The height of the room is 5 m.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Length = 7 m
Width = 2 m
Height = x
Four walls of a room will have,
Two walls of length x height.
Two walls of Width x height.
Now,
Area four walls of the room = 90 m
2 (length x height) + 2 (Width x height) = 90
2 (7x) + 2 (2x) = 90
14x + 4x = 90
18x = 90
x = 5
Thus,
Height of the room = 5 m.
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In bags of Happy Trail Mix, the number of raisins is skewed left with a mean of 33. 6 and a standard deviation of 8. 4, while in bags of a generic trail mix, the number of raisins is skewed right with a mean of 28. 8 and a standard deviation of 12. 7. What is the probability in a sample of 17 randomly selected Happy Trail Mix bags and a sample of 17 randomly selected generic bags that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix?
The probability that the mean number of raisins in the Happy Trail Mix is more than the mean number of raisins in the generic mix is 9.7%.
To solve this problem, we need to use the central limit theorem, which states that the distribution of the sample means approaches a normal distribution as the sample size increases. With a sample size of 17, we can approximate the distribution of the sample means as normal.
Let's call the mean of the Happy Trail Mix sample x and the mean of the generic mix sample y.
Using the formula for the mean of a normal distribution, we can find the mean of x and y:
μx = μ = 33.6
μy = μ = 28.8
Using the formula for the standard deviation of the sample mean, we can find the standard deviation of x and y:
σx = σ/√n = 8.4/√17 = 2.04
σy = σ/√n = 12.7/√17 = 3.08
Now that we have the mean and standard deviation of x and y, we can use a normal distribution calculator or a z-score table to find the probability that x > y.
The z-score is given by:
z = (x - y - μ)/σ = (33.6 - 28.8)/(√(2.04^2 + 3.08^2)) = 1.30
Using a standard normal table, we find that the probability of a z-score being greater than 1.30 is 0.097, or 9.7%.
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evaluate the function f (x) = -3x + 4 when x = -6
Answer:
x=−3⋅−6+4=x=22
Step-by-step explanation:
A company want to decreae their energy ue by 11%. If their electric bill i currently $1,700 a month, what will their bill be if they are ucceful? Give your anwer accurate to at leat the nearet dollar.
$
If the company' electric bill for next month i $1547, hould that be conidered a ucce?
Ye, that i a ucce
No, that i not a ucce
No, that i not a ucce, the electric bill need to be amount $1530 or le to be conidered a ucce.
To calculate the electric bill after the 11% decrease, simply multiply the current electric bill by 0.89, which is 1-11%. This will give you the new electric bill.
$1700 x 0.89 = $1530
Therefore, if the company's electric bill for next month is amount $1530 or less, then that would be considered a success.
The company must reduce their electric bill to $1530 or less in order to be considered successful in decreasing their energy usage by 11%.
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write the expanded form of the expression
4(3x-5)
4 (3x-5)=
One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation. So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
How do you write in a more detailed format?One technique to write numbers such that you can see the mathematical significance of each individual digit is in expanded form or expanded notation.
It is also possible to create a mathematical expression using integers that have been divided into distinct place values and decimal places.
5,000 + 300 + 20 + 5 = 5,325 is the expanded notation for the number.
Expanded form of the given expression.
1) We can expand the given term by the direct formula of the algebra
(A-B)³ = A³-B³-3AB(A-B)2)
We have (3x-5)³on comparing with the formula:
A = 3x
B = 5
(3x-5)³
(3x)³-5³-3×3x×5(3x-5)
27x³-125-45x(3x-5) 27x³-125-135x²+225x
So the expanded form of (3x-5)³ is 27x³-135x²+225x-125.
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A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded. Number of Hours Total Number of Students 0 1 1 3 2 3 3 10 4 9 5 6 6 3 Determine the probability that a student studied for exactly 5 hours. Round to the nearest hundredth.
According to the given information in the question rounded to the nearest hundredth, the probability is 0.14.
How is probability determined?Probability is a measure of how likely something is to occur. The probability is computed by dividing the total possible outcomes by the number of possible ways the event could occur.
