Using the mathematical operation of division, Mrs. Doctor can fill 15 mugs using 10 cups.
What is the division operation?The division operation is one of the basic mathematical operations.
The division operation involves using the divisor to divide the dividend, which results in a quotient.
For instance, since the pot holds 10 cups and the distribution is 2/3 cups for each mug, we can divide 10 cups by 2/3 cups to get 15 mugs.
The quantity of hot chocolate for each mug = 2/3 cups
The total number of cups that the pot holds = 10 cups
The number of mugs that can be filled from 10 cups = 15 (10 ÷ 2/3)
Thus, we can divide 10 cups by 2/3 cups to get the number of mugs Mrs. Doctor can fill.
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Rectangle A measures 12 cm by 3 cm.Rectangle B is a scaled copy of rectangle A.Select all the measurement pairs that could be the dimensions of rectangle B.
The measurement pairs that could be the dimensions of rectangle B include:
A. 6cm by 1.5cm
D. 18cm by 4.5vm
F. 80cm by 20cm
How to illustrate the information?From the information, Rectangle A measures 12 cm by 3cm. Therefore, it should be noted that the scale factor is:
= 12/3
= 4/1
Therefore, the options should also have that same constant of 4:1
In this case, 6cm by 1.5cm, 18cm by 4.5cm, and 80cm by 20cm all possess this. This illustrates the concept of equivalent dimensions since they all have a ratio of 4:1.
The complete question is written below.
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
A. 6 cm by 1.5 cm
B.10 cm by 2 cm
C. 13 cm by 4 cm
D.18 cm by 4.5 cm
E.80 cm by 20 cm
eamonn has just taken a statistics exam, and he wants to calculate a confidence interval to represent the exam scores in his class. the test mean was 75, with a standard deviation of 5. there are 30 students in the class. the 90% confidence interval for the class is:
The 90% confidence interval for the class is [73.49, 76.51].
Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.
CI = μ ± z x SD/√n
where CI = confidence interval
μ = sample mean = 75
z = found by using a z-score table
SD = sample standard deviation = 5
n = sample size = 30
At 90% confidence level, the area in each tail of the standard normal curve is 5, and the cumulative area up to the second tail is 95.
(100 - 90) / 2 = 5
100 - 5 = 95
Find 0.95 in the z-table to get the value of z.
At p = 0.95, z = 1.65
Plug in the values to the formula for confidence interval, CI.
CI = μ ± z x SD/√n
CI = 75 ± 1.65 x 5/√30
CI = 75 ± 1.51
CI = [73.49, 76.51]
Hence, for every 100 samples, at 90% confidence level, the mean will be between 73.49 and 76.51.
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Which inequality is equivalent to 22 ≤x-9?
(A) 13sx
(B) 13zx
(C) 31sx
(D) 31zx
Answer:
31 ≤ x
Step-by-step explanation:
22 ≤ x - 9;
22 + 9 ≤ x - 9 + 9;
31 ≤ x
Assume that a sample is used to estimate a population mean μ . Find the 99% confidence interval for a sample of size 891 with a mean of 20.8 and a standard deviation of 17.6. Enter your answer as a tri-linear inequality accurate to 3 decimal places.19.281Incorrect < μ < 22.319
Solution:
The confidence interval is expressed as
where
[tex]\begin{gathered} \bar{x}\text{ or }\mu\Rightarrow sample\text{ mean} \\ z\Rightarrow confidence\text{ level value} \\ s\Rightarrow sample\text{ standard deviation} \\ n\Rightarrow sample\text{ size} \end{gathered}[/tex]Given a 99% confidence interval for a sample size of 891 with a mean of 20.8 and a standard deviation of 17.6, this implies that
[tex]\begin{gathered} \bar{x}=20.8 \\ s=17.6 \\ n=891 \\ z=2.576 \end{gathered}[/tex]By substituting these values into the above equation, we have
[tex]\begin{gathered} CI=20.8\pm(2.576\times\frac{17.6}{\sqrt{891}}) \\ =20.8\pm1.518866748 \\ Thus,\text{ } \\ \Rightarrow lower\text{ bound:} \\ 20.8-1.518866748=19.28113325 \\ \Rightarrow upper\text{ bound:} \\ 20.8+1.518866748=22.31886675 \end{gathered}[/tex]Hence, we have
[tex]19.281<\mu<22.319[/tex]Hi can someone help me with this?Writing the algebraic equation for the phrase below.. 1. The sum of X and 96 equals half of X .
Given:
1. The sum of X and 96 equals half of X.
To determine the algebraic equation, we note that the sum of x and 96 would be:
x+96
Next, half of x must be like this:
x/2
Then, the phrase equals means we set x+96 equals to x/2.
Therefore, the answer is:
[tex]x+96=\frac{x}{2}[/tex]Hattie drew a box plot of annual rainfall in some cities in the world. Select all the statements that are true about the data in the box plot.
Rainfall anually table data
Then
Option A)
Half of the data are between 6 and 18
TRUE , because there are 8/2 = 4 data in the box plot
Option B)
Data point 27 ,could be an outlier
FALSE, because 27 is a black point. It means it belongs, is not out
Option C)
More points between 6,9 that between 9,18
FALSe,. Area between 6,9. Is smaller than area between 9,18
Option D)
Data are less spread out to the left
TRUE, because box plot is ubicated at left
Option E)
Only one data point is less than 6
TRUE, is data point 3
Find f(0) and find one value of x for which f(x)=-3
given the graph
the point f(0) (x=0) is given at y=-4
then
f(0)= - 4
the point f(x) = -3 (y=-3) is given when x = -1
then
the value of x for which f(x)=-3: -1
What is the result when the number 88 is decreased by 69%? Round your answer to the nearest tenth.
Kelly likes to fish at the lake near her house. She caught 8 fish last week, measured them, and put them back in the lake. The lengths of the fish, in inches, are shown.
9, 12, 10, 8, 11, 12, 13, 6
Assuming this data is representative of the fish in the lake, what is the mean length of the fish in the lake?
Answer:
the mean is 12
Step-by-step explanation:
a mean is a set of numbers of two or more numbers
so becuase 12 repeats there, its your mean
A software company in Burlington used to bill clients $214.79 per hour for work done by its consultants. The company recently adjusted its rates and now charges the same amount. What was the percent of decrease in the billing rate?
The percent of decrease in the billing rate is 2.37%.
How to calculate the percentage?It should be noted that a percentage decrease is calculated as
= Decrease in value / Initial value × 100
Let's assume the following:
Initial amount = $220
New amount = $214.79
Decrease in amount = $220 - $214.79 = $5.21
The percentage decrease will be:
= 5.21 / 220 × 100
= 2.37%
The question is incomplete and the values were assumptions.
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true or false: (justify/explain your answer) state whether a or b is the true statement below and then explain why the other statement is false. a. with a large random sample, the sample histogram will closely resemble the normal curve. b. with a large random sample, the probability density function of the sample mean will close resemble the normal curve.
By central limit theorem ,with a large random sample, the sample histogram will not closely resemble the normal curve but with a large random sample, the probability density function of the sample mean closely resembles the normal curve.
The central limit theorem for samples says that if we keep drawing larger and larger samples and calculating their means, the sample forms their own normal distribution (the sampling distribution). The normal distribution will have the same mean as the original distribution and a variance that equals the original variance divided by the sample size. The variable n is the number of values that are averaged together,and not the number of times the experiment is done.
Hence,with a large random sample, the sample histogram will not resemble the normal curve but with a large random sample, the probability density function of the sample mean will closely resemble the normal curve.
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Write an equation in standard form of the line that passes through the given points.
7. (-3, 2); m = 1
Answer:
y=x+1
Step-by-step explanation:
y-y1=m(x-x1)
y-2=1(x+3)
y-2=x+3
y=x+1
v/8 - 3.1 = -15.9 solve for v
Hello!
So, we are given the following to solve.
Solve for v.
[tex]\frac{v}{8}-3.1=-15.9[/tex]
To solve for v, we to do as follows:
1. Add 3.1 to both sides.
[tex]\frac{v}{8}-3.1+3.1=-15.9+3.1[/tex]2. Simplify.
[tex]\frac{v}{8} =-12.8[/tex]3. Multiply both sides by 8.
[tex]\frac{8v}{8}=8(-12.8)[/tex]4. Simplify.
[tex]v=-102.4[/tex] ← Hence, our solution.Hope this helps!
Find the value of each variable
Answer:
y=9
Step-by-step explanation:
16y and 18y-18 are vertical angles. The definition of Vertical Angles states that both of the measures of the angles are equal to each other. Therefore,
18y-18=16y
2y-18=0
2y=18
y=9
a*c=c*a
what property is this?
associative communitive identity distributive
Answer: its associative property Hope I helped
Step-by-step explanation:
An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem. You can solve it perfectly using math reasoning.
An airship propelled by some mechanical device travels five miles in ten minutes in the direction of the wind, but requires one hour to go back again to the starting point against the same wind. How long would it have taken to go the whole ten miles in a calm day without any wind? Hint: You don't have to use equations to solve this problem.
we have that
5 miles -------> 10 minutes (direction of the wind)
5 miles ------> 1 hour (against the same wind)
therefore
10 miles ------> ? (without any wind)
so
Let
x -----> speed of the wind
y -----> speed of the airship
direction of the wind
speed=d/t ------> 5/10=0.5 miles per min
against the same wind
speed=5/60=1/12 miles per min
so
x+y=0.5 ------> x=0.5-y -----> equation 1
y-x=1/12 -----> equation 2
solve the system
substitute equation 1 in equation 2
y-(0.5-y)=1/12
2y=(1/12)+1/2
2y=7/12
y=7/24=0.2917 miles per min
Find the value of x
x=(1/2)-7/24
x=5/24=0.2083 miles per min
therefore
10 miles without any wind
speed=d/t ------> t=d/speed
t=10/(7/24)
t=34.29 minCan someone help me answer this question about area of trapezium
Answer:
x = 11
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the perpendicular height between the bases b₁ and b₂
here h = 4 , b₁ = x , b₂ = 6 and A = 34 , then
[tex]\frac{1}{2}[/tex] × 4 × (x + 6) = 34
2(x + 6) = 34 ( divide both sides by 2 )
x + 6 = 17 ( subtract 6 from both sides )
x = 11
Bob is planning to start an it business, servicing computers that are infected with viruses. to start his new enterprise, bob estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. all of these costs are fixed. he is planning on charging his customers $250 each to fix an infected computer. for each computer that he fixes, he must spend $25 on parts and software. suppose we let x be the number of computers that bob fixes. if bob only fixes 50 computers, what is his total loss?
If Bob only fixes 50 computers, his total loss is $3,750.
What is the total loss?The total loss results from the negative difference between the total revenue and the total costs.
The total costs consist of variable and fixed costs.
The result is a loss when the total costs exceed the total revenue. This result becomes a profit or income when the total revenue exceeds the total costs.
Fixed Costs:Equipment = $5,000
Premises = $6,000
Advertising = $4,000
Total fixed costs = $15,000
Variable cost per unit = $25
Selling price per unit = $250
Total number of computers fixed = 50
The total variable cost for 50 units = $1,250 (50 x $25)
The total costs (fixed and variable) = $16,250
The sales revenue for 50 units = $12,500 (50 x $250)
Loss = $3,750 ($12,500 - $16,250)
Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.
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Find the measure of the complement for the angle 1 degree
89 degrees
Explanations:
The sum of an angle and its complement is equal to 90 degrees.
Let the measure of the complement be "x"
Given the information below:
Angle = 1 degrees
Taking the sum of the angle and its complement will give:
[tex]x+1^0=90^0[/tex]Subtract 1 from both sides
[tex]\begin{gathered} x+1-1=90-1 \\ x+0=90-1 \\ x=89^0 \end{gathered}[/tex]Therefore the measure of the complement for the angle given is 89 degrees
suppose that the miles per gallon (mpg) rating of passenger cars is a normally distributed random variable with mean of 33.8 mpg and standard deviation of 3.5mpg. what is the probability that a randomly selected car gets less than 40 mpg?
The probability that a randomly selected car gets more than 40 mpg is equal to 0.771.
Let us assume that the miles-per-gallon rating of passenger cars be represented by random variable X. According to the question we know that X ≈ N (μ = 33.8 mpg and σ² = 3.5² mpg). Now, to compute the probability that a randomly selected passenger will gets less than 40 mpg will be given as
P(X < 40) = P(X - μ/σ > 40 - 33.8/3.5)
= P(Z < 1)
= P(Z > 1) - 1
= 1.771 - 1
= 0.771 which is the required probability.
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there are 324 students in a college who have taken a course in calculus, 211 who have take a course in discrete mathematics, and 135 who have taken a course in both calculus and discrete mathematics. how many students at this college have taken a course in either calculus or discrete mathematics?
265 students at this college have taken a course in either calculus or discrete mathematics.
Let X = number of students who have taken a course in calculus
Y = number of students who have taken a course in discrete mathematics
To determine the number of students who have taken a course in calculus only, subtract 135 from 324.
Only X = X - X∩Y
Only X = 324 - 135
Only X = 189
To determine the number of students who have taken a course in discrete mathematics only, subtract 135 from 211.
Only Y = Y - X∩Y
Only Y = 211 - 135
Only Y = 76
To determine the number of students who have taken a course in either calculus or discrete mathematics, add 189 and 76.
either X or Y = only X + only Y
either X or Y = 189 + 76
either X or Y = 265
To better illustrate the X and Y, see the attached photo of the Venn Diagram.
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Use point-slope form to write the equation of a line that passes through the point (19,-12) with slope -3
Answer:
Step-by-step explanation:
The formula is :
(y - y1) = m(x - x1)
the given values are x1 = 19, y1 = -12 and m = slope = -3
putting values
(y + 12)= -3(x-19)
y + 12 = -3x +57
y+ 3x - 35 = 0
This is the required equation.
what is the doubling timefor this population of alligators ?
3 years
Explanations:The given function representing the population of alligators is:
[tex]P(t)\text{ = (}319)2^{\frac{t}{3}}[/tex]Find the intial population at t = 0
[tex]\begin{gathered} P(0)\text{ = 319 }\times2^0 \\ P(0)\text{ = 319 }\times\text{ 1} \\ P(0)\text{ }=\text{ 319} \end{gathered}[/tex]The population will double when:
P(t) = 319 x 2
P(t) = 638
The doubling time is the value of t at which P(t) = 638
[tex]\begin{gathered} P(t)\text{ = 319 }\times2^{\frac{t}{3}} \\ 638\text{ = 319 }\times2^{\frac{t}{3}} \\ \frac{638}{319}=2^{\frac{t}{3}} \\ 2\text{ }=2^{\frac{t}{3}} \\ 2^1=2^{\frac{t}{3}} \\ 1\text{ = }\frac{t}{3} \\ t\text{ = 3} \end{gathered}[/tex]The population will double after 3 years.
Therefore, the doubling-time for this population of alligators is 3 years
Miguel is going to see a movie and is taking his 5 kids. Each movie
ticket costs $12 and there are an assortment of snacks available to
purchase for $5 each. How much total money would Miguel have to
pay for his family if he were to buy 5 snacks for everybody to share?
How much would Miguel have to pay if he bought a snacks for
everybody to share?
Total cost with 5 snacks:
Total cost with a snacks:
Pls give me a good answer
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
Given,
Miguel is going to see a movie with his 5 kids.
Number of people = 6
Cost for one ticket = $12
Cost of one snack = $5
Number of snacks = 5
We have to find the total cost spend by Miguel:
For tickets and 5 snacks:
For tickets and x snacks:
Now,
Total cost for tickets = 6 × 12 = $72
Cost for 5 snacks = 5 × 5 = $25
Therefore,
Total cost = 72 + 25 = $97
Next,
Cost for x snacks = 5x
Then,
Total cost = 72 + 5x
That is,
The total cost for 6 movie tickets and 5 snacks is $97
The total cost for 6 movie tickets and x snacks is $(72 + 5x)
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2x+y = 2
Step 1 of 2: Determine the missing coordinate in the ordered pair (4, ?) so that it will satisfy the given equation.
Answer:
Substitute x = 4 into the equation to find y.
2(4) + y = 2
8 + y = 2
y = -6
To check if it satisfies the equation, substitute values of x and y into the equation.
2(4) + (-6) = 2
8 - 6 = 2
Since, it satisfies the equation, the missing coordinate is -6.
6. Create a systems of inequalities to represent the graph below
System of inequalities
We are given the graph where two lines represent the solution of a system of inequalities.
The solution is the double-shaded region of the graph.
We need to find the equation of the blue line and the red line and then convert them to inequalities.
Let's start with the blue line. We need to find two clear points through which it passes. These are (0,6) and (2,0). Now we write the equation of the line when knowing two points (the point-point form):
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex][tex]\begin{gathered} \displaystyle y-6=\frac{0-6}{2-0}(x-0)=-3x \\ \text{Adding 6:} \\ y=-3x+6 \end{gathered}[/tex]For the red line, the points are (0,0) and (2,2):
[tex]\begin{gathered} y-0=\frac{2-0}{2-0}(x-0)=x \\ y=x \end{gathered}[/tex]Now we have the equations of the lines, we must convert the equation to inequality by inserting one of these symbols instead of the equal sign:
> ≥ < ≤
For the blue line, the equation of the line is:
y = -3x + 6
Testing the origin (0,0):
0 = 0 + 6
0 = 6
To convert this to a true inequality we must replace the = for < or ≤
Since the blue line is solid, the points on the line belong to the solution, thus the first inequality is:
y ≤ -3x + 6
Now for the red line. The equation is
y = x. Let's test the point (2,1)
1 = 2
We must use the sign ≤ to make the expression true, thus the second inequality is:
y ≤ x
Thus, the system of inequalities is:
y ≤ -3x + 6
y ≤ x
In a single experiment, a die is tossed and a spinner with the letters a, b, and c is spun. each letter is equally likely. find the sample space and then find the probability of getting a 2 on the die and a b on the spinner. a. the sample space is 18. the probability of getting 2 and b is startfraction 1 over 18 endfraction. b. the sample space is 9. the probability of getting 2 and b is startfraction 1 over 9 endfraction. c. the sample space is 18. the probability of getting 2 and b is startfraction 1 over 9 endfraction. d. the sample space is 9. the probability of getting 2 and b is startfraction 1 over 18 endfraction.
Answer:c
Step-by-step explanation:
Answer:
Its A. Not C
Step-by-step explanation:
A is The sample space is 18. The probability of getting 2 and B is 1/18.
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an early wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.
The amount he earns by option A can be calculated as follows;
As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;
Option A earning: 40 × 19 = $760
Thus, the salesperson earns $760 through option A.
Consider x to be the amount of weekly sales;
As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.
(8/100)x = 760
0.08x = 760
x = 760 / 0.08
x = 9,500
Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.
Although there is a mistake in your question, you might be referring to this question;
A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option
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Help!!, its a math question... it TIMED! The question is in the pic...
I think
Answer:
23
Step-by-step explanation:
Isolate the variable. Divide each variable
A food truck vendor determined that 42% of his customers order a beverage with their food. What is the ratio of customers who order a beverage to customers who do not order a beverage?
Answer:29
Step-by-step explanation:
