Answer: Hope this helps
Step-by-step explanation:
Let ss be the number of guests that a small tier can serve and mm be the number of guests a medium tier can serve.
The first cake has 3 small tiers, which will serve 3s3s people, and one medium tier, which will serve mm people. The first cake can then serve 3s+m3s+m people. Since the first cake will serve 100 guests, then 3s+m=1003s+m=100.
The second cake has 3 small tiers, which will serve 3s3s people, and 2 medium tiers, which will serve 2m2m people. The second cake can then serve 3s+2m3s+2m people. Since the second cake will serve 140 guests, then 3s+2m=1403s+2m=140.
The system of equations is then { 3s+m=100 3s+2m=140
{
3s+m=100
3s+2m=140
Part B:
The mm-terms have the same coefficients so subtract the first equation from the second equation to eliminate ss and solve for mm:
3s+2m amp;= amp;140 −(3s+m amp;= amp;100) m amp;= amp;40
3s+2m
−(3s+m
m
amp;=
amp;=
amp;=
amp;140
amp;100)
amp;40
Substitute m=40m=40 into either equation and solve for ss:
3s+m amp;=100 3s+40 amp;=100 3s amp;=60 s amp;=20
3s+m
3s+40
3s
s
amp;=100
amp;=100
amp;=60
amp;=20
The solution of the system is then (s,m)=(20,40)
(s,m)=(20,40)
.
Part C:
Since the solution of the system was s=20s=20 and m=40m=40, then a small tier feeds 20 people and a medium teir serves 40 people.
rewrite 9x9x9x9x9 using an exponent
Answer:
9^5
Step-by-step explanation:
9 x 9 x 9 x 9 x 9 can be written as an exponent form 9⁵.
To rewrite 9 x 9 x 9 x 9 x 9 using an exponent, we can represent the repeated multiplication with the base 9 raised to the power of 5. Here's how:
9 x 9 x 9 x 9 x 9 = 9⁵
In this expression, the base is 9, and the exponent is 5. The base represents the number being multiplied repeatedly, and the exponent represents the number of times it is multiplied.
Using the exponent notation, we can simplify and express the result more concisely. The exponent 5 indicates that the base 9 is multiplied by itself five times.
Therefore, 9 x 9 x 9 x 9 x 9 can be written as 9⁵.
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if the game begins at 1 pm and charlie and his friends take 1.5 hours to get to the field what time should they leave
Answer:
11:30am
Step-by-step explanation:
Answer:
Charlie and his friends should leave by 11:30 am at the latest.
someone please help me answer this!
Answer:
72 mi is the answer.
Step-by-step explanation:
a = 30 mi
b = ?
c = 78 mi
According to the Pythagoras theorem,
a² + b² = c²
30² + b² = 78²
900 + b² = 6084
b² = 6084 - 900
b² = 5184
b = 72 mi
∴ the eastbound airplane has travelled 72 mi.
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 29 houses that sold in their neighborhood took an average time of 230 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 35 days.
a. What assumption regarding the population is necessary for making an interval estimate of the population mean?
Assume that the population has a normal distribution.
Assume that the population has a uniform distribution.
b. Construct a 90% confidence interval of the mean sale time for all homes in the neighborhood.
Answer:
a. Assume that the population has a normal distribution.
b. The 90% confidence interval of the mean sale time for all homes in the neighborhood is between 219.31 days and 240.69 days.
Step-by-step explanation:
Question a:
We have to assume normality.
Question b:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{35}{\sqrt{29}} = 10.69[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 230 - 10.69 = 219.31 days.
The upper end of the interval is the sample mean added to M. So it is 230 + 10.69 = 240.69 days.
The 90% confidence interval of the mean sale time for all homes in the neighborhood is between 219.31 days and 240.69 days.
Bob has a bulb factory that produces two types of bulbs: white light (x) and color light (y). It is known that the standard deviation of service life for the population of white light bulbs is hours and hours for color bulbs, both are normally distributed. He tested the mean service life of those two types of bulbs by randomly drawing a sample of 20 bulbs from each type. The estimated mean service life are hours and hours. Assume that . What is the absolute value of the t-statistic if the null hypothesis is that both types of bulbs have the same service life?
