double occupancy room=x
single occupancy room=y
x + y = 80,
90x + 80y = 6930
x=53
y=27
express the ratio as a fraction in it's lowest terms.3kg to 800g
Answer:
15 / 4
Step-by-step explanation:
1 kg = 1000 g
3 kg
= 3 x 1000
= 3000 g
3kg to 800g
= 3kg : 800g
= 3000 : 800
= 30 : 8
= 30 / 8
= 15 / 4
15/4 is the fraction representing the ratio of 3 kilograms to 800 grams.
To express the ratio of 3 kilograms to 800 grams as a fraction in its lowest terms.
we need to convert both the quantities to the same units. Since 1 kg is equal to 1000 g, we can convert 3 kg to grams as follows:
3 kg = 3 * 1000 g = 3000 g
Now, we have the quantities in the same unit, and the ratio becomes:
3000 g to 800 g
To express this ratio as a fraction, we place the quantities over each other:
3000 g
-------
800 g
Now, to simplify the fraction to its lowest terms, we find the greatest common divisor (GCD) of the two numbers (3000 and 800) and divide both the numerator and denominator by this GCD.
The GCD of 3000 and 800 is 200, so dividing both by 200 gives us:
3000 ÷ 200 = 15
800 ÷ 200 = 4
Therefore, the ratio 3 kg to 800 g expressed as a fraction in its lowest terms is 15/4.
In summary, we first converted the units to the same (grams) to make the ratio easier to handle. Then, we represented the ratio as a fraction and simplified it to its lowest terms using the GCD method. The final answer, 15/4, is the fraction representing the ratio of 3 kilograms to 800 grams.
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find the amount on 800 for one year at 10%
Answer:
80
Step-by-step explanation:
You mean the "interest on"
I=800×.1×1=80
The probability that an individual has 20-20 vision is 0.18. In a class of 12 students, what is the probability of finding five people with 20-20 vision?
0.417 or 0.185 or 0.18 or 0.037
Answer:
0.417
Step-by-step explanation:
Just divide 12/5 and the answer is 0.416666666...
Round up and you get 0.417.
Hope this helped!
whats the x and y value? I thought it would be choice d but I'm not sure
please help asap . my question is timed
Answer:
cos(60°) = [tex]\frac{adjacent}{hypotenuse}=\frac{y}{10\sqrt{3} }[/tex]
[tex]cos(60)=\frac{y}{10\sqrt{3} } \\y=cos(60) * 10\sqrt{3} \\y=\frac{1}{2} * 10\sqrt{3}\\y=\frac{10\sqrt{3}}{2} =5\frac{\sqrt{3} }{2} =8.66[/tex]
sin(60°) = [tex]\frac{opposite}{hypotenuse} =\frac{x}{10\sqrt{3} }[/tex]
[tex]sin(60)=\frac{x}{10\sqrt{3} } \\x=sin(60)*10\sqrt{3} \\x=\frac{\sqrt{3} }{2} *10\sqrt{3} \\x=\frac{10(\sqrt{3} ) (\sqrt{3} )}{2} \\x=\frac{10*3}{2} =\frac{30}{2} =15[/tex]
hello can anyone help with this?
Answer:
<2 and <13 are alternate exterior angles.
In simple form, alternate exterior angles are the opposite angle on the opposing parallel line. So, to make you understand better, <4 and <15 are alternate exterior angles.
Hope this helps :D
A survey found that the median number of calories consumed per day in a certain country was 3,304 and the mean was 3,204.9 calories. If a histogram were constructed for the data, would you expect it to be skewed to the right, to the left, or approximately symmetric
Answer:
Skewed to the left
Step-by-step explanation:
Given
[tex]Median = 3304[/tex]
[tex]Mean = 3204.9[/tex]
Required
The type of distribution
From the given data, we have:
[tex]Median \ne Mean[/tex] --- Mean and Median are not equal
and
[tex]Median > Mean[/tex] --- Median is greater than mean
When the median is greater than the mean; the histogram is expected to be left skewed
jimmy had twice as many oranges as grapefruit, 5 more grapefruits than pineapples, how many of each fruit did jimmy have?
Answer:
Step-by-step explanation:
I think he has 7 oranges and 5 grapefruit and ten pineapples
By converting to an exponential expression, solve log2 (x + 5) = 4
Step-by-step explanation:
just insert a base of two at on both sides and solve.
The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The logarithmic equation is given below.
㏒₂(x + 5) = 4
Simplify the equation, then we have
㏒ (x + 5) / ㏒ 2 = 4
㏒ (x + 5) = 4 × ㏒ 2
㏒ (x + 5) = ㏒ 2⁴
Take antilog on both sides, then we have
(x + 5) = 2⁴
(x + 5) = 16
x = 11
The solution of the logarithmic equation ㏒ (x + 5) / ㏒ 2 = 4 will be 11.
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How many cubes with side lengths of 1/2 cm does it take to fill the prism?
Answer:
24
Step-by-step explanation:
You first find out how many cubes can fit into each measurement, then multiply them. (2*4*3=24)
Answer:
It will take 24 cubes to fill the rectangular prism.
Step-by-step explanation:
Find the volume of a cube with side lengths of 1/2 cm:
1/2^3 = 1/8
1/8 cm^3
Find the volume of the whole rectangular prism (lwh):
1 x 3/2 x 2
= 3/2 x 2
= 3
3 cm^3
Divide the volume of the prism by the bolume of one cube:
3 ÷ 1/8 = 24
Therefore it will take 24 cubes to fill the prism. Hope this helps!
A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $100,000 with a standard deviation of $10,000. Assume that salaries follow a bell-shaped distribution. Use the empirical rule:
a. Approximately what percentage of the salaries fall between $90,000 and $110,000?
b. Approximately what percentage of the salaries fall between $80,000 and $120,000?
c. Approximately what percentage of the salaries are greater than $120,000?
Answer:
a) 68%
b) 95%.
c) 2.5%
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 100,000, standard deviation of 10,000.
a. Approximately what percentage of the salaries fall between $90,000 and $110,000?
90,000 = 100,000 - 10,000
110,000 = 100,000 + 10,000
Within 1 standard deviation of the mean, so approximately 68%.
b. Approximately what percentage of the salaries fall between $80,000 and $120,000?
80,000 = 100,000 - 2*10,000
120,000 = 100,000 + 2*10,000
Within 2 standard deviations of the mean, so approximately 95%.
c. Approximately what percentage of the salaries are greater than $120,000?
More than 2 standard deviations above the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean, so approximately 5% are more than 2 standard deviations from the mean.
The normal distribution is symmetric, which means that 2.5% are more then 2 standard deviations below the mean, and 2.5% are more than 2 standard deviations above the mean, which means that 2.5% of the salaries are greater than $120,000.
2 triangles are shown. The first triangle has side lengths 35, 20, and 20. The second triangle has side lengths x, 44, 44.
What value of x will make the triangles similar by the SSS similarity theorem?
15.9
59
77
96.8
Answer:
[tex]x = 77[/tex]
Step-by-step explanation:
Given
[tex]First \to Second[/tex]
[tex]35 \to x[/tex]
[tex]20 \to 44[/tex]
[tex]20 \to 44[/tex]
Required
Find x by SSS
Represent the triangle sides as a ratio
[tex]35 : x = 20 : 44[/tex]
Express as fraction
[tex]\frac{x}{35} = \frac{44}{20}[/tex]
Multiply by 35
[tex]x = \frac{44}{20} * 35[/tex]
[tex]x = \frac{44 * 35}{20}[/tex]
[tex]x = \frac{1540}{20}[/tex]
[tex]x = 77[/tex]
Answer:
ccccccccccccccccccccccccccc
Step-by-step explanation:
Two trains leave the train station at 10:00 a.m. and travel in opposite directions. Their rates are 65 mph and 85 mph. How many hours will it take for them to be 450 miles apart?
Answer:
Step-by-step explanation:
The distance between trains increases by 65+85 = 150 mph.
450 miles × (1 hour)/(150 miles) = 3 hours
An art history professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 56% C: Scores below the top 44% and above the bottom 21% D: Scores below the top 79% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 8.4.
This means that [tex]\mu = 79.7, \sigma = 8.4[/tex]
B: Scores below the top 13% and above the bottom 56%
So between the 56th percentile and the 100 - 13 = 87th percentile.
56th percentile:
X when Z has a p-value of 0.56, so X when Z = 0.15. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.15 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 0.15*8.4[/tex]
[tex]X = 81[/tex]
87th percentile:
X when Z has a p-value of 0.87, so X when Z = 1.13.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.13 = \frac{X - 79.7}{8.4}[/tex]
[tex]X - 79.7 = 1.13*8.4[/tex]
[tex]X = 89[/tex]
The numerical limits for a B grade are 81 and 89, that is, a score between 81 and 89 gets a B grade.
mrs cabrini needs 2 quarts of tomato sauce to make a large batch of her spaghetti sauce. she has 1 1/4 quarts of her own. she borrows 1/2 quart from the neighbor across the hall and 3/8 quart from the neighbor next door . how many quarts does she have in all of her own .
Answer:
Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.
Step-by-step explanation:
Since Mrs. Cabrini needs 2 quarts of tomato sauce to make a large batch of her spaghetti sauce. she has 1 1/4 quarts of her own, and she borrows 1/2 quart from the neighbor across the hall and 3/8 quart from the neighbor next door, to determine how many quarts does she have in all of her own must perform the following calculation:
1/4 = 0.25
1/2 = 0.5
3/8 = 0.375
0.25 + 0.5 + 0.375 = X
1.125 = X
1 + 1,125 = 2,125
Therefore, Mrs. Cabrini has a total of 2 1/8 quarts of tomato sauce.
Two positive integers are 3 units apart on a number line. Their product is 108.
Which equation can be used to solve for m, the greater integer?
m(m – 3) = 108
m(m + 3) = 108
(m + 3)(m – 3) = 108
(m – 12)(m – 9) = 108
Answer:
m(m – 3) = 108
The correct equation can be used to solve for m, the greater integer is,
⇒ m (m - 3) = 108
We have to given that,
Two positive integers are 3 units apart on a number line.
And, Their product is 108.
Let us assume that,
In a number line, first point is m
Then, Second point is, m - 3
So, We get;
The correct equation can be used to solve for m, the greater integer is,
⇒ m (m - 3) = 108
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James determined that these two expressions were equivalent expressions using the values of x = 4 and x = 6. Which statements are true? Check all that apply.
7 x + 4 and 3 x + 5 + 4 x minus 1
Which function has no horizontal asymptote?
Answer:
[tex]{ \tt{f(x) = \frac{x - 1}{3x} }}[/tex]
Answer:
c
Step-by-step explanation:
edge
Lena and Ras drive to work. Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min. Work out the difference between their average speeds in km/h. 1 mile = 1.6 km
Answer:
Difference = 3.2 km/h
Step-by-step explanation:
Given that,
Lena drives 24 miles in 1.5 hours. Ras drives 36 km in 1 hour 15 min.
For average speed of Lena,
d = 24 miles = 38.4 km
t = 1.5 h
[tex]v=\dfrac{38.4}{1.5}= 25.6\ km/h[/tex]
For average speed of Ras,
d = 36 km
t = 1h 15 min = 1.25 h
[tex]v=\dfrac{36}{1.25}=28.8\ km/h[/tex]
Difference = 28.8-25.6
= 3.2 km/h
So, the difference between their average speed is 3.2 km/hr.
Answer:
3.2 km/h
Step-by-step explanation:
The following multiple regression printout can be used to predict a person's height (in inches) given his or her shoe size and gender, where gender = 1 for males and 0 for females.
Regression Analysis: Height Versus Shoe Size, Gender
Coefficients
Term Coef SE Coef T-value P-value
Constant 55.24 1.05 52.61 0.000
Shoe Size 1.164 0.13 0.000
Gender 2.574 0.489 5.26 0.000
Required:
a. Find the value of the test statistic for shoe size.
b. Is the regression coefficient of shoe size statistically significant?
c. Does the variable shoe size belong in the model?
d. Interpret the regression coefficient of Gender.
Answer:
a. 8.95
b. it is
c. yes it belongs
d. males are 2.574 taller than females on average.
Step-by-step explanation:
GIven the regression outpuit that we have in this question, the value of the t test statistics for the shoe size can be solved as
a. test statistic = 1.164/0.13
t test = 8.95
b. the regression coefficient of shoe size is 1.164, this is statistically significant
c. Yes the variable shoe size does belong to the model.
d. The regression coefficient of gender shows that on the average, while holding other variables constant, males are 2.574 inches taller than the their female counterparts.
Sketch the graph of y = 2(x – 2)2 and identify the axis of symmetry
Answer:
x = 2
Step-by-step explanation:
The minimum point of the curve is (2, 0). Hence, axis of symmetry is x = 2
Find an equation for the line with the given properties. Perpendicular to the line 7x - 3y = 68; containing the point (8, -8)
Answer:
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
Step-by-step explanation:
Given that,
A line 7x - 3y = 68 and containing the point (8, -8).
The equation can be written as :
[tex]-3y=68-7x\\\\y=\dfrac{68}{-3}+\dfrac{7x}{3}\\\\y=\dfrac{7x}{3}+(\dfrac{-68}{3})[/tex]
The slope is :7/3
Line is perpendicular so use m = –3/7
[tex]-8=(-\dfrac{3}{7})\times 8+b\\\\-8+\dfrac{3}{7}\times 8=b\\\\b=\dfrac{-32}{7}[/tex]
So, required equation is :
[tex]y=\dfrac{-3}{7}x-\dfrac{32}{7}[/tex]
There is a bag filled with 3 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
JUST NEED THE ANSWER IN A FRACTION PLEASE
[tex]\frac{13}{28}[/tex]
Step-by-step explanation:Given:
Blue marbles: 3
Reb marbles: 5
Total marbles: 8
Two marbles are selected at random, one after the other with replacement.
Getting the same colour of marbles from the selection means the two marbles are both red or both blue.
(a) Probability of getting 2 marbles being red in colour
i. Probability of picking a red at the first selection:
Number of red marbles ÷ Total number of marbles
=> 5 ÷ 8 = [tex]\frac{5}{8}[/tex]
ii. Probability of picking a red at the second selection:
Number of remaining red marbles ÷ Total number of remaining marbles
Since after the first pick, the marble is not replaced, the remaining red marbles is 4 while the total number of remaining marbles is 7
=> 4 ÷ 7 = [tex]\frac{4}{7}[/tex]
iii. The probability of getting both marbles being red is the product of i and ii above. i.e
[tex]\frac{5}{8}[/tex] x [tex]\frac{4}{7}[/tex] = [tex]\frac{5}{14}[/tex]
(b) Probability of getting 2 marbles being blue in colour
i. Probability of picking a blue at the first selection:
Number of blue marbles ÷ Total number of marbles
=> 3 ÷ 8 = [tex]\frac{3}{8}[/tex]
ii. Probability of picking a blue at the second selection:
Number of remaining blue marbles ÷ Total number of remaining marbles
Since after the first pick, the marble is not replaced, the remaining blue marbles is 2 while the total number of remaining marbles is 7
=> 2 ÷ 7 = [tex]\frac{2}{7}[/tex]
iii. The probability of getting both marbles being blue is the product of i and ii above. i.e
[tex]\frac{3}{8}[/tex] x [tex]\frac{2}{7}[/tex] = [tex]\frac{3}{28}[/tex]
(c) Probability of getting 2 marbles of the same colour.
The probability of getting 2 marbles of same colour is the sum of the probability of getting both marbles of red colour and the probability of getting both marbles as blue colour. i.e The sum of a(iii) and b(iii)
[tex]\frac{5}{14}[/tex] + [tex]\frac{3}{28}[/tex] = [tex]\frac{13}{28}[/tex]
The probability of getting 2 of the same colour is [tex]\frac{13}{28}[/tex]
12. A professor creates a boxplot of test scores for 26 students in a statistics course. What percentage of students scored above 81
Answer:
25%
Step-by-step explanation:
Based on the boxplot given ;
The boxplot can be summarized as follows :
Lower quartile, Q1 = 50 (starting point of the box)
Median (Q2), 50th percentile = 70 (vertical line in between the box)
The upper quartile marks the 75th percentile, Q3 = 81 (end point of the box)
The total distribution is 100% and hence, the percentage above the score 81 will be :
100% - 75% = 25%
Which of the following are exterior angles? Check all that apply.
ots
65
A. 22
1
B. 21
C. 23
1
D. 24
I E. 26
DE 25
Answer:
A
C
D
E
Step-by-step explanation:
Exterior angles can be described as the angles that are formed between the side of a polygon and the extended adjacent side of the polygon.
Or an exterior angle is the angle that is not inside the triangle formed.
The angles inside the triangle are interior angles.
Exterior angles are :
2
3
4
6
Interior angles are :
1
5
Integration of [(x+1)/(x-1)]dx
Hello!
∫[(x+1)/(x-1)dx
∫t+2/t dt
∫t/t + 2/t dt
∫1 + 2/t dt
∫1dt + ∫2/t dt
∫t + 2In (|t|)
x - 1 + 2In (|x-1|)
x + 2In (|x-1|) + C, C ∈ R
Good luck! :)
What is the coefficient of x2 in the expansion of (x + 2)??
O A.
2
OB.
3
O C.
4
OD.
6
x+2 in expansion of (x+2) ?
A
Complete the following statement.
The mean of Restaurant A's service ratings is _____ the mean of Restaurant's B service ratings.
A. The same as
B. Worse than
C. Better than
PLZZZZ HELPP WILL GIVE BRAINLIEST
Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?
AAS
SSS
SAS
HL
Answer:
HL
Step-by-step explanation:
Since both triangles are right angle triangles that means one angle is 90°. other two sides are given congruent .
that means lengths of hypotenuse and the leg of the one right angle triangle is equal to the corresponding other hypotenuse and leg of other triangle.
This fulfills the condition of HL congruency.
A riverboat travels 52 km downstream in 2 hours. It travels 66 km upstream in 3 hours. Find the speed of the boat and the speed of the stream
The speed of the boat is
and the speed of the stream is
Answer:
The speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Step-by-step explanation:
Given that a riverboat travels 52 km downstream in 2 hours, and it travels 66 km upstream in 3 hours, the following calculations must be performed to find the speed of the boat and the speed of the stream:
Downstream = 52/2 = 26
Upstream = 66/3 = 22
Stream = 4/2 = 2
Therefore, the speed of the boat is 24 kilometers per hour, and the speed of the stream is 2 kilometers per hour.
Pls someone help these answers are on chegg so if u have a subscription pls answer these ill make u brainliest ! Below is a table representing data, measuring the percentage of various
groups owning a home
Percentage owning a
home
1st Generation
Hispanic Americans
N=899
43
50
2nd Generation
Hispanic Americans
N=351
1st Generation Asian
Americans N=2,684
2nd Generation Asian
Americans N=566
58
51
Test whether there is a significant difference in the proportion of
homeowners between 1st and 2nd generation Hispanic Americans. Set alpha at .05
The obtained Z test is ?
The probability of obtaining
this Z-test statistic is ?
This is _? Than our alpha level. Therefore we ___? The null hypothesis and conclude that there ____? A significant difference in the proportion of homeowners between 1 st generation and 2nd generation hispanic americans.
The table is not clear, so i have attached it.
Answer:
z statistic is -2.26
This is less than our alpha level,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans
Step-by-step explanation:
From the attached table, we can see that;
first-generation hispanic americans; (N = 899 and percentage = 43%
second-generation hispanic americans; N = 351 and percentage = 50%
first-generation asian americans; (N = 2,684 and percentage = 58%
second-generation asian americans; N = 566 and percentage = 51%
Z-score formula in this case is;
z = (p1^ - p2^)/(√(p^(1 - p^)((1/n1) + (1/n2))
Where;
p^ = (p1 + p2)/(n1 + n2)
For, hispanic americans we have;
p1^ = 0.43 × 899 = 386.57
p2^ = 0.5 × 351 = 175.5
p^ = (386.57 + 175.5)/(899 + 351)
p^ = 0.45
Thus;
z = (0.43 - 0.5)/(√(0.45(1 - 0.45)((1/899) + (1/351))
z = -2.26
From z-distribution table, we have;
P-value = 0.01191
Since we have 2 samples, then probability = 2 × 0.01191 = 0.02382
This is less than our alpha level of 0.05,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans.
