A rectangular prism has a base of 19 ft by 8 ft and a diagonal of 25 ft. Identify its height. Round to the nearest tenth.
Answer:
14.1
Step-by-step explanation:
To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.
d=l2+w2+h2−−−−−−−−−−√
Substitute 8 for l, 19 for w, and 25 for d
Then solve for h
25=82+192+h2−−−−√
Simplify.
25=64+361+h2−−−−√
Square both sides.
625=425+h2
Subtract 425 from both sides.
200=h2
Take the positive square root of both sides.
200−−−√=h
Round to the nearest tenth.
14.1≈h
Therefore, the height of the rectangular prism is about 14.1ft
Pretest: Unit 2
Question 3 of 20
Determine the number of solutions for the equation shown below.
4x+6=4x+6
A. 2
B. 0
C. Infinitely many
D. 1
SUBMIT
Answer:
infinitely many
Step-by-step explanation:
this equation is true for each and every value.
so its solutions are infinite
Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?
Answer: $200,000
Step-by-step explanation:
The price of her home is $200,000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
The closing costs run from 2% to 7% of the purchase price.
Approximate closing costs would range from $4,000 to $12,000.
Price of her home = x
This means,
2% of x = 4000
(2/100)x = 4000
(1/50)x = 4000
x = 4000 x 50
x = 200,000 ____(1)
7% of x = 12,000
(7/100)x = 12,000
x = (12,000 x 100)/7
x = 171428.57
x = 171429 _____(2)
Now,
From (1) and (2) we can say that,
x = $200,000
Thus,
$200,000 is the price of her home.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
The complete question:
The closing costs run from 2% to 7% of the purchase price.
Becky was told that based on the price of her home, her approximate closing costs would range from $4,000 to $12,000. How much was the price of her home?
what is The equation of The line
Answer:
y = (2/3)x + 10
Step-by-step explanation:
To find the equation of the line in slope-intercept form, y=mx+b, we need to know the slope and the y-intercept. The slope, or m, is rise over run. To find slope, we need to look at 2 points. For this question, I will be using the points (0,10) and (30,30). The rise, or change in y value, is 20, while the run, or change in x value, is 30. This means our rise over run in 20/30, or 2/3. Now that we have established the slope, or m, let's find the y-intercept, or b. To do this, you just need to look at where the line passes through the y-axis. In the image, you can see the line passes through the y-axis as x=10, making our y-intercept, or b, 10. Using this information, we can now find the equation of the line:
y = mx + b
m = slope, 2/3
b = y-intercept, 10
y = (2/3)x + 10
So, the equation of the line is y = (2/3)x + 10
If this answer helped you, please leave a thanks or a Brainliest!!!
Have a GREAT day!!!
HELP ASAPPPPPPPPPPP DUE IN TWO HOUR
The graph shows a function of the form f(x) = ab^x.
Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function.
The function shown in the graph must be the function f(x)=2×4ˣ
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: f(x)=abˣ and when x is equal to 0 then f(0)=2
also if x increases by the functions gets multiplied by 4
Thus if f(0)=2 then f(1)= 8 , f(2)=32
or the function can be rewritten as f(x)=2×4ˣ
Thus f(0)=2×4⁰
=2
f(1)=2×4¹
Hence, The function shown in the graph must be the function f(x)=2×4ˣ
Learn more about functions here:
https://brainly.com/question/28303908
#SPJ1
suppose x has a geometric distribution with probability 0.3 of success and 0.7 of failure on each observation. the probability that x is 4 is
the probability that x is 4 is given by the formula P(x) = [tex](1 - p)^(x-1) * p[/tex]
The formula for the probability of a geometric distribution is [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Given the probability of success (p) is 0.3, the probability of x being 4 would be:[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
P(x) = 0.0729 or 7.29%
The geometric distribution is a probability distribution for the number of failures before the first success in a series of independent trials.
In this problem, the probability of success (p) is 0.3 and the probability of failure (1-p) is 0.7.
Therefore, the probability that x is 4 is given by the formula [tex]P(x) = (1 - p)^(x-1) * p[/tex]
Plugging in the values of p and x, we get:
[tex]P(x) = (1 - 0.3)^(4-1) * 0.3[/tex]
This simplifies to
P(x) = 0.0729 or 7.29%
Learn more about probability here
https://brainly.com/question/11234923
#SPJ4
Prove the following vector identities which, among other ideas, extend the chain rule to vector operations. Use index notation. a(x), b(x)-vector functions of position x; ф(x) - scalar function of position NOTE: Begin with the expression on the left and derive the expression on the right. Try not to simply expand both sides and show that they are identical (iii) V - (V xa)-0 (vii) V ab (V aba (Vb)
Vector identities can be derived using index notation. The following vector identities are to be proved: (iii) V - (V xa) = 0, (vii) V ab = (V a)b + a(V b).
