from Star A to Star C (120 lightyears).
So, we have:
(Star B to Star C)^2 = (Star A to Star B)^2 + (Star A to Star C)^2
(Star B to Star C)^2 = 50^2 + 120^2
(Star B to Star C)^2 = 2500 + 14400
(Star B to Star C)^2 = 16900
Taking the square root of both sides:
Star B to Star C = √16900
Star B to Star C = 129 lightyears
So, Star B and Star C are 129 lightyears apart.
Step-by-step explanation:
MANUFACTURING The profit P of a company in thousands of dollars can be modeled by P = 8.5√³, where c is
the number of customers in hundreds. What is the profit of the company if the company has 1800 customers. Round
to the nearest dollar.
The profit of the company if the company has 1800 customers is 649124 dollars
What is profit ?
A monetary gain, specifically the sum remaining after expenses for purchasing, running, or producing an item have been deducted.
P = 8.5√c³ ------->(1)
c = 1800 customers = 18 hundreds
(1) => P = 8.5√(18)³
= 8.5 √5832 ( cube of 18=5832
= 8.5 * 76.3675
= 649.124 thousands of dollars
( convert into dollars by multiplying by 1000)
= 649124.025 dollars
≈ 649124 dollars
The profit of the company if the company has 1800 customers is 649124 dollars
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Answer: 48148
Step-by-step explanation:
what is the interest rate on an investment of $470 at for seven years with an ending balance of 683.85
Answer:
Step-by-step explanation:
To find the interest rate on an investment of $470 for seven years with an ending balance of $683.85, you can use the formula for simple interest:
I = P * r * t
Where I is the interest earned, P is the principal amount ($470), r is the interest rate, and t is the number of years (7).
Rearranging the formula to solve for r:
r = I / (P * t)
Substituting the given values:
r = (683.85 - 470) / (470 * 7)
r = 213.85 / 3290
r = 0.0649 or 6.49%
So, the interest rate on the investment of $470 for seven years with an ending balance of $683.85 is 6.49%.
Anthony makes 6 1/8 gallons of lemonade for a family picnic. His family drinks 2 1/4 gallons of the lemonade. Which of these containers is the SMALLEST Anthony can use to store the remaining lemonade?
Answer:
3 and 7/8 gallons remaining
Step-by-step explanation:
You did not give the container options, but hopefully this will help
please help me I'm frustrated at this problem i know nothing about percentaes and im in 10th grade cryin inside...
Step-by-step explanation:
To find a percentage, it's the portion divided by the total. 100% represents the total between the children or adults respectively in the maintee and evening.
So, to answer, let's find the total of children and adults.
34+27 = 61 is the total for children.
38+46 = 84 is the total for adults.
Now, to find each percentage, take one of the numbers (Children-Maintee, Children-Evening) and divide it by the total we found.
34/61 = 0.557 or 55.7%
27/61 = 0.442 or 44.2%
I'm leaving it in fractional form in case you need a specific decimal answer.
As for adults, it's the same procedure.
38/84 = 0.452 or 45.2%
46/84 = 0.548 or 54.8%
Find the polynomial function k(x) of lowest degree in standard form if it has roots:
x=1,3,2i
Answer:
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
Step-by-step explanation:
A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),
From the above data we can get,
k(x) = (x - 1)(x - 3)(x - 2i)
After expanding the equation ,
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
So the polynomial function is
k(x) = x^3 - 6x^2 + 11x - 6 - 6i
m ∠ a = ____ degrees
Answer:
m<a = 44°
Step-by-step explanation:
Left triangle:
95 + 39 + x = 180
x = 46
Right triangle:
46 + 90 + a = 180
a = 44
please help
On a coordinate plane, the fountain is at (7, 5), the gardens are at (3, negative 5), the pond is at (negative 1, 7), and concessions are at (negative 7, 0). Your sister texted you, but the text cut off. Her text read, “Meet me at the trails located at (–2,”. Assuming that the trails are not located on the x-axis and given the content of her text, you can conclude that the trails must be located in either .