Answer:
The answer is "3.51".
Step-by-step explanation:
[tex]\to t=\frac{\bar{x}-\bar{y}}{\sqrt{\frac{\sigma_x^2}{n_x}+\frac{\sigma_y^2}{n_y}}}\\\\[/tex]
[tex]=\frac{960-945}{\sqrt{\frac{14^2}{20}+\frac{13^2}{20}}}\\\\=\frac{15}{\sqrt{\frac{196}{20}+\frac{169}{20}}}\\\\=\frac{15}{\sqrt{\frac{196+169}{20}}}\\=\frac{15}{\sqrt{\frac{365}{20}}}\\\\=\frac{15}{\sqrt{18.25}}\\\\=\frac{15}{4.27}\\\\=3.51[/tex]
Question 5: 10 pts
There are 40 pieces of building blocks in a bag. 10 each of blue, green, red, and yellow. Two pieces are chosen
at random. Identify the probability that both of the pieces chosen are green
Answer:
The answer is 3/52
Step-by-step explanation:
I need helppppppppppppppppp
Answer:
Are you giving any exam or what?
Answer:
C. 3x^2-2x=0
Step-by-step explanation:
3x^2+2x=x(3x+2)=0
x=0 or 3x+2=0⇒3x=-2⇒x=-2/3
Please help!! Due in 45 minutes.
Answer:
[tex]x = \frac{56}{9} , y =-\frac{26}{3}[/tex]
Step-by-step explanation:
Calculator work :)
Pls help I'm sleep deprived rn and am almost done with this
Answer:
6π units
Step-by-step explanation:
Given::
Radius = 4
Angle measure of partial circle (θ) = 360° - right angle = 360° - 90° = 270°
Arc length = θ/360 × 2πr
Plug in the values
= 270/360 × 2 × π × 4
= 0.75 × 8 × π
= 6π units
Jason had to determine the solution set of x squared + StartFraction y squared Over 49 EndFraction greater-than 1. Examine the graph he drew.
Which element, if any, is incorrect in the graph?
The graph is correct.
The boundary should be a solid line.
The major axis should be horizontal.
The shaded region that represents the solution set should be inside the ellipse.
ITS A:The graph is correct.
Answer:
a the graph is correct
Step-by-step explanation:
edg 21 ^u^
The graph x² + ( y²/49 )>1 is correct. The correct option is A.
What is inequality?Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
The given inequality is x² + ( y²/49 )>1;. The graph is plotted on the x-y plane. The curves of the graph cut the y-axis at positive 7 and negative 7 and cut the x-axis at positive 1 and negative 1.
Hence, the correct option is A.
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Last month the amount on Jaden's bank account statement went from $200 to $150.
What was the percent change?
Answer:
That is a 25% change.
Step-by-step explanation:
Who can figure out the answer (3 x 1) +(6x 100)=X
Answer:
26
Step-by-step explanation:
Morty spent $54 on tulips and roses and bought a total of 14 flowers. If tulips cost $5 and roses $3
Let t = number of tulips bought
Let r = number of roses bought
a) Write the system.
b) How many of each flower did Morty buy? (Solve the system)
Answer:
a) Let's define the variables:
t = number of tulips bought
r = number of roses bought
We know that each tulip costs $5, and each rose costs $3.
Then the total cost will be:
$5*t + $3*r
We know that Morty spent a total of $54, then we have the equation:
$5*t + $3*r = $54
We also know that he bought a total of 14 flowers, then:
r + t = 14
Then the system of equations is:
$5*t + $3*r = $54
r + t = 14
b) To solve the system, first, we need to isolate one of the variables in one of the equations. I will isolate r in the second one:
r = 14 - t
Now we can replace this into the other equation:
$5*t + $3*r = $54
$5*t + $3*(14 - t) = $54
Now we can solve this for t.