Starting with the left-hand side:
V - (V x a) = V + (a x V) (by definition of cross product)
Using the vector triple product, a x (b x c) = (a . c) b - (a . b) c, we get:
V + (a x V) = V + (V . a) a - (V . a) a
= V (since the second term cancels out with the first term)
Thus, V - (V x a) = 0.
(vii) V ab = (V x (b x a))
Starting with the left-hand side:
V ab = V (ab)
Using the scalar triple product, a . (b x c) = (a x b) . c, we get:
V (ab) = (V x b) . (a x a)
= (V x (b x a)) (since a x a = 0)
Thus, V ab = (V x (b x a)).
To learn more about index notation please click on below link.
https://brainly.com/question/15521685
#SPJ4
In preparation for the upcoming school year, a teacher looks at raw test scores on the statewide standardized test for the students in her class. Instead of looking at the scores relative to the norms in the state, the teacher wants to understand the scores relative to the students who will be in the class. To do so, she decides to convert the test scores into z-scores relative to the mean and standard deviation of the students in the class. The mean test score in her upcoming class is 202, and the standard deviation is 38.2. The following are the scores for some (not all) of her students. Complete the table using the dropdown menus. The teacher wants to identify those students who may need extra challenge or extra help. As a first cut, she decides to look at students who have z-scores above z = 2.00 or below z = -2.00. Identify the test score corresponding to each of the following z-scores. Round to the nearest whole number. For z = 2.00, test score = .For z - -2.00, test score = .
Z-scores are used to standardize a raw score by converting it into the number of standard deviations it is above or below the mean.
The formula to convert a raw score into a z-score is:
z = (X - Mean) / Standard Deviation
Where X is the raw score, Mean is the mean of the population, and Standard Deviation is the standard deviation of the population.
For z = 2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (2.00 * 38.2) + 202 = 238.4 + 202 = 440.4 (rounded to nearest whole number = 440)
For z = -2.00:
z = (X - Mean) / Standard Deviation
X = (z * Standard Deviation) + Mean
X = (-2.00 * 38.2) + 202 = -76.4 + 202 = 125.6 (rounded to nearest whole number = 126)
So for z = 2.00, the corresponding test score is 440, and for z = -2.00, the corresponding test score is 126.
To learn more about standard deviations please click on below link.
https://brainly.com/question/23907081
#SPJ4
Click on all the values that are equivalent to
-(2/3).
A.-2/-3
B.2/-3
C.-2/3
D.-3/-2
E.-3/2
F.3/-2
Answer:
-2/-3
Step-by-step explanation: Because -2/-3=2/3.
fill in the blank. because it is typically too expensive and too time consuming, researchers often select a/n___, a group of people that are representative of the larger population.
Because it is typically too expensive and too time consuming, researchers often select a sample, a group of people that are representative of the larger population.
A sample is a smaller group of individuals selected from a larger population for the purpose of studying and making inferences about the population. Sampling is used when studying the entire population is not feasible due to limitations in time, resources, or practicality. The goal is to select a sample that accurately represents the population in terms of key characteristics such as age, gender, education level, etc. The sample must be representative of the population, meaning that it should accurately reflect the characteristics of the population. This is important because any biases or inaccuracies in the sample can lead to incorrect inferences about the population. A well-selected sample should also have a large enough size to provide meaningful results, yet not be so large that it becomes difficult to manage or too expensive to study.
In conclusion, sampling is a crucial step in research because it enables researchers to study a portion of the population, rather than the entire population, in order to make inferences about the larger group.
Learn more about inferences :
https://brainly.com/question/29774121
#SPJ4
find two positive numbers that satisfy the given requirements. the second number is the reciprocal of the first number and the sum is a minimum
The two positive numbers are 1 and 1, depending on the given information.