What is the simplest approach to answer questions about probability?Adding the probabilities together will yield the chance of a simple event occurring. Your total chances of acquiring something are 10% + 25% = 35%, for instance, if you have an 10% opportunity to win $10 and a 25 percentage chance of getting $20.
The probability of a student studied for exactly 5 hours can be calculated using the formula for probability of a discrete event:
P(X = 5) = (number of ways to get a 5) / (total number of outcomes)
From the data provided, we know that 5 students studied for 5 hours. And there were a total of 35 students surveyed. So the probability is:
P(X = 5) = 5/35 = 0.14
Rounded to the nearest hundredth, the probability is 0.14.
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Determine whether the pairs of triangles are congruent.
~Circle yes, no, or not enough information. Explain your choice.
Three equidistant dots on each of two parallel lines are joined in all possible ways, how many triangles can be formed ?
Answer:
only one triangle can be formed ...
simplify (6 x 10^-3) (4 x 10^-3) Write the answer in scientific notation.
Answer: 2.4 x 10^-2
Step-by-step explanation:
6 x 4 = 24 (you can do this because powers are the same)
24 x 10^-3
2.4 x 10^-2
A car travels down the road at a constant speed of 120 meters in 5 seconds. What is the velocity of the car
Answer: 17 m/s
Step-by-step explanation:
what is WD?
what is AB + DC
what is the perimeter of the trapezoid?
Perimeter (P) = AB + BC + CD + DA.
What is perimeter of trapezoid?The perimeter of a trapezoid is the sum of the lengths of each side of the trapezoid. A trapezoid is a quadrilateral that has two sides parallel to each other and two non-parallel sides termed as bases and legs respectively. Let us learn how to calculate the perimeter of the trapezoid in this article.
perimeter of the trapezoid=sum of 4 side
=AB+BC+CD+DA
Perimeter (P) = AB + BC + CD + DA.
It can also be written as a sum of lengths of parallel sides and the sum of lengths of non-parallel sides where AB and CD are the parallel sides and AD and BC are the non-parallel sides.
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Find the probability of rolling
a 7 when you toss two fair 6-
sided dice and add the result
from each die.
Answer:
B. [tex]\frac{1}{6}[/tex]
Step-by-step explanation:
imma human calculator and no one can stop me
Does 4x - 8 = 3x +13 have one solution, no solution or infinite solutions
Answer:
only one solution
Step-by-step explanation:
4x - 8 = 3x + 13
x = 21
Hey there!
Given:
[tex]4x-8=3x+13[/tex]
Solution(s):
One Solution; [tex]x=21[/tex]
Hope this helps!
i do a lot of exrcice but in the exame i can"t anwer any quetion i don t know what i the recent
Exercise can be beneficial for academic performance in a variety of ways.
Improved cardiovascular health, for example, can lead to improved blood flow to the brain, providing a better environment for learning and memory formation. Exercise can also improve mental health, reduce stress, and increase energy levels, helping to better prepare for tests and exams. Finally, exercise can help to improve concentration, focus, and overall cognitive function.
The formula for calculating the potential benefits of exercise on academic performance is:
Academic Performance = Exercise + Improved Cardiovascular Health + Mental Health + Stress Reduction + Energy + Concentration + Focus + Cognitive Function
By increasing the amount of exercise, the individual can increase their academic performance. This is done by improving cardiovascular health, mental health, stress levels, energy, concentration, focus, and cognitive function. All of these factors play a role in academic performance, and increasing any one of them can lead to an overall improvement in academic performance.
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PLS HELP
What is in decimal form?
16
O 0.3125
O 0.6875
O 1.45
OI don't know.
Answer:
decimal form is limited of 3 numbers after the point only.
so it will be 1.45
I hope I help you in this ans and tq.
a spinner has eight equal-sized sections numbered 1 through 8. the spinner is spun twice. what is the probability of first spinning an odd number then spinning an even number?
The probability of spinning an odd number first then spinning an even number is 3/8 x 4/8 = 12/64.
This can be expressed as a fraction, decimal, or percentage. As a fraction, this probability is 12/64. As a decimal, this probability is 0.1875. As a percentage, this probability is 18.75%.