$5*t + $3*14 - $3*t = $54
$2*t + $42 = $54
$2*t = $54 - $42 = $12
t = $12/$2 = 6
t = 6
He bought 6 tulips.
Now we can use the equation r = 14 - t
r = 14 - 6 = 8
r = 8
He bought 8 roses.
Preston has a car washing business. Last year he washed 20 cars a week. This year, he washed 1,200 cars. How many more cars did he wash this year than last year? *52 weeks=1 year
Answer:
160 cars
Step-by-step explanation:
The computation of the number of more cars he washed this year is given below;
Last year, he washed 20 cars a week so on yearly basis he washed
= 20 cars × 52 weeks
= 1,040 cars
And, this year he washed 1,200 cars
So, the number of more cars he washed this year is
= 1,200 cars - 1,040 cars
= 160 cars
A sewing machine sews at a constant rate of 1,500 stitches per minute. If the equation, y = 1,500x represents the relationship between the number of minutes, x, and the total number of stitches, y, what is the independent and dependent variable? (EE.C.9b)
Answer:
Step-by-step explanation:
x is the independent variable. y is the dependent variable.
Dependent variables take their values based on values of independent variables. In the considered case, we have:
Independent variable is x = number of minutesDependent variable is y = total number of stitchesWhat are independent and dependent variables?Even though everything can be almost always related to its reason, when we talk about two related things, there might happen that one of those things is dependent on other.
If a variable is taking its values independently of any visible direct cause, then that variable is called independent variable.
The variables who take their values based on some other variables' values are called dependent variables.
For the considered case, the two variables in consideration are:
x = number of minutesy = the total number of stitchesTime doesn't depend on number of stitches. Its thus, measuring an independent quantity.
The total number of stitches depends on how much time it passed since sewing. So the quantity 'y' depends on the value of 'x'
Thus, variable 'y' is dependent variable.
Therefore, in the considered case, we have:
Independent variable is x = number of minutesDependent variable is y = total number of stitchesLearn more about dependent and independent quantities here:
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Plz help me, ASAP look at the photo
Answer:
Input Output
0 1
2 2
-8 -3
100 51
Step-by-step explanation:
Given
The rule: input ⇒ ÷2+1 ⇒ output
Solve
0 ⇒ 0÷2+1 ⇒ 1
2 ⇒ 2÷2+1 ⇒ 2
-8 ⇒ -8÷2+1 ⇒ -3
100 ⇒ 100÷2+1 ⇒ 51
Hope this helps!! :)
Please let me know if you have any questions
please help! Your swag ! :)
this my answer not sure you like it or not
Answer:
8: 0,-2 9: 7,-3 10: 7,1/2
Step-by-step explanation:
Hello, for question 8 (the top equation), you trying to find y and x so lets find y first. You need y to be by itself so you divide all the numbers by -3 like this:
6x/-3-3y/-3=6/-3
The equation simplifies to -2x+y=-2. You need y to be by itself so you move it to the other side and you get -2 for y. Now you need x. Go to the second equation and take the number that is y and plug it into the equation like this:
6x+8(-2)=-16
Multiply 8 with -2 which is -16. Then, you add -16 with -16 which makes 0.
6x=0
You then divide 6 on both sides and x is 0. You basically do the same process for questions 9 and 10 which are 7,-3 and 7,1/2. And your done!
12.
The Mills Library has 1,007,199 books. The Springvale Library
has 907,082 books. Which of the following is the best
estimate of how many more books the Mills Library has than
the Springvale Library?
A.
100,000 books
B.
80,000 books
C.
10,000 books
D.
8,000 books
E.
1,000 books
sphere has a diameter of 14 ft. What is its surface area?
using a=12bh what is an equation to represent the area of a triangle?
Answer:
1/2 base × height
Step-by-step explanation:
a triangle has three sides and if we divide it into two, we have two right angle triangle in which we are using one part. that why it is 1/2 base x height
Answer:
You legit just told yourself
Step-by-step explanation:
[tex]\frac{1}{2}*b*h[/tex] IS the equation to represent the area of a triangle.
These three side lengths make a triangle.
3 cm, 5 cm, 9 cm
A. True
B. False
Answer:
aa
Step-by-step explanation:
aaaaaaaaa i need points sorry
The annual profits for a company are given in the following table where X represents the number of years since 2004 and Y represents the profit in thousands of dollars write the linear regression equation that represents the set of data rounding are Koi fishes to the nearest 10th using this equation find the projected profit in thousands of dollars for 2016 rounded to the nearest thousand dollars
Answer: number of years since 2012, and y represents the profit in thousands of ... Write the linear regression equation that represents this set of data, ... calendar year in which the profits would reach 234 thousand dollars.
Step-by-step explanation:
Classify the angle pair using all names that apply
Answer:
Adjacent
Step-by-step explanation:
∠3 and ∠4 share a common vertex & arm
Which is the graph of f(x)=4(1/2)x
Answer:
here's the graph
Step-by-step explanation:
PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answer: angles HIL and MLI are supplementary angles.
Hope this helps! :D
From Barbie dolls to runway models, women in Western countries are exposed to unrealistically thin and arguably unhealthy body standards for their gender. A body mass index (BMI) between 18.5 and 24.9 is considered healthy. Using a 3D computer avatar, participants built what they considered the ideal body of an adult of their own gender. Below appears a summary of the results for a sample of 40 female heterosexual Caucasian undergraduate students from British universities that had been recruited by the researchers. Mean BMI was recorded to be 18.85 with standard deviation 1.75. Does the data provide evidence that young Caucasian women in British Universities, on average, aim for an unhealthy ideal body type (corresponding to a BMI less than 18.5)? Use α = 0.10.
Required:
a. Construct a 99% confidence interval for the mean BMI for young Caucasian women in British universities using R. Use at least 2 decimals in your answer.
b. Would a 99% CI (for the mean BMI) constructed using a smaller sample than the one used for part a) tend to be wider or narrower? Explain.
Answer:
(18.1361 ; 19.5639) ;
using a smaller sample will widen the margin
Step-by-step explanation:
Given :
Xbar = 18.85
Standard deviation, s = 1.75
Sample size, n = 40
Confidence interval is obtained using the relation :
Xbar ± Margin of error
Margin of Error = Zcritical * s/ √n
Zcritical at 99% = 2.58
Margin of error = 2.58 * (1.75/√40) = 0.7139
Lower boundary = 18.85 - 0.7139 = 18.1361
Upper boundary = 18.85 + 0.7139 = 19.5639
(18.1361 ; 19.5639)
B.)
The sample size, n being the denominator in the margin error formula increases the error value as it reduces or decreases in value Hence widens the interval. Conversely, increasing the sample size reduces the error margin value and ultimately narrows the interval.
Therefore, using a smaller sample will widen the margin
PLZ HELP!!
Given the expression: 3x10 − 48x2
Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)
Part B: Factor the entire expression completely. Show the steps of your work. (6 points)
3*10 = 30 - 48*2 = 96
30 - 90
= -60
Answer:
If you want free brainliest, click on my profile piture, go to my answers, and look for the one that says give my brainly you will get free brainly!!
Step-by-step explanation:
NEED ANSWER ASAP WILL GIVE BRAINLIEST FOR CORRECT ANSWER
A fitness instructor measured the heart rates of the participants in a yoga class at the conclusion of the class. The data is summarized in the histogram to the right. There were fifteen people who participated in the class between the ages of 25 and 45. Use the histogram to answer the question. What is the approximate percentage of participants that had a heart rate less than 130 bpm?
Answer and Explanation:
Please find full question attached
From the bar chart, we can see that the the interval 130-150 has two bars in it:
Interval 130-140 with the highest frequency of 5
Interval 140-150 with frequency of 2
Therefore to find the percentage between 130-150 we add up the frequencies 2+5=7 and divide by the total frequency of 15 people all multiplied by 100
=7/15×100= 46.67%
Percentage of participants with heart rate between 130 and 150 =46.67%
someone please help me answer this!!
Answer:
39
Step-by-step explanation:
You should use the pythagorean theorem!