Let first number be x. So, the second number is 1/x. Now, their sum is minimum, so representing the expression for given information -
Sum (x) = x + 1/x
Rewriting the expression -
Sum (x) = x + [tex] {x}^{-1} [/tex]
Finding the derivative
Sum' (x) = 1 + (-1) [tex] {x}^{-2} [/tex]
Sum' (x) = 1 + (-1)/[tex] {x}^{-1} [/tex]
Sum' (x) = (x² - 1)/x²
Now, to find the minimum -
x² - 1/x² = 0
Multiplying x² on Right Hand Side of the equation
x² - 1 = 0
Rewriting the equation
x = ± 1
As the numbers are positive, so x will be 1.
Learn more about derivative -
https://brainly.com/question/28376218
#SPJ4
A painting contractor determined the average amount of time needed to paint a house. When 2 painters are used, it takes 15 hours to paint • When 6 painters are used, it takes 5 hours to paint. If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?
The statement that is true about the proportional relationship is that; The time required to paint a house varies directly with the number of painters.
How to find proportional Relationship?The parameters are;
p represents the number of painters.
h represent the number of hours required to paint the house
In this case, the number of hours will be the output variable while the number of painters will be the input variable. Thus, we will have the relationship;
h = kp
where k is the constant of proportionality
When 2 painters are used, it takes 15 hours to paint and as such;
k = 15/2
k = 7.5 hours per painter
When 6 painters are used, it takes 5 hours to paint. Thus;
k = 5/6
k = 0.833 hours per painter
Thus, we can say that the time required to paint a house varies directly with the number of painters.
Read more about Proportional Relationship at; https://brainly.com/question/12242745
#SPJ1
Determine whether the mean, median, or mode would be the best choice to describe the center of the following set of data.
An elementary school has 92 first graders. They take a vocabulary test that estimates the number of vocabulary words they know. Most of the first-graders had a good start on language acquisition and knew between about 15,000 and 20,000 words. However, there were a few first-graders who were a little behind in language acquisition and only knew about 7,000 words.
Would it be best to use the mean, median, or mode to describe the number of vocabulary words that are understood by the first-graders?
To describe the number of vocabulary words that are understood by the first-graders is better to use the mode.
What is the difference between the mean, the mode, and the median?Mean= This refers to the average, which is obtained y adding all the data and dividing by the number of numerical values.Median= This is obtained by organizing the data and choosing the value that is right in the middle.Mode= This refers to the most common value or the value that is the most frequent.Based on this, the factor to be considered to know the number of words first-graders know is the mode because this is the most common number of words and the most accurate information.
Learn more about the mode in https://brainly.com/question/28566521
#SPJ1
Which of the following is equivalent to the rational expression below, where x≠1
?
The equivalent expression is x + 3 + 4/(x - 1)
Option A is the correct answer.
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,
(x² + 2x + 1) / (x - 1)
Now,
x² + 2x + 1
= x² + (1 + 1)x + 1
= x² + x + x + 1
= x(x + 1) + 1(x + 1)
= (x + 1)(x + 1)
= (x + 1)²
Now,
(x² + 2x + 1) / (x - 1)
= (x + 1)² / (x - 1)
Now,
x + 3 + 4/(x - 1)
((x - 1)x + 3(x - 1) + 4) / (x - 1)
= (x² - x + 3x - 3 + 4) / (x - 1)
= (x² + 2x + 1) / (x - 1)
Thus,
x + 3 + 4/(x - 1) is the equivalent expression.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ1
Simplify
6 (2x^2-5)=
x= -3
The value of the expression for x=-3 is 78.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6(2x²-5).
Here, x=-3
Substitute x=-3 in the expression 6(2x²-5), we get
6(2(-3)²-5)
= 6(18-5)
= 78
Therefore, the value of the expression is 78.
To learn more about an expression visit;
https://brainly.com/question/28170201.
#SPJ1
u can get brainliest just help me out asap
Which of the following results in the expression 0.86 x 22
0.22 of 86%
22% of 0.86
86% of 22
0.86 of 22%
86% of 22 is the correct answer
Superior Segway Tours gives sightseeing tours around Chicago, Illinois. It charges a one-time fee of $40, plus $35 per hour. What is the slope of this situation?
80
65
40
35
Answer:
d. 35
Step-by-step explanation:
y = 35x + 40
The slope is 35 as 'm' is the slope of the equation
LMK IF IT WAS RIGHT!!
Answer:
D (35)
Step-by-step explanation:
Given the rate per compounding period, find r, the annual rate.
0.425% per month
Answer:
Step-by-step explanation:
To find the annual rate given the rate per compounding period, we need to convert the rate from the compounding period to the annual period. In this case, the rate is given as 0.425% per month.
One way to convert the rate is to multiply it by the number of compounding periods in a year:
r = 0.425%/month * 12 months/year
r = 5.1%/year
Therefore, the annual rate, r, is 5.1%.
the following items are found around the house. they have weight. select the items that are most likely to be measured in ounces. paper bag frying pan can of pop table
The items that are most likely to be measured in ounces are a Paper bag, a can of pop, and a table.
The weight of objects is typically measured in units of mass, such as grams or kilograms, or in units of weight, such as ounces or pounds. In general, smaller and lighter objects are measured in ounces, while heavier objects are measured in pounds or kilograms.
In this case, the paper bag, can of pop, and table are likely to be measured in ounces. These objects are relatively light and can be easily lifted and weighed on a scale, which would make it convenient to use ounces as a unit of measurement. On the other hand, a frying pan is likely to be a heavier object and would typically be measured in pounds or kilograms.
Read more on Weights here:
https://brainly.com/question/2335828
#SPJ4
Find the measure of each angle please help
(picture included) show work please
1,3
Step-by-step explanation:
A car leaves a city at the rate of 60 mi/h and goes 80 miles before a second car follows at a rate of 70 mi/h. In this situation, let x= the number of hours, and y= the distance the car travels. The distance the first car travels can be represented by the equation y=60x+80.
Write the equation that represents the distance traveled by the second car.
The equation that represents the distance traveled by the second car is 60(t + 1.33).
Let t = travel time of the 2nd car when it overtakes the 1st
:
Find the travel time of the 1st car to go 80 mi; time = dist/speed
time = 80%2F60
time = 1.33 hrs for the 1st car to go 80 mi
therefore
(t+1.33) = travel time of the 1st car when it is overtaken
:
When the 2nd overtakes the 1st, they will have traveled the same distance
Write a distance equation, dist = speed * time
:
2nd car dist = 1st car dist
70t = 60(t+1.33)
70t = 60t + 80
70t - 60t = 80
10t = 80
t = 8 hrs travel time of the 2nd car to overtake the 1st
:
;
Confirm this by finding the actual distances, should be equal
70*8 = 560 mi
60*9.33 ~ 560 mi
Hence , the equation that represents the distance traveled by the second car is 60(t + 1.33).
Learn more about distance at:
https://brainly.com/question/24283318
#SPJ1
if x = 3 when y = 6, what is y when x = -2
Answer:
If y=6 when x=3 find y when x =-33.
Step-by-step explanation:
i need help with percentage homework
The percentage values are as follows: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
What is percent?A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount. percentage. Mathematics percentile is a related topic. A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100.
Here,
1a. 150% of 50
=1.5*50
=75
1b. 150% of 90
=1.5*90
=135
2a. 100% of 60
=1*60
=60
2b. 50% of 100
=0.5*100
=50
3a. 350% of 70
=3.5*70
=245
3b. 150% of 70
=1.5*70
=105
4a. 350% of 50
=3.5*50
=175
4b. 350% of 90
=3.5*90
=315
5a. 450% of 100
=4.5*100
=450
5b. 200% of 30
=2*30
=60
6a. 250% of 50
=2.5*50
=125
6b. 350% of 40
=3.5*40
=140
7a. 350% of 80
=3.5*80
=280
7b. 150% of 100
=1.5*100
=150
8a. 400% of 80
=4*80
=320
8b. 300% of 50
=3*50
=150
The value of percent are: 75, 135, 60, 50, 245, 105, 175, 315, 450, 60, 125, 140, 280, 150, 320, 150.
To know more about percent,
https://brainly.com/question/29172752
#SPJ1
Consider the following balls-and-bin game. We start with one black ball and one white ball in a bin. We repeatedly do the following: choose one ball from the bin uniformly at random, and then put the ball back in the bin with another ball of the same color. We repeat until there are n balls in the bin. Show that the number of white balls is equally likely to be any number between 1 and n − 1.
The number of white balls is equally likely to be any number between 1 and n−1.
Let W be the number of white balls in the bin after the nth iteration. W can be any number between 1 and n−1. We can calculate the probability of obtaining a specific number of white balls in the bin by considering the number of possible sequences of choices. There are 2^n possible sequences of choices as each choice is either a white ball or a black ball. The number of sequences in which W white balls are selected is (W choose 1)*(n−W choose 1), which is equal to W*(n−W). Therefore, the probability of W white balls in the bin after the nth iteration is P(W) = (W*(n−W))/(2^n).