To calculate this probability, we first need to calculate the probability of spinning an odd number first. Since there are eight sections and four of them are odd numbers (1, 3, 5, 7), the probability of spinning an odd number is 4/8. We then need to calculate the probability of spinning an even number. Since there are four even numbers (2, 4, 6, 8), the probability of spinning an even number is 4/8. Finally, we multiply these two probabilities together to get the probability of spinning an odd number first then spinning an even number, which is 3/8 x 4/8 = 12/64.
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How many solutions does the equation 6x + 12 = 2(3x + 6)
Answer: Infinite, or unsolvable
Step-by-step explanation:
6x + 12 = 2(3x+6)
6x + 12 = 6x + 12 <-- opening up the bracket
Because both sides of the equation are the same, the answer is either that there are an infinite amount of solutions for x, or that the equation is unsolvable.
If a steel nail is wrapped 8 times with an insulated copper wire and each end of is attached to a 1.5 V single-A battery we find that it will lift the weight of 2 paper clips. Hypothesis: If 8 more coils are added to the nail we will be able to pick up twice as many paper clips. When we ran the experiment, we observed and recorded that when we added 8 more wraps around the nail (16 coils) we could lift 4 paper clips and when we added 8 more wraps (24 coils) we could lift 6 paper clips. Which of the following is/are true?
I. Something went wrong with the experiment since it didn't give us the results we expected.
II. The hypothesis was supported with the results of the experiment.
III. It can be concluded that every time 8 wraps are added to the nail, the total number of paper clips lifted doubles.
II and III only
II only
I only
I and III only
All of the statements that are true include the following:
II. The hypothesis was supported with the results of the experiment.
III. It can be concluded that every time 8 wraps are added to the nail, the total number of paper clips lifted doubles.
Therefore, the correct answer option is: A. II and III only.
What is a hypothesis?In Science, a hypothesis is primarily considered to be a tentative or an educated guess and it can be defined as a testable explanation for an observation, result, or a specific experimentation (scientific) problem, especially through the use of the "if . . . then . . . because" format.
Based on the information provided about this experiment, we can reasonably infer and logically deduce that the hypothesis developed about the steel nail is true because when eight (8) wraps of an insulated copper wire are added to the steel nail, the total number of paper clips that would be lifted is twice as many paper clips.
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a college runner set a school record of 3 minutes and 59.37 seconds in the mile run. assuming that the distance was measured accurately to five significant figures, what was the runner's average speed in kilometers per hour? assume 1 km
The runner's average speed in kilometers per hour is 24.257 km.
The total distance covered by the runner is 1 mile. The relation between kilometers and miles is given as 1 km = 0.62 mi. Converting 1 mile to km by using the given relation, we get-
Distance = 1 mile
= 1 mile × [1 km/0.62 mile]
= 1.6129 km
The time taken to complete a 1-mile run is 3 minutes and 59.37 seconds. The relation between hours and minutes is given below.
1 hour = 60 minutes ……(1)
Converting 3 minutes to hours using equation (1), we get-
3 minutes = 3 minutes × [1 hour/60 minutes]
= 0.05 hours
The relation between hours and seconds is given below.
1 hour = 3600 second …….(2)
Converting 59.37 seconds to hours using equation (2), we get-
59.37 seconds = 59.37 seconds × [1 hour/3600 seconds]
= 0.016492 hours
Total time to cover 1 mile = (0.05 + 0.016491) hours = 0.066492 hours
The average speed of the runner is calculated by the following relation-
Average Speed = Distance (km)/time (hours)
= 1.6129 km/0.066492 hours
= 24.257 km/hour
Therefore, the average speed in kilometers per hour is 24.257km.
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Solve quadratic functions
Identify the a,b and c for each quadratic equations . The substitute into the quadratic formula to solve .find the solutions using technology.
1) b^2 -4=0
The required solution of the given quadratic equation are 2 or -2.
What is Quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x ax² +bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution.
According to question:We have,
b² -4=0
Here we will use identity a² - b² = (a+b)(a-b)
Then,
b² -4=0
b² - (2)² = 0
(b + 2)(b - 2) = 0
b + 2 = 0
b = -2
Or b - 2 = 0
b = 2
Thus,required solution of the quadratic function are 2 or -2.
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7. If WXWZ, what theorem
can be used to show that
APXW = APZW?
