Answer: Let the width of the rectangle be w and the length be l. We are given that the area of the rectangle is 45 cm^2, so we can write the equation:
w * l = 45
To find the lengths of the sides, we need to solve for w and l. We can divide both sides of the equation by any non-zero number to find an equivalent expression. For example, we can divide both sides by 9:
(w/9) * (l/9) = 45/9
Simplifying, we get:
w/9 * l/9 = 5
So, w/9 = 5/l and w = 5l/9.
Substituting the expression for w into the original equation, we get:
(5l/9) * l = 45
Expanding and simplifying, we get:
5l^2/9 = 45
Multiplying both sides by 9, we get:
5l^2 = 405
Dividing both sides by 5, we get:
l^2 = 81
Taking the square root of both sides, we get:
l = 9
So, the length of the rectangle is 9 cm. To find the width, we can substitute the value of l back into the expression we derived earlier:
w = 5l/9
w = 5 * 9 / 9
w = 5
So, the width of the rectangle is 5 cm.
The lengths of the sides of the rectangle, both exactly and approximately, are 9 cm and 5 cm.
Step-by-step explanation:
cylinder has a volume of 157 cm³. If the radius of the cylinder is 1 cm, what is its height? 3.14
The height of the cylinder whose volume has been given above would be = 50cm
How to calculate the height of a cylinder?The volume of a cylinder can be calculated with the formula = πr²h
Where Volume = 157cm³
radius = 1 cm
height = X cm
π = 3.14
That is, 157 = 3.14 × 1² × X
make X the subject of formula;
X = 157 /3.14
X = 50cm
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A room measures 10m by 6m by 3m the volume of airspace needed for one person is 5m3 find the maximum number of person who may use the room at the same time
The number of persons that can use the room at the same time is 36.
The volume of the cuboid = length x width x height
The room is a cuboid.
Volume of the room = length x width x height
L = 10m, W = 6m, Height = 3m.
Volume = 10 x 6 x 3 = 180 cubic meter.
If each person takes 5 cubic meter of air space,
Then the total person who can occupy the room at the same time is 180/5 = 36.
A cuboid is a three-dimensional geometric shape that is bounded by six rectangular faces, where each face is a parallelogram. It is also known as a rectangular prism. The faces of a cuboid are called its base and lateral faces. The base of a cuboid is the top and bottom rectangular faces, while the lateral faces are the four rectangular faces that connect the base.
Cuboids have eight vertices or corners, where three edges meet, and 12 edges, which are the straight lines that connect the vertices. The length, width, and height of a cuboid are the dimensions of the three pairs of parallel sides of its rectangular faces, and these measurements are usually denoted by l, w, and h, respectively.
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There are 800 students. Sixth grade has 226 and seventh grade had 275 how many eighth graders are there ?
We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. So, there are 299 eighth graders in the school.
We are given that there are 800 students in total, with 226 students in sixth grade and 275 students in seventh grade. To find the number of eighth graders, we can use the fact that the total number of students is the sum of the number of students in each grade level:
Total number of students = Number of sixth graders + Number of seventh graders + Number of eighth graders
Substituting the given values, we get:
800 = 226 + 275 + Number of eighth graders
Simplifying and solving for the number of eighth graders, we get:
800 = 501 + Number of eighth graders
Number of eighth graders = 800 - 501
Number of eighth graders = 299
Therefore, there are 299 eighth graders in the school.
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A pet store has 6 cats. Here are their weights (in pounds).
13,9 ,9 ,15 ,12 , 16
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
Answer: About 50 lbs
Step-by-step explanation:
Answer:
12.3
Step-by-step explanation:
To find the mean you have to add all the numbers and divide by the number of numbers.
They add up to 74 and divided by the number of numbers(6)
you get 12.333...
Then yiu round up to 12.3
Can someone help me with this question ??
The length of x is given as follows:
x = 3.6.
What are similar polygons?Similar polygons share these two features listed as follows:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.In the context of this problem, the proportional relationship for the side lengths of the polygons is given as follows:
x/3 = 2.4/2 = 4.8/4 = 6/5.
The relationship can be simplified as follows:
x/3 = 1.2.
