With Combination, There are the 98280 ways by which we place books on the shelf.
According to the statement
We have to find that the number of ways can by which place books on the shelf.
So, For this purpose, we know that the
A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
From the given information:
The library has 28 science fiction books. Each shelf holds 5 books
Then
apply the combination,
Then
C(n,r) = C(28,5)
after solving it become
C(28,5) = 28! /(5!(28-5)!)
And
C(28,5) = 28! /(5!(23)!)
Then after rearranging the terms and solving the value becomes
C(28,5) = 98280.
So, With Combination, There are the 98280 ways by which we place books on the shelf.
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Problem 2: A storm causes a 14m hydro pole to lean over. The pole leans at an angle of 72° to
the ground. How high is the top of the pole from the ground?
The top of the pole from the ground is 13.314798.
Given condition, formulate :
= 14 * sin (72°)
= 4 sin 72°
= 14 * 0.951057
= 13.314798
The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions) comprising trigonometry are the cosecant, cosine , cotangent , secant , sine , and tangent .
The trigonometric function can be described as being even or odd.
Odd trigonometric functions: A trigonometric function is said to be an odd function if f(-x) = -f(x) and symmetric with respect to the origin.
Even trigonometric functions: A trigonometric function is said to be an even function, if f(-x) = f(x) and symmetric to the y-axis.
Hence, the top of the pole from the ground is 13.314798.
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A casual fast food restaurant offers 4 different toppings that each can be served over one of 3 bases: a piece of fry bread, a salad, or on rice. Further, customers can choose one of 3 different sauces to be served with their order.
How many distinct filling-base-sauce combinations does a customer at this restaurant have to choose from?
Answer: 36 combinations
Step-by-step explanation:
Since you have 4 toppings, 3 bases and 3 sauces, you can just multiply them to get the different combos.
4 * 3 * 3
= 36
532,8 g = kg? [1]
O 5,328 kg
O 5 328 kg
O 0,532 8 kg
O 53,28 kg
O None of the given answers
Which set of numbers includes both rational and irrational numbers? Please HELPP IVE BEEN TRYING FOR 2 HRS
Answer: Option 2 should be the answer.
Step-by-step explanation: Real numbers are divided into two groups called rational and irrational numbers. Irrational numbers cannot be expressed as fractions.
Hopefully, this question will help you.
Have a great day!
Members of a softball team raised $1353 to go to a tournament. They rented a bus for $943.50 and budgeted $31.50 per player for meals. Write and solve an equation which can be used to determine x, the number of players the team can bring to the tournament.
equation:
x=
Answer:
13 players
Step-by-step explanation:
1353 - 943.50 = 409.50
$31.50 per player for meals
31.50*x = 409.50
x = 13
13 players
PLS HELP!! Write an equation in point-slope form for a line that passes through the given set of points. (-1,-2)(-3,1)
represent the expression please help
Answer:
10,350.98
Step-by-step explanation:
The decimal number is the sum of the terms of the expression.
Sum(1×10,000) +(3×100) +(5×10) +(9×1/10) +(8×1/100)
= 10,000 +300 +50 +0.9 +0.08
= 10,350.98
__
Additional comment
If you can't do this in your head, you can input the expression to your calculator, and it will give this same result.
Alejandro's goal was to ride 36 kilometers. His app says he rode 75% of his goal. How far did he ride?
Answer:
27 kilometers
Step-by-step explanation
i big brain and u not
u can use a calculator lol
Step up an inequality for this situation below. Define your variable, but do not solve.
Mr. Bass charges his music students $25 per lesson plus a recital fee of $50. How many lessons can a student take if they pay no more than $175?
The student can take 5 number of lessons if they pay no more than $175
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of music lessons. The student can pay no more than $175, hence:
25x + 50 ≤ 175
x ≤ 5
The student can take 5 number of lessons if they pay no more than $175
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LeAnn wants to gift wrap a present she got for her little brother. How many square inches of gift wrap will be needed to cover a box that is 4 in x 6 in x 2 in ? In your final answer, include all of your calculations.
All calculations for answer in picture form
Answer:
There are 88 square inches needed to cover a box that is 4 in • 6 in • 2 in
Step-by-step explanation:
In order to cover the box you need to find the surface area of it. The formula for finding the surface area of a rectangular prism is 2 • ((w•l) + (h•l) + (h•w)). The dimensions of the box is 4 inches in length, 6 inches in width, and 2 inches in height.
Apply the dimensions into the formula of the rectangular prism when the numbers are plugged in it results in 2 ( (6•4) + (2•4) + (2•6) )Multiply the dimensions the area of length• width is 24 (six times four is twenty-four), the area of height•width is 8 (two times four is eight), and the area of height•width is 12 (two times six is twelve). At the end of this step it becomes 2 • ((24) + (8) + (12))Add all the numbers inside the parentheses then it becomes 2 • (44) Multiply the number in parentheses by 2 the final answer is 88 in²if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2
The average velocity is -10 ft/s.
What is Average velocity?Average velocity is just the average speed with a direction. If a trip starts and ends at the same point, the total displacement is zero, so the average velocity is zero.
For example, someone who takes 40 minutes to drive 20 miles north and then 20 miles south (to end up at the same place), has an average speed of 40 miles divided by 40 minutes, or 1 mile per minute (60 mph).
Given:
f(t) = 20t - 10t²
Now, from t=1 to t=2
f(1)= 20*1 - 10 * 1*1
f(1)= 10
and, f(2)=20*2-10*2*2
f(2)= 40-40
f(2)=0
Now,
Average velocity:
v = ( 0-10 ) / ( 2- 1 )
= -10 ft/s
hence, the average velocity is -10 ft/s.
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Which number set is the most reasonable to describe a baby’s weight at birth?
Whole numbers
Rational numbers
Irrational numbers
Integers
Bailey Co earns $13249 of revenue on account and in $6167 cash revenue transactions in Year 1. Cash collections of receivables amount to $5849 in Year 1 with the remainder being collected in Year 2. Based on this information alone the company’s financial statements would show
Based on this information alone the company’s financial statements would show Cash inflows for Year 1 $13,567
What is cash inflow from sales?
The cash inflow from sales indicates the amount of cash received from customers in the current based on sales made to customers, which is the sales revenue, cash and credit added together minus the balance of credit sales left uncollected from customers at the end of the year.
Cash inflows for Year 1=credit sales+cash sales+receivables
credit sales=$13249
cash sales=$6167
receivables= $5849
Cash inflows for Year 1=$13249+$6167-$5849
Cash inflows for Year 1=$13,567
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Full question:
Bailey Co earns$13249 of revenue on account and in $6167 cash revenue transactions in Year 1. Cash collections of receivables amount to $5849 in Year 1 with the remainder being collected in Year 2. Based on this information alone the company’s financial statements would show Cash inflows for Year 1 $_
trista has 3 3/4 yards of ribbon to use for making decorative pillows. if the first pillow used 2 1/6yards of ribbon then how much risson is remaining
Answer:
1 1/2 yards
Step-by-step explanation:
Give Brainliest if I helped!
Round 24,990 to the nearest ten thousand
Answer:
30,000
Step-by-step explanation:
If not, try 25,000
Answer:
25,000
Step-by-step explanation:
brainlest please
Find the mean of the data set shown in the table below.
Data Set E
1.69
0.85
0.23
1.6
0.08
Answer this!!!!!!!!!!!!!!!!!!!!!!!!
Based on the distance between the park bench and the basketball court, the distance between the park bench and the pond is 57¹/₈ feet
What is the distance between the park bench and pond?The distance between the park bench and the basketball is the sum of the distance between the park bench and the pond and the pond and the basketball court.
The distance between the park bench and the pond is therefore:
= Distance between park bench and basketball court - Distance between pond and basketball court
Solving gives:
= 75³/₄ - 18⁵/₈
= 75.75 - 18.625
= 57.125
= 57¹/₈ feet
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Answer:h
el]lo you commented on a post that helped me alot
Step-by-step explanation:
Shreya is training for a marathon. The graph shows the miles she ran each day of her training. Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. How far did Shreya run on day 5 of her training? Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
She ran the distance on the day of 5 is 2miles.
Shreya did not plot the distance she ran on day 5 of her training, but you can calculate the distance she ran that day using the trend in the data she did record. Shreya ran 8 miles on day 5. Shreya ran 6 miles on day 5. Shreya ran 3 miles on day 5. Shreya ran 7 miles on day 5.
⇒ (8-6-3-7)/5
⇒ (-8)/5
⇒ 1.8
⇒ 2 miles
The fraction whose numerator is 8 minus 6 minus 3 minus 7, whose denominator is 5 which is equal to the fraction of 2 miles.
Hence, Shreya ran on the day of 5 in her training is 2 miles.
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The data represents the time in minutes spent reading a political blog in a day construct a frequency distribution focuses in the table include the midpoint related frequencies and cumulative frequencies which class has the greatest frequency in which class has the least frequency
The required midpoint of the given data is 16, and, class interval 10 - 15 has the higher frequency, and class interval 5 - 10 has a null frequency.
Here,
Arranging the time in minutes spent on reading a political blog in a day,
3 3 11 12 13 13 15 16 19 19 20 22 25 26 26
The required mid-point is 16.
Since the values vary from 3 to 26 and we have to make 5 classes,
So the number of
classes midpoint frequency cumulative
0 - 5 2.5 2 2
5 - 10 7.5 0 2
10 - 15 12.5 5 7
15 - 20 17.4 4 11
20 - 25 22.5 3 14
25 - 30 27.5 2 16
Thus, the required midpoint of the given data are shown, and, class interval 10 - 15 has the higher frequency, and class interval 5 - 10 has a null frequency.
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PLEASE HELP ME WITH THIS I HAVE A TEST TMR
Answer:
Go to Khan Academy and Search "Finding Slope from graph"
Step-by-step explanation:
That video will help better instead of typing it!
6. Bill can afford a monthly payment of $475. He wants to take out a $20,000 loan at 4.25%
interest rate. What should the length of the loan be? Round your answer to the nearest year.
====================================================
Work Shown:
L = 20,000 = loan amountP = 475 = monthly paymenti = 0.0425/12 = 0.0035417 approximately is the decimal form of the monthly interest raten = unknown number of monthsLet A = P/i = 475/0.0035417 = 134116.384787 approximately
Then,
[tex]n = \frac{\text{Ln}(A) - \text{Ln}(A-L)}{\text{Ln}(1+i)}\\\\n \approx \frac{\text{Ln}(134116.384787) - \text{Ln}(134116.384787-20000)}{\text{Ln}(1+0.00354)}\\\\n \approx \frac{11.80646 - 11.64497}{0.00353}\\\\n \approx \frac{0.16149}{0.00353}\\\\n \approx 45.74788\\\\n \approx 46[/tex]
It will take about 46 months to pay off the loan.
Divide by 12 to convert from months to years.
46 months = 46/12 = 3.83333 years approximately
That rounds to 4 years
I have no clue, someone help me out
An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Hills region has the advantage for sheep production because when a farmer raised 2 bushels of grain, then gaze 4 sheep.
The most popular animal fiber is sheep's wool, which is often gathered by shearing. In Commonwealth nations, ovine meat is referred to as lamb when it comes from younger animals and mutton when it comes from older ones; in the United States, meat from both older and younger animals is often referred to as a lamb.
Today, sheep are still farmed for their meat and wool, as well as on occasion for their pelts, as dairy animals, or as scientific model organisms. Most of the world's populated areas engage in sheep farming, which has been a foundational activity for several civilizations.
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An accounting machine operator wanted to divide a 65 minute job between two identical machines so that one machine would take one and a half times as long as the other. How much time was taken by the machine doing the longer job?
The slow machine did the job is 39 minutes as calculated with the help of a linear equation in one variable.
A linear equation in one variable is given by the combination of the variable with constants and coefficients such that a unique relationship is established between the terms.
Let us consider the faster machine takes x minutes the finish the job.
Hence the slower machine will take one and a half times .
∴ slower machine takes 1.5 x minutes.
Total time taken by the two machines = x + 1.5x = 2.5 x
But together the two machines will take 65 minutes to complete the job .
So now we form a linear equation with the variable x to solve for the value of x
∴ 2.5 x = 65
or, x = 65 ÷ 2.5
or, x = 26 minutes
Therefore the faster machine takes 26 minutes.
Hence the slower machine will take 1.5 x = 1.5 × 26 = 39 minutes.
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Use algebraic methods to prove that the given function has an x-intercept that is equal to its y-intercept. In your final
answer, include all of your calculations.
y= x/x^2-1
Step-by-step explanation:
the y-intercept is the y value when x = 0.
the x-intercept is the x value when y = 0.
for x = 0
y = 0 / (0² - 1) = 0/-1 = 0
this automatically answers also our question about the x value when y = 0. we found this out already with the y-intercept.
the interception point with both coordinate axis is (0, 0).
please help
maths geometry
Step-by-step explanation:
ABCD is a rectangle.
so, it has 2 pairs of equal and parallel sides.
all 4 angles are 90°.
both diagonals are equally long and intersect each other at their midpoint. so, all 4 half-diagonal segments are equally long.
(1)
2x + 4y = 4x - y = 36/2 = 18 cm
we can split this into 2 equations
2x + 4y = 4x - y
5y = 2x
x = 5y/2
and e.g.
4x - y = 18
now we use the first equation in the second
4(5y/2) - y = 18
20y/2 - y = 18
10y - y = 18
9y = 18
y = 2
x = 5y/2 = 5×2/2 = 5
(2)
I cannot draw here, but the shortest distance between a point and a line is always a height (a line segment from the point meeting it intersecting the line at a right angle, 90°).
(3)
e.g.
AE, AD/2 and the drawn height from E to AD create a right-angled triangle.
we know AD/2 = 15 cm
from (1) we know AE = 4x - y = 4×5 - 2 = 20 - 2 = 18 cm.
the height E to AD we get via Pythagoras
AE² = (AD/2)² + height²
height² = AE² - (AD/2)² = 18² - 15² = 324 - 225 = 99
height = sqrt(99) = sqrt(9×11) = 3×sqrt(11)
remember trigonometry ?
this height = sin(theta) × AE
sin(theta) = height / AE = 3×sqrt(11) / 18 = sqrt(11)/6 =
= 0.552770798...
theta = 33.55730976...° ≈ 34°
(4)
the diagonals of a square bisect the angles of the square, so that theta would become 90/2 = 45°.
Evaluate. Write your answer as a fraction in simplest form. 3/8 - 1/6 + 5/12
Answer:
5/8
Step-by-step explanation:
Get LCD of 24 and do the math
9/24 - 4/24 - 10/24
15/24
Divide top and bottom by 3
5/8
To test the ability of mechanics to identify simple engine problems, a car with a single such problem was taken in turn to 72 different car repair facilities. Only 42 of the 72 mechanics who worked on the car correctly identified the problem. Does this strongly indicate that the true proportion of mechanics who could identify this problem is less than 0.75?
a) Perform the appropriate test of hypothesis using = 0.01. Clearly show the eight (8) steps
Using the z-distribution, it is found that since the p-value is less than 0.01, there is strong indication that the true proportion of mechanics who could identify this problem is less than 0.75.
What are the hypotheses tested?At the null hypotheses, it is tested if there is not enough evidence that the proportion is less than 0.75, that is:
[tex]H_0: p \geq 0.75[/tex]
At the alternative hypotheses, it is tested if there is enough evidence that the proportion is less than 0.75, that is:
[tex]H_1: p < 0.75[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.For this problem, the parameters are given as follows:
[tex]n = 72, \overline{p} = \frac{42}{72} = 0.5833, p = 0.75[/tex]
Hence the test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.5833 - 0.75}{\sqrt{\frac{0.75(0.25)}{72}}}[/tex]
z = -3.27.
What is the p-value of the test?Considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -3.27, the p-value is < 0.01.
Since the p-value is less than 0.01, there is strong indication that the true proportion of mechanics who could identify this problem is less than 0.75.
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You order two coffees and a cookie. The cookie costs $2.40. You pay 5% sales tax
and leave a $1.75 tip. You pay a total of $11.20. How much does one coffee cost?
Answer:
~ $3.29
Step-by-step explanation:
$11.20 - $1.75 = $9.45
$9.45 - $0.48 5% = $8.97
$8.97 - $2.40 = $6.57
$6.57 ÷ 2 = $3.285 rounded to $3.29
To find the quotient 104/8 104 as an expression with partial products
The value of the quotient 104/8 is 13
How to rewrite the expression as a partial product?The quotient expression is given as
104/8
Express 104 as 80 + 24
So, we have
104/8 = (80 + 24)/8
Split the fraction in the above expression
So, we have
104/8 = 80/8 + 24/8
Evaluate the quotients
So, we have
104/8 = 10 + 3
Evaluate the sum
So, we have
104/8 = 13
Hence, the value of the quotient 104/8 is 13
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