8. If XZ LWY and XY = ZY, what
theorem can be used to show that
AXYP = AZYP?
9. If XW || YZ and ZXWZZZYX,
what theorem can be used to show
that AXWZ = AZYX?
For the right triangles below, find the values of the side lengths c and h.
Answer:
the answer is
c = 4
and h = √2/10
Find the 9th term of the geometric sequence
9
,
−
18
,
36
,
.
.
.
9,−18,36,...
Answer: This is a geometric sequence, because each term is obtained by multiplying the previous term by a constant ratio. In this case, the ratio is -2.
To find the 9th term, we can use the formula for the nth term of a geometric sequence:
a_n = a_1 * r^(n-1)
where:
a_n is the nth term of the sequence
a_1 is the first term of the sequence (9)
r is the common ratio (-2)
n is the term number (9)
Plugging in the values:
a_9 = 9 * (-2)^(9-1) = 9 * (-2)^8 = 9 * -256 = -2304
So the 9th term of the sequence is -2304
what is the x-intercepts of the following equation: f(x)=x^2+1
X intercept is none , y intercept is (0,1)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
the distance from the origin to a point where a graph crosses a coordinate axis. : interception.
The x- and y-intercepts of a line, or linear equation intercepts, are often used in problems involving lines and their graphs. Linear equation intercepts are important points to be able to understand and decipher in applications of linear equations problems and can also be used when graphing lines.
f(x)=x^2+1=0
so the x intercept is none and y intercept is (0,1)
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A. Sketch a cube and label its side length as 4cm (this will be Cube A).
B. Sketch a cube with sides that are twice as long as Cube A and label its side length (this will be Cube B).
C. Find the volumes of Cube A and Cube B.
Answer:
see attached
Step-by-step explanation:
The area of the cross section of the prism is 30 cm2.
The length of the prism is 25 cm.
Work out the volume of the prism?
The required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.
Area of cross section of the prism = 30 cm²
Length of the prism = 25 cm
Volume of the prism = ?
A prism is a polyhedron consisting of an n-sided polygon base. The relation between volume, base area and height of the prism is mathematically given as,
V = B H
where, B is Base area
H is Height of prism
V = 30 × 25 = 750 cm³
Thus, the required volume of the prism when area of cross section of the prism and the length of the prism are given is calculated to be 750 cm³.
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How can I set up an equation to help solve this problem?
Check the picture below.
Question 4(Multiple Choice Worth 2 points)
(Slope MC)
A linear relationship is given in the table.
x −2 −1 0 1 2
y −13 −9 −5 −1 3
What is the slope of the relationship?
one fourth
negative one fourth
4
−4
The slope of the relationship is equal to; C. 4.
How to calculate the slope of a line?In Mathematics, the slope of any straight line can be calculated by using this mathematical expression;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
From the information provided above, we have the following data points on the line:
Points on x-axis = (-2, -1).Points on y-axis = (-13, -9).Substituting the given points into the slope formula, we have;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-9 + 13)/(-1 - (-2))
Slope (m) = 4/1
Slope (m) = 4
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rosie says she could solve 24*25 with the arry above. do you agree with her why or why not.
She could only solve 24 * 25 if the array has 24 rows and 25 columns or vice versa
How to determine the true statementFrom the question, we have the following parameters that can be used in our computation:
Product expression = 24 * 25
An array is a set of items that has rows and columns
The array is not given
However, the true statement is that: for Rosie to evaluate the expression using an array, then the array must be a 24 x 25 array or 25 x 24 array
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Please anwser this...
Check the picture below.
sing horizontal analysis, the increases and decreases are shown as a.amounts and percentages for each line item. b.amounts for the highest three lines. c.amounts only for each line item. d.percentages only for each line item.
Answer: D. percentages only for each line item.
Horizontal analysis, also known as trend analysis, is a method of financial statement analysis that compares line items over time by expressing them as a percentage of a base year. The base year is typically the most recent year, and the comparison is typically made to the prior year. In horizontal analysis, the increases and decreases are shown as percentages for each line item, so that the changes in the line items can be easily compared and analyzed. This is different from vertical analysis, which shows the line items as a percentage of a total, such as total assets or total revenue.
Step-by-step explanation: