Answer:
53 teachers
Step-by-step explanation:
Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:
6,734 / 25 = 269.36
Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).
If we take 269 teachers and 25 students per class, we get:
269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.
That means that the number of teachers needed is 270.
It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.
52 more teachers must the district have to supplement their staff of 217 teachers.
Given that,
A school district has a student population of 6,734 students.
If the maximum class size is 25 students.
We have to determine,
How many more teachers must the district have to supplement their staff of 217 teachers?
According to the question,
Total number of students = 6,734
Maximum class size = 25 students
Then,
The number of teachers needed is,
[tex]= \dfrac{6734}{25}\\\\= 269.36[/tex]
Here, 269 teachers are needed for each group of 25 students.
Therefore,
The number of more teacher must the district have to supplement their staff of 217 teachers is,
269 - 217 = 52
Hence, 52 more teachers must the district have to supplement their staff of 217 teachers.
For more details refer to the link given below.
https://brainly.com/question/1504132
Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations).
Answer:
(8π -8√3) cm²
Step-by-step explanation:
The area of a circle with radius 4 cm is given by ...
A = πr² = π(4 cm)² = 16π cm².
The red shaded portion is part of a semicircle. That semicircle will have an area half that of the circle, so ...
A/2 = 8π cm²
__
The triangle OCB is an equilateral triangle, so the angle at B is 60°. The side AC is then √3 times side BC*, so is 4√3 cm. The area of triangle ABC is then ...
A = (1/2)AC·BC = (1/2)(4√3 cm)(4 cm) = 8√3 cm²
This area is subtracted from that of the semicircle to obtain the red shaded area:
red area = semicircle area - triangle area
red area = (8π -8√3) cm²
____
* AC can be found either from the Pythagorean theorem (√(8²-4²)), using trig functions (4tan(60°)), or using your knowledge of 30°-60°-90° triangles.
Given: F(x) = 3x^2+1, G(x) = 2x - 3, H(X) = x
Find F(x) + G(x) =
[tex]F(x)+G(x)=3x^2+2x-2.[/tex]
Solution:
Given data: [tex]F(x)=3x^2+1[/tex] and [tex]G(x)=2x-3[/tex]
To find F(x) + G(x):
Adding two functions which gives another function.
Substitute F(x) and G(x), we get
[tex]F(x)+G(x)=(3x^2+1)+(2x-3)[/tex]
[tex]=3x^2+1+2x-3[/tex]
[tex]=3x^2+2x-3+1[/tex]
[tex]=3x^2+2x-2[/tex]
[tex]F(x)+G(x)=3x^2+2x-2[/tex]
Hence, [tex]F(x)+G(x)=3x^2+2x-2.[/tex]
PLZ Help Picture included. Thanks+brainlyest is correct.
Answer: [tex]\angle GFH[/tex]
Step-by-step explanation:
A Transversal is defined as a line that intersect two or more lines.
For this exercise it is important to know that when a Transversal cut two parallel lines, several angles are formed. These are grouped in pairs.
One of those pairs are called "Alternate exterior angles".
Alternate exterior angles are those non-adjacent angles that are located outside the parallel lines and on opposite sides of the Transversal.
Alternate exterior angles are congruent, which means that they have equal measure.
In this case you know that the Transversal [tex]CH[/tex] cuts the parallel lines [tex]AD[/tex] and [tex]EG[/tex].
Therefore, based on the explanation given before, you can identify in the picture given in the exercise that the angles [tex]\angle ABC[/tex] and [tex]\angle GFH[/tex] are Alternate exterior angles.
Use substitution to solve the system of linear equations. In your final answer, include all of your work.
y = -3x + 4
y + 1/3y = 4/3
The solution is [tex](1,1)[/tex]
Step-by-step explanation:
The system of linear equation is
[tex]y=-3x+4[/tex] and [tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
Using substitution method, let us substitute [tex]y=-3x+4[/tex] in the equation
[tex]y+\frac{1}{3} y=\frac{4}{3}[/tex]
[tex]-3 x+4+\frac{1}{3}(-3 x+4)=\frac{4}{3}[/tex]
Multiplying the term [tex]-3x+4[/tex] by [tex]\frac{1}{3}[/tex], we get,
[tex]-3 x+4-x+\frac{4}{3}=\frac{4}{3}[/tex]
Subtracting both sides by [tex]\frac{4}{3}[/tex],
[tex]-3x+4-x=0[/tex]
Simplifying, we get,
[tex]\begin{aligned}-4 x+4 &=0 \\-4 x &=-4 \\x &=1\end{aligned}[/tex]
Now, substitute [tex]x=1[/tex] in [tex]y=-3x+4[/tex]
[tex]y=-3(1)+4\\y=-3+4\\y=1[/tex]
Thus, the solution is [tex](1,1)[/tex]
Answer:
y = -3x + 4
x + 1/3y = 4/3
Substitute the first expression into the second equation for y:
x + 1/3(-3x + 4) = 4/3
x - x + 4/3 = 4/3
4/3 = 4/3
Thus, all real numbers are solutions.
Step-by-step explanation:
HOPE THIS HELPS, GOOD-LCK, and Brainliest, also let me know if i am wrong.
An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a building is 38°. The engineer knows the building is 300 ft tall. What is the distance from the engineer to the base of the building to the nearest whole foot? ✓ 384 ft 487 ft X 234 ft 185 ft
Answer:
My best guess is 384 ft
Step-by-step explanation:
Tangent 38° = opposite side / adjacent side
Tangent 38° = 300 ft / x ft
The value of x from the equation is 383.98 ft. Thus, the engineer is 383.98 ft.
Rounding it up gives us 384 ft.
Answer:
384 ft.
Step-by-step explanation:
We know the opposite side of the triangle and we need the adjacent side.
So tan 38 = opposite / adjacent
= 300 / x
x = 300 tan 38
x = 383.98 feet.
You have just bought a new Sony 55” 3D television set for $2300. The TV’s value decreases at a rate of $250 per year. Construct a linear function to represent this situation. Clearly indicate what your variables represent.
Answer:
2300-x(250) is the best i could think of hope it helps
Step-by-step explanation:
We need to represent the value of a TV whose value decreases yearly.
The required equation is [tex]y=2300-250x[/tex]
The cost of the TV set is $2300.
The decrease in value is $250 per year.
Let [tex]x[/tex] be the number of years that has passed after buying the TV
and [tex]y[/tex] be the cost of TV after [tex]x[/tex] years have passed.
The linear equation that represents the situation is [tex]y=2300-250x[/tex]
Learn more:
https://brainly.com/question/11897796
https://brainly.com/question/2263981
Solving a right triangle ‼️ Can someone help me find A,a and c❓ (Round to the nearest tenth)
Answer:
see explanation
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the given angles from 180 for A
A = 180° - (90 + 48)° = 180° - 138° = 42°
----------------------------------------------------------
tan48° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{18}{a}[/tex]
Multiply both sides by a
a × tan48° = 18 ( divide both sides by tan48° )
a = [tex]\frac{18}{tan48}[/tex] ≈ 16.2 ( to the nearest tenth )
-----------------------------------------------------------
sin48° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{18}{c}[/tex]
Multiply both sides by c
c × sin48° = 18 ( divide both sides by sin48° )
c = [tex]\frac{18}{sin48}[/tex] ≈ 24.2 ( to the nearest tenth )
Use 10 for m. Then find the value of the expression 3.5m.
Answer:
30
Step-by-step explanation:
the required ans 30 or the valuse is 30
What part of an hour elapses from 4:56 P.M. to 5:32 P.M.?
Answer:
[tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex]
Step-by-step explanation:
Given hours is from 4:56 P.M. to 5:32 P.M.
Now, finding the part of an hour elapases.
We know the starting time is 4 minutes to 5:00 P.M and end time is 32 minutes past 5 P.M.
∴ Total times elapses= [tex]4\ minutes + 32\ minutes= 36\ minutes[/tex]
Hence, 36 minutes elapses out of an hour.
