an arts academy requires there to be 5 teachers for every 115 students and 6 tutors for every 54 students. how many students the academy have per teacher? per tutor? how many tutors does the academy need if it has 72 students
The number of students per teacher is 23.
The number of students per tutor is 8.
The number of tutors needed for 72 students is 9.
What is the number of students per teacher and per tutor?In order to determine the number of students per teacher, divide the total number of teachers by the total number of students.
Students per teacher = total number of students / total number of teachers
115 /5 = 23 students per teacher
In order to determine the number of students per tutor, divide the total number of tutors by the total number of students.
Students per tutor = total number of students / total number of tutors
54 / 6 = 9 students per tutor
The number of tutors needed for 72 students = total number of students / students per tutor
72 / 9 = 8 tutors
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Is anyone able to solve this?
Explanation:
To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:
a² + b² = c² (c is always hypotenuse)
So:
a² + 6² = 9²
a² = 9² - 6²
a² = 81 - 36
a² = 45
a = sqrt45
Now we do the same thing for the other triangle:
x² + 5² = sqrt45²
x² + 25 = 45
x² = 20
x = 2√5 or 4.5...
Find the sum of 0.45 and .5 using the fraction approach.
Answer:
[tex]\frac{19}{20}[/tex]
Step-by-step explanation:
0.45 can be written as [tex]\frac{9}{20}[/tex] in fractional form and 0.5 can be written as [tex]\frac{1}{2}[/tex].
Whenever adding fractions you need like bases. To do this, multiply the 0.5 fraction by 10/10. This would get you [tex]\frac{10}{20}[/tex].
Adding fractions:
[tex]\frac{9}{20} + \frac{10}{20}[/tex] ** only add the numerators and leave the denominator as is
= [tex]\frac{19}{20}[/tex]
The cost to replace a water pump in a sports car was $899. This included $365 for the water pump and $89 per hour for labor. How many hours of labor were required to replace the water pump?
Explanation:
We know the final price is $899 and $365 is constant price:
899 = 365 + 89x
We need to find x, the amount of hours, by simplifying:
534 = 89x
x= 6
6 hours of labor
Your utility company charges 13 cents per kilowatt-hour of electricity. Complete parts (a) and (b) below.
a. What is the daily cost of keeping lit a 60-watt light bulb for 10 hours each day?
b. How much will you save in a year if you replace the bulb with an LED bulb that provides the same amount of light
using only 15 watts of power?
a. The daily cost of keeping lit a 60-watt light bulb for 10 hours each day is $
(Round to three decimal places as needed.)
b. The yearly savings of replacing the 60-watt light bulb with a 15-watt light bulb is $
(Round to two decimal places as needed.)
Answer: a) $78 per day
b) $21,352.50
Step-by-step explanation:
a) 60x10=600
600x0.13= $78 per day
b) 15x10=150
150x0.13=$19.50 per day
19.50x365= $7,117.50 per year (with a 15watts lightbulb)
$78x365=$28,470 per year (with a 60watts lightbulb)
$28,470-7,117.50= $21,352.50
The area of a rectangular field is 8624 m².
If the width of the field is 88 m, what is its length?
Answer:
98 m
Step-by-step explanation:
A = l * w
8624 = l * 88
l = 8624/88 = 98 m
Harper's car used 9 gallons to travel 171 miles. How many miles can the car go for each gallon of gas?
Answer:
Step-by-step explanation:
7
Find the chi-square value x2l corresponding to a sample size of 4 and a confidence level of 98 percent.
The critical values for the chi-square distribution, with a sample size of 4 and a confidence level of 98 percent, are of:
0.2971 and 13.2767.
How to obtain the critical value for the chi-square distribution?The critical value for the chi-square distribution is obtained inserting these following information into a calculator:
The tail of the test, whether it is left tailed, right tailed or two tailed.The number of degrees of freedom, which is one less than the sample size.The significance level, which is one subtracted by the decimal equivalent of the confidence level.In the context of this problem, with a sample size of 4 and a confidence level of 98 percent, the parameters are given as follows:
Two-tailed test, as it is standard since it says nothing about the tail.3 degrees of freedom, which is one less than the sample size of 4.Significance level of 0.02, as the subtraction of one by the confidence level of 0.98 is of 0.02.Inserting these information into the calculator, the critical values are given as follows:
0.2971 and 13.2767.
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An exercise machine with an original price of $890 is on sale at 24% off.
a. What is the discount amount?
b. What is the exercise machines sale price?
The discount amount is $213.6
The sale price for the exercise machines is $676.4
How to calculate the discount amount ?The first step is to calculate the discount amount
890 × 24/100
= 890 × 0.24
= 213.6
The next step is to calculate the sale price
890(1-0.24)
890(0.76)
676.4
Hence the discount amount is $213.6 and the sale price of the exercise machine is $676.4
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An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.10 ounces and a standard deviation of 0.20 ounce. Suppose that you select a sample of 16 oranges.
a. What is the probability that the sample mean amount of juice will be at least 4.03ounces?
b. The probability is 74% that the sample mean amount of juice will be contained between what two values symmetrically distributed around the population mean?
c. The probability is 78% that the sample mean amount of juice will be greater than what value?
The measures, using the normal distribution and the central limit theorem, are given as follows:
a) Probability of at least 4.03 ounces: 0.9192 = 91.92%.
b) Probability of 74% that it is between 4.04 ounces and 4.16 ounces.
c) Probability of 78% that it is greater than 4.06 ounces.
Normal Probability DistributionThe z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The parameters regarding the amount of juice squeezed from these oranges are given as follows:
[tex]\mu = 4.10, \sigma = 0.2, n = 16, s = \frac{0.2}{\sqrt{16}} = 0.05/tex]
The probability that the sample mean amount of juice will be at least 4.03 ounces is one subtracted by the p-value of Z when X = 4.03, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (4.03 - 4.10)/0.05
Z = -1.4.
Z = -1.4 has a p-value of 0.0808.
1 - 0.0808 = 0.9192.
Considering the symmetry of the normal distribution, the middle 74% of the measures is bounded by:
The 13th percentile, which is X when Z = -1.125.The 87th percentile, which is X when Z = 1.125.Hence the lower bound is:
[tex]Z = \frac{X - \mu}{s}[/tex]
-1.125 = (X - 4.10)/0.05
X - 4.10 = -1.125 x 0.05
X = 4.04.
The upper bound is:
[tex]Z = \frac{X - \mu}{s}[/tex]
1.125 = (X - 4.10)/0.05
X - 4.10 = 1.125 x 0.05
X = 4.16.
The probability is 78% that the sample mean amount of juice will be greater than the 22th percentile, which is X when Z = -0.77, hence:
[tex]Z = \frac{X - \mu}{s}[/tex]
-0.77 = (X - 4.10)/0.05
X - 4.10 = -0.77 x 0.05
X = 4.06 ounces.
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(15x + 3)
108
Solve for x
Answer:
(15x+3)° = 108 (vertically opposite angles)
15x = 108-3
15x = 105
x = 105/15
x =7
y = -x + 10| what is the axis of summetry
The axis of symmetry of function y = -|x + 10| is at y = 0
Axis of symmetry is an imaginary straight line which divide the function into two equal parts.
Axis of symmetry creates a mirror image of other part.
If we fold the two parts then the parts will superimposed.
Given function,
y = -|x + 10|
is in form y = a |x - h| + k
here , (h, k) is vertex
Comparing the form to the given equation
(h, k) = (-10 , 0)
which means graph is opens upward
and a = -1
Hence, the equation of axis of symmetric is at y = 0
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Select all of the following that are quadratic functions. x = 3y2 – 6y + 5 y + 3 = –2 x 2+ 5 y = 2 x 2 – 8 x + 6 y= –7 x – 4 y – 3 x = 4 x 3 – x2 + 9 y = 5 x(x + 9) – 8 y – 2 x 2 = 3 x – 2 x 2 + 4
The quadratic functions in this problem are listed as follows:
x = 3y2 – 6y + 5.y + 3 = -2x² + 5.y = 2x² - 8x + 6.y = 5x(x + 9) - 8.What is the definition of a quadratic function?The definition of a quadratic function is presented as follows:
y = ax² + bx + c.
In which the leading coefficient a has to assume a value different of zero.
Another format to represent a quadratic function is making the input variable y and the output variable x, which is an exchange of the conventional notation, hence:
x = ay² + by + c.
The non-quadratic functions in this problem are:
y = -7x - 4 -> Linear function, as the highest exponent is of one.y - 3x = 4x³ - x² + 9. -> Cubic function, as the highest exponent of three.All the other functions are quadratic functions, as they have two as the highest exponent, with a leading coefficient different of zero.
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The length of the base of an isosceles triangle is x. The length of a leg is 4x−6. The perimeter of the triangle is 42. Find x
Answer:
x = 6
Step-by-step explanation:
x + 2(4x-6) = 42
x + 8x - 12 = 42
9x = 42 + 12
9x = 54
9/9 x = 54/9
x = 6
I need help with this please help me
Answer:
y = 122
x = 58
Step-by-step explanation:
Parallel line angle rule, corresponding angle are equal
so y = 122
A flat line has 180degree angle
to get x, flat line - y = 180 - 122 = 58
PLEASE HELP !!! I NEED THE ANSWER IN THE NEXT HOUR
This is not a prime factorization.
The correct prime factorization is [tex]2^5*3*5^4*11^2[/tex]
=======================================================
Further Explanation:
The expression your teacher gave you is not a prime factorization because the 8 isn't prime.
8 = 2*2*2 = [tex]2^3[/tex]
If we replace 8 with [tex]2^3[/tex], then we go from
[tex]2^2*3*5^4*8*11^2[/tex]
to
[tex]2^2*3*5^4*2^3*11^2[/tex]
and that rearranges to
[tex]2^2*2^3*3*5^4*11^2[/tex]
Then we can simplify the [tex]2^2*2^3[/tex] portion to get [tex]2^5[/tex] since we add the exponents while keeping the base '2' the same.
We therefore end up with
[tex]2^5*3*5^4*11^2[/tex]
as the correct prime factorization. Each base (2,3,5,11) is a prime number.
---------------
As a check, use your calculator to type in
2^2*3*5^4*8*11^2
and also
2^5*3*5^4*11^2
and you should get the result of 7,260,000 each time. Since we get the same result, this confirms 2^2*3*5^4*8*11^2 = 2^5*3*5^4*11^2
33. The systolic blood pressure (given in millimeters) of males has an approximately normal distribution
with mean 125 and standard deviation 14. Systolic blood pressure for males follows a normal
distribution.
Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure Kyle's blood pressure : 149.5
What is blood pressure?
Blood pressure (BP) is the force exerted by moving blood against blood vessel walls. The heart's action of pumping blood through the blood vessels is largely responsible for this pressure. The pressure in the major arteries is meant when the term "blood pressure" is used without qualification. Systolic pressure, or the highest pressure during one heartbeat, is typically expressed as the ratio of diastolic pressure, or the lowest pressure between two heartbeats, in blood pressure measurements. It is expressed as a millimetre of mercury (mmHg) above the atmospheric pressure in the immediate vicinity.
The z-score of a measure X in a set with mean and standard deviation is given by:
Z = (X - μ) / σ
The Z-score calculates the deviation of the measure from the mean in standard deviations. We look at the z-score table after determining the Z-score to determine the p-value connected to it. The likelihood that the measure's value is less than X, or the percentile of X, is represented by this p-value. The likelihood that the value of the measure exceeds X is calculated by deducting 1 from the p-value.
This issue involves that:
μ = 125
σ = 14
The z-score for Kyle's systolic blood pressure is 1.75, according to his physician.
He therefore has a 1.75 standard deviations higher systolic blood pressure than the mean.
Which of the following best describes how this standardized score should be interpreted?
Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure.
Calculate Kyle's blood pressure in part (b). (Enter a precise quantity as a decimal, fraction, or integer.)
If Z = 1.75, then this is X.
Z = (X - μ) / σ
1.75 = (X - 125) / 14
1.75 x 14 = (X - 125)
24.5 = X - 125
X = 24.5 + 125
X = 149.5
Hence, a) Kyle's systolic pressure is 1.75 standard deviations higher than the male average for systolic pressure.
b) Kyle's blood pressure is 149.5
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Lesbian Anna close cylinder have the same radius the height of the cylinder is four times the radius what is the ratio of the volume of the cylinder to the volume of the sphere
The ratio of the volume of the cylinder to the volume of the sphere = 3:1
Let take the volume of a closed cylinder as V1.
And take the volume of a closed sphere as V2.
And the radius of the cylinder = radius of the sphere = r
Height of the cylinder = h
If height of the cylinder is four times the radius of the cylinder which means h = 4r
Volume of the closed cylinder V1 = π × r^2 × h
if h = 4r
Then V1 = π × r × r × 4r
V1= 4π × r^3
Volume of the closed cylinder V1= 4π × r^3
Volume oh the sphere V2 = 4/3 × π × r^3
The ratio of the volume of the cylinder to the volume of the sphere
= V1 / V2 = V1 : V2
V1 : V2 = (4π × r^3) ÷ (4/3 × π × r^3)
V1 : V2 = 4 ÷ 4/3 = 4/1 × 3/4 = 3/1 = 3 : 1
The ratio of the volume of the cylinder to the volume of the sphere = 3:1
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When choosing the linear equation that represents the graph, I can look at the direction of the line and automatically know if the slope is a positive or negative number
Question 1 options:
True
False
True. You can look at the direction of the line and automatically know if the slope is a positive or negative number.
The linear equation with positive value of slope goes upwards from left to right and linear equation with negative value of slope goes downwards from left to right.
Thus, it is true that you can look at the direction of the line and automatically know if the slope is a positive or negative number.
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a waste bin is in the shape of a cylinder. the diameter of the base is 20cm and the height is 25cm . what is the volume of the waste bin.
If a waste bin is in the shape of a cylinder. the diameter of the base is 20cm and the height is 25cm. The volume of the waste bin is: 7,853.98 cm³.
How to find the volume?Using this formula to find the volume
Volume (v) = π (d/2)² h
Where:
d= diameter = 20 cm
h = height =25 cm
Let plug in the formula
Volume (v) = π × (20/2)² × 25
Volume (v) = π × 100 × 25
Volume (v) = 7,853.98 cm³
Therefore 7,853.98 cm³ is the volume.
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700 bags of onions were purchased at $2.57 per bag. The desired markup is 41% based on selling price, but 20% spoilage is expected. What should the selling price per bag be?
The selling price per bag whose purchasing price is $2.57 and profit is 41% should be $4.52
What is selling price?
The amount a buyer pays for a good or service is known as the selling price. Selling price may differ based on the price that buyers are prepared to pay, the seller's acceptance threshold, and how competitive the price is in relation to those of other companies in the market.
Given in the question,
Number of bags = 700
Purchase per bag = $2.57
Spoilage = 20%
Profit = 41%
Cost of 700 bags of onion = 700*2.57 = $1799
Spoilage of 20% = 700*20% = 140 bags, which means only 560 bags left to sell
Desired profit = 41 percent
Assume Selling Price be SP
Profit percentage = (560*SP - 1799)/1799
0.41 = (560*SP - 1799)/1799
SP = $4.52
Therefore, selling price is $4.53
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The distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres. What percent of the journey did he run?
A student ran 6% of the journey.
In this question, we have been given the distance between two village is 8km a student walk from one village to the other he walk most of the way buy runs the last 480metres.
We know that 1 km = 1000 meters
So, 8 km = 8000 meters
So, the percent of the journey he ran,
480/8000 * 100
= 6%
Therefore, A student ran 6% of the journey.
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The polynomial function f(x) is graphed below. Fill in the form below regarding the features of this graph.