Answer: B quadrant 2 or quadrant 3
Step-by-step explanation:
If P is the centroid, and GP=2.2, find the indicated
lengths.
A
PC =
GC =
ttt
B
++
H
type your answer...
type your answer...
C
The length of PC and GC is 4.4 and 6.6 respectively.
What is centroid of a triangle?
A centroid of a triangle is defined as a equidistant from all the point present on the triangle. It is always lies on the interior of the triangle. The centroid divided the median in the ratio 2:1
Given ABC is the triangle.
In which G, H, J are the midpoints on AB, BC, AC sides respectively.
Then, AH, CG, BJ are the medians and they are intersect at the point P.
P is the centroid of the triangle.
Given, GP =2.2 we have to find the PC and GC.
We know that the centroid divided the median in 2:1 ratios.
i.e., AP:PH = CP:PG = BP:PJ = 2:1
We know , GP = 2.2, then, [tex]\frac{CP}{PG} = \frac{2}{1}[/tex]
⇒CP= 2(2.2)= 4.4then, GC = GP+PC= 2.2 + 4.4= 6.6.
Hence, the length of PC and GC is 4.4 and 6.6 respectively.
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At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12
feet and is 10 feet tall. Which of the following best describes the volume of the sand?
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
What is the volume of the cone?Let h be the height of the cone and A be the base area of the cone.
Then the volume of the cone will be given as,
Volume = (1/3) × A × h
At a construction site, sand is poured from a truck into a conical pile. The pile has a diameter of 12 feet and is 10 feet tall.
The base area of the cone is given as,
A = π × (d/2)²
A = 3.14 × (12 / 2)²
A = 3.14 × 36
A = 113.04 square feet
Then the volume of the cone is given as,
V = 1/3 × 113.04 × 10
V = 376.8 cubic feet
The volume of the sand which is equal to the volume of the cone will be 376.8 cubic feet.
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[tex]20x+18=58[/tex]
suppose that a senate committee is composed of 15 senators of whom 4 are left-handed. what proportion of the committee are left-handed? either give the exact fraction or decimal, or round to three decimal places.
The proportion of the committee that is left-handed is 4/15, which is equivalent to 0.267 when rounded to three decimal places.
A proportion is a way of expressing the relationship between two quantities. It is often written as a fraction, where the numerator represents the quantity of interest, and the denominator represents the total quantity.
In this case, we are interested in the proportion of left-handed senators, so the numerator will be the number of left-handed senators, which is 4. The denominator will be the total number of senators in the committee, which is 15. Therefore, the proportion of left-handed senators can be written as:
4/15
This fraction can also be expressed as a decimal by dividing the numerator (4) by the denominator (15) using a calculator or long division. When rounded to three decimal places, the decimal equivalent of the fraction is:
0.267
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how do you do it please help
Answer:
5.1
Step-by-step explanation:
11.5 + 5.6 + 8.8 = 29.5
31 - 29.5 = 5.1
a population of 100 frogs increases at an annual rate of 22%. after how many years will the population of the frogs double?
The population of the frogs will be double after 4 years when the current number of frogs were 100 and the annual rate of increment is 22%.
In the given question,
the current population of frogs are: 100
Annual rate of increase in population of frogs = 22%
Population required = double the current population = 2 x 100
= 200
Using the compound interest formula for amount, we can calculate the number of years in which the population of the frogs will be double:
Amount = principal ((1 + r%)^n) ,
here we will consider the amount to be population required, principal will be the current population, r is the annual rate of increment, and n is the time in years.
200 = 100 ((1 + 0.22) ^ n)
⇒ 200/100 = (1.22)^n
⇒ 2 = (1.22) ^ n
We plug digits in place of n and check for the closest result as 2.
We observe that (1.22)^4 = 2.2153 ≈ 2
Hence, we can say that the population of the frogs will be double after 4 years.
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if we have a data set with a mean of 25, what are the new mean if we multiply the values by 3 and then add 4?
If we multiply the values by 3 and then add 4 the new mean are 79 and and variance are 144.
Mean = E(x) = 25 , and variance = var(x) = 16 multiply by the value by 3 and add 4
mean = 3 x 24 + 4 = 79
Variance = 3^2 x 16 = 9 x 16 = 144
=> mean = 79 , variance = 144
Variance is a statistical measure that represents the degree of dispersion or variation in a set of data. It is the average of the squared differences between each value and the mean of the data set. The variance shows how spread out the data is and how much each value deviates from the average.
A high variance indicates that the data points are spread out over a wide range, while a low variance indicates that the data points are clustered around the mean. Variance is useful in various fields, including finance, engineering, and social sciences, where it is used to analyze data, test hypotheses, and develop predictive models. Standard deviation is a more intuitive measure of variation as it is expressed in the same units as the data, while variance is expressed in squared units.
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Complete Question: -
If we have a data set with a mean of 25 and a variance of 16, what are the new mean and variance if we multiply the values by 3 and then add 4?
A. Mean - 79, variance - 144
B. Mean - 79, variance - 48
C. Mean - 87, variance - 144
D. Mean - 87. variance - 48 ОООО
lily's car has a fuel efficiency of 8 88 liters per 100 100100 kilometers. what is the fuel efficiency of lily's car in kilometers per liter?
The fuel consumption per liter of Lilly's car is 12.5 kilometers per liter .
Average mileage The average mileage of a vehicle is the ratio of the distance traveled by the vehicle and the total amount of fuel used for that distance.
You can specify:
where (d) is the distance traveled and (n) is the fuel consumption.
Lily's car consumes 8 liters per 100km. This is your car's mileage or efficiency.
average mileage = 100/8 = 12.5 kilometers per liter
Therefore, the fuel efficiency in kilometers per liter of a Lily car with a fuel efficiency of 8 liters per 100 kilometers is 12.5 kilometers per liter.
Complete Question - Lily’s car has a fuel efficiency of 8 liters per 100 kilometers. What is the fuel efficiency of Lily’s car in kilometers per liter ?
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A jar contains four marbles: three red ones and one white one
If one marble is drawn from a bag containing three red ones and one white one , then probability that it is a red one is 3/4 .
Total number of marbles in the jar is = 4 marbles ;
the number of red marbles in the jar is = 3 marbles ;
the number of white marbles in the jar is = 1 marble ;
The probability of drawing a red marble from the jar can be calculated as the number of red marbles divided by the total number of marbles in the jar:
⇒ P(red marble) = number of red marbles / total number of marbles
⇒ 3/4
⇒ 0.75
⇒ 75%
Therefore, the probability of drawing a red marble from the jar is 0.75 or 75%.
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The given question is incomplete , the complete question is
A jar contains four marbles: three red ones and one white ones , if one marble is drawn from the jar , find the probability that it is a red one ?
What does the Pythagorean Theorem and its converse state if each triangle is a right triangle?
The Pythagorean Theorem is a fundamental theorem in Euclidean geometry that relates to the sides of a right triangle.
The Pythagoras Theorem states that : in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of lengths of other two sides.
Mathematically, the Pythagoras Theorem is written as:
⇒ c² = a² + b² ;
where c is = length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.
The Converse of Pythagoras Theorem states that : If in a triangle, the square of the length of the longest side is equal to the sum of squares of lengths of other two sides, then triangle is a right triangle.
Both the Pythagorean Theorem and its converse apply only to right triangles, which are triangles that have a right angle .
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assume you have applied to two different universities (let's refer to them as universities a and b) for your graduate work. in the past, 10% of students (with similar credentials as yours) who applied to university a were accepted, while university b accepted 50% of the applicants. assume events are independent of each other. a. what is the probability that you will be accepted to both universities?
If 10% of students who applied to university a were accepted, while university b accepted 50% of the applicants. The probability of being accepted to both universities is 0.05, or 5%.
The probability of being accepted at University A is 10%, which means the probability of not being accepted at University A is 90% (or 0.9). The probability of being accepted at University B is 50%, which means the probability of not being accepted at University B is 50% (or 0.5).
Since the events of being accepted at each university are independent of each other, we can use the multiplication rule of probability to find the probability of being accepted at both universities.