Remember; 1 hours= 60 minutes
Next, finding the fraction of an hour elapses.
[tex]Part\ of\ an\ hour\ elapses= \frac{36}{60}[/tex]
∴ [tex]Part\ of\ an\ hour\ elapses= \frac{3}{5} \ hour[/tex]
Hence, [tex]\frac{3}{5} \ of \ an\ hour\ elapses[/tex] from 4:56 P.M. to 5:32 P.M.
Which of the following describes the graph of y = x² - 7x + 12?
1) The graph has zeroes at x = -4 and x = -3 and it opens downward.
2) The graph has zeroes at x = 4 and x = 3 and it opens downward.
3) The graph has zeros at x = -4 and x = -3 and it opens upward.
4) The graph has zeroes at x = 4 and x = 3 and it opens upward.
Answer:
4
Step-by-step explanation:
its a parabola that opens upward, the zeros are x=4 and x=3
explain how you know the numbers of the decimal places that should be in the product when you multiply two decimal numbers together
Answer:
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
Step-by-step explanation:
Let's remember that multiplying decimals is the same as multiplying whole numbers except that you have to put the decimal point in the answer. When you multiply decimals, the decimal point is placed on the product so that the number of decimal places in the product is the sum of the decimal positions of the factors.
Example:
214 * 32 = 6,848
0.214 * 0.32 = 0.06848 (3 + 2 = 5 decimal places)
7 * 11 = 77
0.7 * 0.11 = 0.077 (1 + 2 = 3 decimal places)
What is the x intercept and y intercept of this equation.
Answer:
x intercept is 15 and y intercept is -3.75
Step-by-step explanation:
The first thing is to form equation with the given tow point using the formula
y-y1/x - x1 = y2 - y1/ x2 - x1
y + 5/x + 5 = -2 + 5/7 + 5
y + 5/x + 5 = 3/ 12
3x + 15 = 12y + 60
12y - 3x = -45
On x intercept y = 0
x = 15
On y intercept x = 0
y = -3.75
Water tower. Model depth 32cm actual depth is ?m
The question involves converting the model depth from centimeters to meters, which typically requires dividing by 100. However, without a specific scale or additional detail, the direct conversion of 32cm would be 0.32 meters.
Explanation:The student's question is about converting the depth of a model water tower, provided in centimeters, to its actual depth in meters without giving a specific depth in the question. This concept usually involves understanding the scale of models and how to apply proportional reasoning to determine actual sizes. However, without a specific scale or the actual depth given in the question, we can't calculate the actual depth.
Generally, to convert from centimeters to meters directly, we divide the length in centimeters by 100, because 1 meter equals 100 centimeters. For example, if a model tower's depth is 32cm, to find this depth in meters, you would divide 32 by 100, which equals 0.32 meters.
Write each decimal as a fraction in simplest form
0.8
Answer:
4/5
Step-by-step explanation:
.8 is the same as 8/10
8/10 simplifies to 4/5 as both the numerator and denominator can be divided by 2
Answer:
Step-by-step explanation:
0.8 = 8/10 = 4/5
Writing and graphing linear equations
Answer:
whats the question?
Step-by-step explanation:
In the piece-wise function graphed below, which is the correct equation for when − 2 ≤ x ≤ 2
y=-2x+2
y=-1/2x+2
y=-2x+4
y=-1/2x+4
Answer:
y=-1/2x+2
Step-by-step explanation:
y = mx + p
m=slope = -1/2
p= y-intercept = 2
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 2
Step-by-step explanation:
The segment for - 2 ≤ x ≤ 2 is a straight line
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
To calculate m use the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (2, 1) ← the endpoints of the line
m = [tex]\frac{1-3}{2+2}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
Note the line crosses the y- axis at (0, 2) ⇒ c = 2
y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation for - 2 ≤ x ≤ 2
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (5,4) and (2,-7)?