Answer:
Even and Positive
Step-by-step explanation:
Workbook Reference:
Perform the indicated operations. Write answer in descending order.Add -13x + 9 - 10y, 9x - 7y and -12x - 3y + 8
Answer:
−16x − 20y + 17
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100
The equation that is used to find the length of the legs of the triangle is
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0
The area of the triangle is 24 square feet.
We know that the area of a triangle is given by the formula
1/2 × base × height.
Now in the attached figure we can see that the length of the base is x feet
The height of the right-angled triangle is (x+2) feet.
So the area of the triangle will be:
area = 1/2 · (x) · (x+2)
or, area = 0.5x(x+2)
But the area of the triangle is 24 square feet. Therefore the Equation to find the legs will be 0.5x(x+2) = 24.
Now if we use the properties of Pythagoras theorem we can write the formula as
hypotenuse² = sum of squares of legs
10² = x² + (x+2)²
Therefore we get the second equation.
Now simplifying the above equation we get:
10² = x² + (x+2)²
or, 2x² + 4x - 96 = 0
or, x² + 2x - 48 = 0
This is the third option.
Therefore the required equation are:
0.5(x)(x + 2) = 24 , x² + (x + 2)² = 100 and x² + 2x – 48 = 0 .
Disclaimer: The missing image of the triangle is attached below.
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Lisa collected leaves from different trees for a science project. Every day for a week (7 days), she collected 7 leaves. How many leaves did she collect by the end of the week?
The photography club is selling hot chocolate at soccer games to raise money for new cameras. The table shows their profit per game for the first five games.
the graph is below
Game Profit ($)
1 −12.50
2 −10.15
3 18.65
4 25.90
5 45.75
Based on the average profit per game, how much total money can the club expect to earn by the end of the 10-game season?
__ dollar(s)
Based on the average profit per game, the total money which this club should expect to earn by the end of the 10-game season is $80.21.
How to find a trend line for the data?In order to determine a linear equation of the trend line (line of best fit) that models the data points contained in the table, we would have to use a scatter plot.
In this scenario, the number of games would be plotted on the x-axis of the scatter plot while the profit (in dollars) would be plotted on the y-axis of the scatter plot.
On the Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the trend line on the scatter plot.
From the scatter plot (see attachment) which models the relationship between the data points in the table, a linear equation of the trend line is given by:
y = 8.23x - 2.09
By the end of the 10-game season, the average profit per game is given by:
y = 8.23x - 2.09
y = 8.23(10) - 2.09
y = 82.3 - 2.09
y = $80.21.
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8. Given that the total distance travelled is 1.4 km, and the
acceleration is 4 m/s² for the first T seconds, find:
a) the value of V
b) the value of T.
Step-by-step explanation:
Formula for distance travelled:
x= ut + 1/2at^2
x is 1.4km, convert this to m since acceleration is in m, = 1400m
u is initial velocity, in this case assume 0
a is acceleration, = 4m/s^2
t is unkown and what we want to find out
Substitute value into formula,
1400 = 0t + 1/2(4)t^2
1400 = 2t^2
t^2 = 1400/2
t^2 = 700
t = 26.458s
Formula for acceleration:
a = (v-u)/t
at= v-u
Substitute value,
4(26.458) = v - 0
v = 105.832 m/s
HELP!! Will give brainiest
Answer:
C ≈ 207.3 ft
Step-by-step explanation:
the circumference (C) of a circle is calculated as
C = 2πr ( where r is the radius ) , then
C = 2π × 33 = 66π ≈ 207.3 ft ( to the nearest tenth )
Answer:
103.67 feet
Step-by-step explanation:
using C = pi d
When buying stock, there are often fees with the purchase. If a broker is charging a flat percentage of 2% for a trade, and you trade 1,000 shares at $5 each, what is the total amount charged by the broker?
The broker charged $100.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total shares = 1000
Price for each shares= $5.
So, the total price of 1000 shares= $5000
If broker is charging a flat percentage of 2% for a trade.
Then, the broker charged for 1000 trade
= 5000 x 0.02
= $100.
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