Applying cross multiplication, the value of x is obtained as follows:
x = 3 x 1.2
x = 3.6.
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Which equation uses a unit fraction and a whole number to write a multiplication equation equal to 712
An equation that uses a unit fraction and a whole number to write a multiplication equation equal to 712 can be represented as:
712 = (1/N) * X
Where N is the unit fraction and X is the whole number. To find the values of N and X, we can isolate X on one side of the equation and divide both sides by (1/N):
X = (712 * N) / (1)
X = 712 * N
Now we can substitute the value 712 for the right side of the equation:
X = 712 * N
X = 712 / (1/N)
Finally, we can simplify the equation by dividing 712 by the reciprocal of N:
X = 712 * N
X = 712 / (1/N)
X = 712 * N / (1/N)
X = 712 * N * N
Now we have an equation in which X is equal to 712 times N times N. To find the values of N and X, we can use trial and error or other mathematical methods.
It is important to note that there may be multiple solutions to this equation, as there can be many unit fractions and whole numbers that multiply to equal 712. The goal is to find a combination of N and X that satisfies the equation and produces the desired result.
In conclusion, writing a multiplication equation equal to 712 using a unit fraction and a whole number is a common mathematical problem that can be solved by isolating the variable and dividing both sides by the unit fraction.
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given f(x)=2x^{2}+4 find f(3)
Answer: 22
Step-by-step explanation:
f(x) is basically the y of the function and we sent x=3. go back to the function and plug in 3 in the x. then solve 3^2=9 2x9=18 18+4=22 BOOOM MATHH
If the sum of two angles is 90 then angles are called ___angles
If the sum of two angles is 90 degrees, then the angles are called complementary angles.
Complementary angles are a type of angle relationship where two angles add up to exactly 90 degrees. In other words, when you add the measures of two complementary angles together, the sum is always equal to 90 degrees.
For example, if angle A measures 30 degrees, and angle B measures 60 degrees, then angle A and angle B are complementary angles, because 30 degrees + 60 degrees = 90 degrees.
Complementary angles are important in geometry and trigonometry, because they often appear in problems involving right triangles. In a right triangle, one of the angles measures 90 degrees, which means that the other two angles must be complementary.
For example, if one angle in a right triangle measures 30 degrees, then the other angle must measure 60 degrees, since 30 degrees + 60 degrees = 90 degrees.
Understanding complementary angles can be useful in a wide range of mathematical and real-world contexts. For example, in construction or engineering, understanding complementary angles can help ensure that structures are built at the correct angle to provide the necessary support and stability.
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move the lenghts to the lines in order from shortest to longest
shortest________ _________ __________ __________longest
1 kilometer 1 meter 1 millimeter 1 centimeter
Mackenzie has 8 markers. Ty has three times as many. If they combine their markers, how
many do they have?
Show your work
Answer:
32 markers
Step-by-step explanation:
Ty has 8 x 3 = 24 markers.
Together, they have 8 + 24 = 32 markers.
Given the following frequency table of preferred weekend activities
a. Complete the table and find the value of x.
X =
Movies Theme Totals
Parks
379
Male
X
Female 180
Totals
575
1000
Here is the completed table:
Movies Theme park Totals
Males 245 379 624
Females 180 196 376
Totals 425 575 1000
How to complete the table?Total number of people that watch movies = totals - total number of people that go to theme parks
1000 - 575 = 425
Total number of males that watch movies = total number of people that watch movies - number of males that go to the theme park
425 - 180 = 245
Total number of males = Total number of males that watch movies + males that go to the theme park
245 + 379 = 624
Total number of females = totals - total number of males
1000 - 624 = 376
Total number of females that go to theme parks = total number of females - total number of females that go to the theme park
376 - 180= 196
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Please Help WILL MARK BRANLIEST
Answer:
n = 7
Step-by-step explanation:
You have a geometric sequence with first term 625 and common ratio 1/5, and you want to know the number of the term whose value is 1/25.
Geometric sequenceThe general term of a geometric sequence is ...
tn = t1·r^(n-1)
Using the given values, we can solve for n:
1/25 = 625·(1/5)^(n-1)
1/(5^2·5^4) = 1/5^(n-1) . . . . . . divide by 625; write as powers of 5
Comparing exponents of 5, we have ...
6 = n -1
7 = n
The value of n for which tn = 1/25 is 7.
__
Additional comment
The attachment shows the first 7 terms of the sequence.
<96141404393>
PLEASE HELP ME ASAP
The equation of the graph is y = (5x + 10)/(x²-1).
The correct option is c.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The graph of the equation is given in the image.
From the graph:
When x = 0, then y = -10.
And when y = 0, then x = -2.
y = (5x + 10)/(x²-1)
Substituting the values,
we get,
when x = 0, then y = -10.
And when y = 0, then x = -2.
From the given choices:
The equation,
y = (5x + 10)/(x²-1) satisfies the points.
Hence, the equation is y = (5x + 10)/(x²-1).
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Find a vector equation and parametric equations for the line segment that joins P to Q.
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
The vector equation for a line segment that joins two points P and Q can be found by subtracting the position vectors of P and Q and representing the result as a vector from P.
The position vector of point P is given by [0, -4, 4] and the position vector of point Q is given by [1/2, 1/3, 1/4]. So, the direction vector of the line segment is found by subtracting the position vectors:
d = Q - P = [1/2, 1/3, 1/4] - [0, -4, 4] = [1/2, 5/3, -3/4]
The vector equation of the line segment can be written as:
r(t) = P + t * d = [0, -4, 4] + t * [1/2, 5/3, -3/4] = [t/2, -4 + 5t/3, 4 - 3t/4]
where t is a scalar parameter that varies from 0 to 1 to give the points on the line segment between P and Q.
The parametric equations of the line segment are:
x(t) = t/2
y(t) = -4 + 5t/3
z(t) = 4 - 3t/4
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Find a vector equation and parametric equations for the line segment that joins P to Q?
P(0, −4, 4), Q ( 1/2, 1/3, 1/4 )
vector equation r(t)
parametric equations x(t), y(t), z(t)
Which of the following equations has no solution?
A.m + 9 = 8
B.m - 3 = m + 3
C.m + 9 = 9 + m
D. All the choices
Answer:
B. m-3=m+3
Step-by-step explanation:
Because the others have a solution such as 0 and -1.
And That would eliminate D
Question in picture.
he possible values for c would be 31 and 41.
Option (D) is correct.
What is the quadratic equation?
A quadratic equation is a polynomial equation of the second degree, which means that it contains a variable raised to the power of two (usually x^2). The general form of a quadratic equation is:
[tex]ax^2 + bx + c = 0[/tex]
where a, b, and c are constants and x is the variable.
We have [tex](ax+2)(bx+7)=abx^2 +7ax+2bx+14=abx^2+(7a+2b)x+14[/tex]
Given, it is equal to 1[tex]5x^2+cx+14[/tex]
⇒ab=15 --- (1)
⇒7a+2b=c
Also given a+b=8 --- (2)
From equations (1) and (2), we can interpret that either of a or b are equal to 3 or 5
When a=3 and b=5, we have c=7(3)+2(5)=21+10=31
When a=5 and b=3, we have c=7(5)+2(3)=35+6=41
Hence, the possible values for c would be 31 and 41.
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Forest rangers at a state park have observed a decline in the rate of trees per
acre over a 5-year period. At the beginning of their observations, there was an average of 48 trees per acre. At the end of the 5-year period, there was an
average of 42 trees per acre. If this trend continues, how many trees per acre
will there be 412 years from the end of the 5-year observation period?
After 412 years there will be no trees at the state park.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
From the given information,
Slope(m) = (42 - 48)/(5 - 0).
Slope(m) = - 6/5.
b = 48, As y-intercept(0, 48).
Therefore, y = - (6/5)x + 48.
Now, y = - (6/5)×412 + 48.
y = - 446.4 trees per acre, But there will be no trees as it came out to be a negative value.
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QUESTION FOR FOR LIH04
i need answers to these fast!!
Answer: 4.) 9.4 inches, 5.) 12.6 inches
Step-by-step explanation:
4.) So basically one revolution is going around a circle which will be finding the circumference. The equation to finding the circumference is (2)x(pi)x(radius) so if the diameter is 3 inches then half of that is 1.5 inches which is the radius. Multiply 1.5 times pi and 2 which is 9.4 inches.
5.) Same thing multiply the radius which is 2 times 2 and pi. The answer is 12.6.
what is f(-3) given that f(x)=-x+2
Answer:
f(-3) = 5
Step-by-step explanation:
f(-3) → x = -3
f(x) = -x+2
f(-3) = -(-3)+2
f(-3) = 3+2
f(-3) = 5
one reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a popu- lation mean is that (a) z can be used only for large samples. (b) z requires that you know the population standard deviation s. (c) z requires that you can regard your data as an srs from the population. (d) z requires that the sample size is at most 10% of the population size. (e) a z critical value will lead to
One reason for using a t distribution instead of the standard normal curve to find critical values when calculating a level c confidence interval for a population mean is that (b) z requires that you know the population standard deviation s.
The t distribution is used when the population standard deviation is unknown and is estimated from the sample. The t distribution has fatter tails than the standard normal curve, which makes it more appropriate for smaller sample sizes. When the sample size is large, the t distribution approaches the standard normal curve, and the z distribution can be used instead.
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Question 6: Question 6 E 0/2 pts Which source of bias is most relevant to the following situation: A group of first time offenders are asked to rate their court-appointed defense attorney while their case is still being argued in court. Self-interest study voluntary response bias O nonresponse bias or missing data perceived lack of anonymity loaded or leading question Question 7: Question 7 < > In a study, the data you collect is Mood on a Happy/OK/Sad scale. This data is: Quantitative Qualitative (Categorical) Question 8: Question 8 < > Does this describe an observational study or an experiment? The gender of children born in January were tallied Experiment Observational Study
Perceived lack of anonymity is the source of bias that is most relevant to the given situation.
The data collected in the study, which is Mood on a Happy/OK/Sad scale, is qualitative or categorical data.
This describes an observational study.
What is Statistics?
Statistics is a field of study that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of mathematical and statistical methods to extract meaningful insights from data and to draw conclusions or make decisions based on the findings.
When individuals are asked to provide feedback on a court-appointed defense attorney while their case is still being argued in court, they may feel that their responses are not anonymous and that the attorney or the court may retaliate against them if they provide negative feedback. This can lead to a perceived lack of anonymity, which can influence their responses and bias the feedback they provide. They may feel pressured to provide positive feedback or may choose not to provide any feedback at all, leading to nonresponse bias or missing data.Therefore, the perceived lack of anonymity can introduce bias into the feedback collected in this situation.Qualitative data is data that represents characteristics or qualities, rather than quantities or numbers. In this case, the mood of the respondents is being measured using categories or labels, such as Happy, OK, or Sad. This type of data cannot be easily measured or expressed in numerical terms, and therefore is considered qualitative.On the other hand, quantitative data is data that can be measured and expressed in numerical terms. This type of data is usually represented by numbers and can be analyzed using statistical methods to draw meaningful conclusions. Examples of quantitative data include age, weight, temperature, and number of hours worked.In an observational study, the researcher observes and records data on the subjects without intervening or manipulating any variables. In this case, the researcher is simply tallying the gender of children born in January, which does not involve any intervention or manipulation of variables.On the other hand, in an experiment, the researcher manipulates one or more variables to observe the effect on the outcome variable. The researcher randomly assigns participants to different groups or conditions and controls one or more variables to determine cause-and-effect relationships.Since the gender of children born in January is being observed and recorded without any intervention or manipulation of variables, it is an observational study.Learn more about Statistics click here:
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Savi and Suri had a total of 40.00 savi had 3 times as many as suri how much does each have? Show working
Suri has 10.00, and Savi has 3 times as much, or 30.00.
What is algebraic expression?
When we use numbers and words to solve a mathematical problem, we are using algebraic expressions.
Let's use algebra to solve the problem.
Let's say Suri has x amount of money. Then we know that Savi has 3 times as much money, or 3x. We also know that together they have 40.00. So we can write an equation:
x + 3x = 40
Simplifying this equation, we get:
4x = 40
Dividing both sides by 4, we get:
x = 10
So Suri has 10.00, and Savi has 3 times as much, or 30.00.
To check, we can verify that their total is 40.00:
10 + 30 = 40
So, the solution checks out.
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Select all the statements that are true about rectangles
The statements that are true about rectangles are mentioned in options
A,B,C,E.
Rectangles -A shape with four sides and internal angles is a rectangle. The lengths of the other two sides are offset by two. The rectangle's diagonal sides are of identical length.
The opposite sides of a rectangle are equal and parallel to one another.
The diagonals cut each other in half, but not exactly.
All diagonals are the same length.
The rectangle's diagonals line up.
The total internal angles add up to the same value
Every internal angle has the same value.
A rectangle has congruent angles on all sides.
A rectangle's opposing angles are congruent.
We may thus infer that the statements about rectangles in the options are accurate based on the aforementioned features.
Q. Select all the statements that are true about rectangles.
A Diagonals are congruent.
B Diagonals bisect angles.
C Opposite angles are congruent.
D Diagonals are perpendicular.
E Diagonals bisect each other.
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Gary has 20 more candies than Mary. If Gary gives Mary 19 of his candies, Mary would have how many more candies than Gary?
Help!
Answer:
Mary would have 18 more candies than Gary
Step-by-step explanation:
x/2+4x=2 pls send a good explanation
Diego’s history teacher writes a test for the class with 30 problems. The test is worth 50 points and has two types of problems: multiple choice worth 1 point each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning
By using a system of equations of two variables the number of short answer problems is 10.
Total number of problems in the Test = 30
Maximum points of test = 50
Point of multiple choice = 1
Point of short answer problems = 3
Let the number of multiple choice questions is x and the number of short answer problems is y
So, x + y = 30 - (1)
and 1.x + 3.y = 50 ⇒ x + 3y = 50 -(2)
Equation (2) - Equation (1)
x + 3y - (x + y) = 50 - 30
2y = 20
y = 10
Put y = 10 in equation (1)
x = 30 - 10 = 20
Hence, the number of multiple-choice questions = 20 and the number of short answer problems = 10.
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a person stands on a bathroom scale. the reading is 150 lb. after the person gets off the scale, the reading is 2 lb. a. is it possible to estimate the uncertainty in this measurement? if so, estimate it. if not, explain why not. b. is it possible to estimate the bias in this measure- ment? if so, estimate it. if not, explain why not.
a) Yes, it is possible to estimate the uncertainty in this measurement. the measurement of 150 lb has an uncertainty of +/- 0.5 lb.
b) It is not possible to estimate the bias in this measurement without further information.
a) Uncertainty represents the range of possible values that a measurement can have due to the limitations of the measuring instrument or the process of measurement. In this case, the uncertainty can be estimated by considering the precision of the bathroom scale.
If the scale is precise to the nearest pound, then the uncertainty can be estimated to be half of the smallest graduation of the scale, which is 0.5 lb.
b)Bias represents a systematic error in a measurement, which can arise due to various factors such as the design of the measuring instrument or the process of measurement.
In this case, we do not have any information about the design of the bathroom scale or the conditions under which the measurement was taken. Therefore, we cannot estimate the bias in this measurement.
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i need to reask this:
I need help with this since my school switched teachers and we didnt take it and the new teacher is refusing to teach us it
let's pry open the triangles a bit and plug their values for the pythagorean theorem to get the hypotenuse, Check the picture below, those are only the first 4 triangles, notice the hypotenuse.
now let's move like the crab, backwards, let's do D first and then C
D)
well, since for the 1st triangle the root has a "2", that means "1+1", and it's pretty much the same for any subsequent triangle, so the rule must be
[tex]{\Large \begin{array}{llll} P_{n}=\sqrt{n+1} \end{array}}\hspace{5em}\textit{rule for the }n^{th}~triangle[/tex]
C)
what does that make the 9th one?
[tex]{\Large \begin{array}{llll} P_{9}=\sqrt{9+1}\implies P_9=\sqrt{10} \end{array}}[/tex]
help i dont understand this fully