P(A and B) = P(A) x P(B)
where P(A and B) represents the probability of being accepted at both universities, P(A) represents the probability of being accepted at University A, and P(B) represents the probability of being accepted at University B.
Plugging in the values we have:
P(A and B) = 0.1 x 0.5 = 0.05
Therefore, the probability of being accepted to both universities is 0.05, or 5%. This means that there is a very low chance of being accepted at both universities, given the acceptance rates provided.
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A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red 4
Blue 3
Green 2
Yellow 2
Purple 6
Based on these results, express the probability that the next spin will land on blue as a fraction in simplest form.
Answer: 3/17 or 17.64%
Step-by-step explanation:
Just add everything (adds up to 17), then you put the color frequency number as the numerator of the fraction, then have the added up number as the denominator.
10-1/2x<-18 which inequality represents the solution to this inequality?
The solution for inequality 10 - 1/2x < -18 is 0 < x < 1/56.
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The given inequality is -
10 - 1/2x < -18
Solve the inequality to get the value for x.
First collect all the like terms -
-1/2x < -18 + (-10)
Then use arithmetic operation of addition -
-1/2x < -28
Multiply (-1) to both the sides -
-1/2x × (-1) < -28 × (-1)
1/2x < 28
Then move the coefficient of variable to right hand side of the equation -
x < -1 / (2 × (-28))
Then use arithmetic operation of multiplication and division-
x < 1/56
Therefore, the inequality is 0 < x < 1/56.
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If m∠HZJ = 38°, what is m∠FZG
Answer: 38 degrees
Step-by-step explanation:
HZJ and FZG are congruent angles so then that means that they are the same 38 degrees.
(PLEASE HELP ME ASAP THIS IS DUE TODAY)
An image of a parallelogram is shown.
A parallelogram with a base of 22 and one-half feet and a height of 19 and one-fourth feet.
What is the area of the parallelogram?
423 1/2 ft
427 1/2 ft
433 1/8 ft
455 1/8 ft
Answer:
433 1/8ft
Step-by-step explanation:
this is my answer
Write an equivalent expression without parentheses. Then simplify the result.
7m- (2+4m)
Which expression is equivalent to 7m - (2 + 4m)?
OA. 7m-2-4m
OB. 7m.-2+ 4m
OC. 7m+2-4m
OD. 7m + 2 + 4m
The equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m. The first option from the given options is
Equivalent expressions.Algebraic expressions that produce the same final expression are said to be equivalent expressions. If the values of two algebraic expressions can be obtained by replacing the variables, then the expressions are equivalent. Using the equal symbol (=), equivalent phrases are represented or illustrated to one another.
From the information given;
= 7m - (2 + 4m)
= 7m - 2 - 4m
Therefore, we can conclude that the equivalent expression to 7m - (2 + 4m) is 7m - 2 - 4m.
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Farmer Quect started with 110 rews on his farm. Every hour, he destoryed 6 more of them. Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them?
Write a systems of equations in slope intercept form. Farmer's rews (y), hours (x)
The systems of equations in slope intercept form is
y = -6x + 110
y = 9x + 54
What is Slope- intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
As, We know Slope-intercept form is
y = mx + b
where b is the starting value and m is the change per day.
Farmer Quect started with 110 rews on his farm. Every hour he destroyed 6 more of them.
So, the Equation to show the Situation
y = -6x + 110
and, Farmer Mimstone started with 54 rews on her farm. Every hour she collected 9 more of them.
So, the Equation to show the Situation
y = 9x + 54
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Which one of the following points lies on the line 3x=2x-1
The point (-1, 2) lies on the line 3x = 2x - 1.
The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.
So the line passes through the point (-1, y) for any value of y.
To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.
a) (0, -1)
3(0) = 2(0) - 1
0 = -1
This point does not lie on the line.
b) (-1, 2)
3(-1) = 2(-1) - 1
-3 = -3
This point does lie on the line.
c) (1, -4)
3(1) = 2(1) - 1
3 = 1
This point does not lie on the line.
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