Since P(W) is equal for all values of W between 1 and n−1, it follows that the number of white balls is equally likely to be any number between 1 and n−1.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
Solve the problem below. Be sure to show all calculations. Explanations given to justify your solutions must be given in complete sentences.
Given the figure to the right and the fact that m∠ABD= 133°, find the measurements of the angles below.
m∠ABC=___ m∠BCD=___ m∠ACB=___
The angle measures for this problem are given as follows:
m∠ABC = 112º.m∠BCD = 34º.m∠ACB = 34º.How to obtain the angle measures?ADC is an isosceles triangle, with an angle of 44º, hence the base angles have the measure given as follows:
2x + 44 = 180. (sum of the internal angles of a triangle).
2x = 136
x = 136/2
x = 68º.
Hence the measure of angles ACB and BCD is of 34º, as the bisection divides the angle into two angles of equal length.
Considering the two base angles of 34º, the measure of angle ABC is given as follows:
m < ABC + 2 x 34 = 180
m < ABC = 112º.
More can be learned about angle measures at https://brainly.com/question/30385318
#SPJ1
} problem 9. (10 pts) determine which of the following subsets of r 3 are subspaces of r 3 . you should use the subspace test from the lectures to show that a given subset is a subspace, or, if it is not a subspace, exhibit one of the axioms of a vector space that fails to be satisfied. (a) a
Options C and D are subsets of R³, which are {(-5x,4x,3x)| x arbitary} and {(x,y,z)| x+y+x=0}
A) Correct. We have to check whether the potential subspace containing the zero vector is a great place to start on these sorts of problems. No zero vector so this is not a subspace.
B) This is a subspace. The set of solutions of a homogeneous linear system is always a subspace it is known as a "null space" of some corresponding linear transformation.
Let, [tex]M=\left[\begin{array}{ccc}2&9&0\\8&0&-5\\\end{array}\right][/tex] then the set in B) is just Null(M). Again, Nullspaces are always subspaces.
Alternatively, you could solve the corresponding system Mx=0 and find the elements of that set [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex] for any choice of z∈R. So this
can be a set in the span of [tex]x=\left[\begin{array}{c}5/8&-5/36&1\\\\\end{array}\right][/tex]
C) Correct. we can see a subspace because the elements are just multiples of (−5,3,4) and again spans are subspaces.
D) Correct. This can be a subspace for the same reasons as part B.
E) Correct. Not a subspace. An easier counter-example: (1,1,1) is in there. But (−1)(1,1,1)=(−1,−1,−1) is not.
F) Not a subspace. (0,0,0) is not in there.
To know more about subsets:
https://brainly.com/question/14813912
#SPJ4
What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
The present value of the cash flows is $30,030.78.
What is the present value?In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.
Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78
To learn more about present value, please check: https://brainly.com/question/26537392
#SPJ1
What is the value today of $6,500 that is due in 414
years if the interest rate is 3.96% compounded semi-annually?
Answer:
approximately $4,609,968.67
Step-by-step explanation:
To calculate the future value of a lump sum after compounding over a certain number of years with a specific interest rate, you can use the formula:
FV = PV * (1 + r/n)^(nt)
Where:
FV is the future value
PV is the present value (6500)
r is the annual interest rate (3.96%)
n is the number of times compounded per year (semi-annually, so 2)
t is the number of years (414)
Plugging in the values, you get:
FV = 6500 * (1 + 0.0396 / 2)^(2 * 414)
The future value of $6,500 in 414 years at an interest rate of 3.96% compounded semi-annually is approximately $4,609,968.67.
_ /12 > 11/12 what is the missing ?
Answer: 12
Step-by-step explanation:
12/12 is greater than 11/12
12/12>11/12
Determine a the domain and range
The domain and range of a function is discussed above.
What is a function?An function in mathematics defines a relationship between one variable (the independent variable {x}) and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.
Given is the graph of the function as shown in the image.
Domain represents the set of values along the {x} - axis or the possible values of {x} for which f{x} exists.
Range represents the set of values along the {y} - axis or the possible existing values of f{x} for a specific value of {x}.
Therefore, the domain and range of a function is discussed above.
To solve more questions on functions, visit the link below -
brainly.com/question/26182329
#SPJ1