Answer:
slope = [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, - 7)
m = [tex]\frac{-7-4}{2-5}[/tex] = [tex]\frac{-11}{-3}[/tex] = [tex]\frac{11}{3}[/tex]
It took mr. Raleigh a total of 9 hours to drive to his grandpa’s house. He drove m miles before lunch 240 miles after lunch. If he drove at a constant speed, what expression can be used to find how many miles Mr.Raleigh drove each hour?
What is 2 3/4 • 6 2/3
The total temperature change over 3 days in Gritty City was −6 degrees Celsius.
What was the average temperature change each day?
Answer:
-2 degrees celcius
Step-by-step explanation:
-6/3
Answer:
Each day, the temperature rises plus -6 Celsius
“ The Science Club went on a two-day field trip. The first day the members paid $70 for transportation plus $15 per ticket to the planetarium. The second day they paid $90 for transportation plus $12 per ticket to the geology museum. Write an expression to represent the total cost in dollars for two days for the n members of the club. An expression that represents the total cost in dollars for two days for the n members of the club is given by .”
Answer:
[tex]x = \$187n[/tex]
Step-by-step explanation:
let x be the total cost in dollars for two days for the n members
Given:
The first day the members paid $70 for transportation plus $15 per ticket to the planetarium.
The second day they paid $90 for transportation plus $12 per ticket to the geology museum.
We need to write an an expression to represent the total cost in dollars for two days for the n members of the club.
Solution:
First day each member pay $70 for transportation and $15 for ticket,
[tex]Cost\ per\ member\ for\ the\ first\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = 70+15[/tex]
[tex]Cost\ per\ member\ for\ the\ first\ day = \$85[/tex]
Therefore, cost for n members for the first day.
[tex]Cost\ for\ n\ member\ for\ the\ first\ day = \$85n[/tex]
Similarly for the second day each member pay $90 for transportation and $12 for ticket,
[tex]Cost\ per\ member\ for\ the\ second\ day = transportation\ cost+ticket\ cost[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = 90+12[/tex]
[tex]Cost\ per\ member\ for\ the\ second\ day = \$102[/tex]
Therefore, .
[tex]Cost\ for\ n\ member\ for\ the\ second\ day = \$102n[/tex]
Now, we write an expression to represent the total cost in dollars for two days for the n members of the club, so cost for n members for two days is equal to sum of the two days expenses for n members.
[tex]Cost\ for\ n\ member\ for\ the\ two\ day = \$85 + \$102n[/tex]
[tex]x = \$85n + \$102n[/tex]
[tex]x = \$187n[/tex]
Therefore, total cost for two days for the n members [tex]x = \$187n[/tex]
How do I solve this?
Answer:
The equation of the required straight line is y = 4x + 1.
Step-by-step explanation:
The equation of all the straight lines that are parallel to the straight line y = 4x - 3 is given by
y = 4x + c .............. (1)
where, c is any real constant and c ≠ - 3.
{Since parallel straight lines have the same slope and different y-intercept }
Now, we have to find the value of c such that the parallel straight line passes through the point (-1,-3).
Now, putting x = - 1 and y = - 3 in equation (1) we get,
- 3 = 4(- 1) + c
⇒ c = 1
Therefore, the equation of the required straight line is y = 4x + 1. (Answer)
412 Divided by four show your work
Answer:
103
Step-by-step explanation:
You start with long division 4 goes into 4 1 time and then 0 cause you have nothing else drop the 12 and then 4 goes into 12 3 times 103
Answer:
103
Step-by-step explanation:
If you solve it using partial quotients, it would be eaisier to demonstrate than using another method like standard division.
Hope this helps!
-Coconut;)
Carmen often orders party trays from her favorite Mexican food restaurant For company events. For a recent company party, she spent $58 on one burrito platter and one taco platter. For a company meeting, she spent $90 on to burrito platters and one taco platter. How much does each type of platter cost?
By setting up a system of equations from the given scenarios, we find that the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Explanation:To solve Carmen's problem about the cost of burrito and taco platters, we need to set up a system of equations based on the information given.
We know she spent $58 on one burrito platter and one taco platter and $90 on two burrito platters and one taco platter.
Let's denote the cost of a burrito platter as B and the cost of a taco platter as T.
Step 1: Establish the Equations
The first scenario gives us the equation: B + T = 58.
The second scenario gives us the equation: 2B + T = 90.
Step 2: Solve the Equations
From the first equation, we can express T in terms of B: T = 58 - B.
Substitute the expression for T in the second equation: 2B + (58 - B) = 90.Simplify and solve for B: B = 32.Substitute the value of B back into any of the original equations to find T: T = 26.Therefore, the cost of a burrito platter is $32 and the cost of a taco platter is $26.
Which of these equivalent
ratios is the unit rate?
90 miles
3 hours
60 miles
2 hours
30 miles
1 hour
Answer:
30 miles/1 hour is the unit rate.
Step-by-step explanation:
This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.
ILL GIVE BRAINLESS AND POINTS.I need step by step explanation
The answer for P(A∪B) is 40/45 (or) 8/9.
Step-by-step explanation:
Given,
The number of students that play only stringed instruments (A) = 35 students.
The number of students that play only brass instruments (B) = 10 students.
The number of students that play both of the instruments = 5 students.
The number of students that play none of the instruments = 5 students.
Probability = Number of required events / Total events
To find the total number of students,
TOTAL = A + B - both + neither.
TOTAL = 35 + 10 - 5 + 5 = 45 students.
P(A∪B) = P(A) + P(B) - P(A∩B)
Probability of A, P(A) = 35 students / 45 students = 35/45
Probability of B, P(B) = 10 students / 45 students = 10/45
Probability of A∩B (both), P(A∩B) = 5 students / 45 students = 5/45
P(A∪B) = (35/45) + (10/45) - (5/45)
= 40/45
P(A∪B) = 8/9
A college with a graduating class of 4000 students in the year 2008 predicts that its graduating class
will grow 5% per year. Write an exponential function to model the number of students y in the graduating class t years
after 2008.
Answer:
[tex]y=4000*(1.05)^t[/tex]
Step-by-step explanation:
The graduating class grows by 5% each year, this means after 1 year the number of students graduating will be 105% of 4000, or
[tex]4000*\frac{105}{100} =4000*1.05[/tex]
And after 2 years it will be
[tex](4000*1.05)*1.05[/tex]
and so on. Thus, after [tex]t[/tex] years the number of students [tex]y[/tex] will be
[tex]\boxed{ y=400*(1.05)^t}[/tex]
An exponential function to model the number of students y in the graduating class t years after 2008 is y = 4000(1.05)^t
Exponential functionsThe standard exponential function is expressed as:
y = ab^x
a is the initial populationb is the rate x is the timeIf a college with a graduating class of 4000 students in the year 2008 predicts that its graduating class will grow 5% per year, hence the required exponential equation will be:
y = 4000(1.05)^t
Learn more on exponential function here: https://brainly.com/question/12940982
Given Angle 1 = Angle 2,
find x.
Answer:
x = 6
Step-by-step explanation:
Given ∠ 1 = ∠ 2 then the segment is an angle bisector and the ratios of sides to base are equal, that is
[tex]\frac{3}{x-4}[/tex] = [tex]\frac{x}{4}[/tex] ( cross- multiply )
x(x - 4) = 12 ← distribute left side
x² - 4x = 12 ( subtract 12 from both sides )
x² - 4x - 12 = 0 ← in standard form
(x - 6)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 2 = 0 ⇒ x = - 2
However, x > 0 , thus x = 6
suppose the hot dogs come in packs of 9 and the buns come in packs of 12.it was the least number of each for which this is possible.
Answer:
Step-by-step explanation:
Least common number for 9 and 12 is 36
36/9=4
36/12=3
4 packs of hot dogs and 3 packs of buns
A line passes through the point (4,-7) and has a slope of 3/2. Write an equation in point-slope form for this line.
Answer:
Step-by-step explanation:
y - y1 = m(x - x1)
slope m = 3/2, y1 = -7, x1 = 4
y + 7 = 3/2(x - 4)
y + 7 = 3x/2 - 6
y = 3x/2 - 6 - 7
y = 3x/2 - 13