The University of Texas system consists of 9 campuses and has a budget of $2.4 billion in state funding. If the money were to be allocated equally based on total student enrollment, how much would be appropriated per student, rounded to the nearest cent?
Answers
Step 1:
Given data
Total number of campuses = 9
Total budget = $2.4 billion
Total students
= 33629 + 52359 + 8912 + 21493 + 23049 + 20353 + 5431 + 28923 + 7776
= 231925
Step 2
Convert $2.4 billion to cent, multiply $2.4 billion by 100.
[tex]2.4\text{ b}illion\text{ dollars = 2400000000 dollars = 240000000000 cent}[/tex]Step 3:
Divide the total budget in cent by total number of students
[tex]\begin{gathered} \text{Money appropriated per student = }\frac{240000000000}{231925} \\ =\text{ 1034817.29} \\ =\text{ 1034817 cent} \end{gathered}[/tex]Final answer
1034817 cent
Related Questions
This table shows the rainfall (in centimeters) for a city in different months. The quadratic regression equation that models these data is y=-0.77x^2+6.06x - 5.9Using this model, the predicted rainfall for month 11 is about -32.4 centimeters. Does this prediction make sense? Why or why not?A. No, because you can’t have a negative amount of rainfall.B. Yes, because the rainfall is declining.C. Yes, because it is the result of substituting x=11D. No, because you can’t measure rainfall in centimeters
Answers
The quadratic regression equation model given is;
[tex]\begin{gathered} y=-0.77x^2+6.06x-5.9 \\ \text{where y is the rainfall measure in cm} \\ x\text{ is the month} \end{gathered}[/tex]For month 11, substituting x = 11 in the equation,
[tex]\begin{gathered} y=-0.77x^2+6.06x-5.9 \\ y=-0.77(11)^2+6.06(11)-5.9 \\ y=-93.17+66.66-5.9 \\ y=-32.41\operatorname{cm} \end{gathered}[/tex]The predicted rainfall in month 11 is -32.4cm
From the options given, the correct answer is option A because the prediction does not make sense because there can not be a negative amount of rainfall.
Therefore, option A is the right answer.
I have no idea how to do this please help.
Answers
In this problem, we have an exponential growth function of the form
[tex]y=a(b)^x[/tex]where
a is the initial value (value of y when the value of x=0)
looking at the table
For x=0, y=8
that means
a=8
[tex]y=8(b)^x[/tex]Find out the value of b
For x=1, y=16
substitute
[tex]\begin{gathered} 16=8(b)^1 \\ 16=8(b) \\ \frac{16}{8}=b \\ b=2 \end{gathered}[/tex]therefore
the equation is
[tex]y=8(2)^x[/tex]Chords WP and KZ intersect at point L in the circle shown.Wzr3.x - 22LK5РWhat is the length of KZ?7.5910O 12
Answers
If the chords intersect inside the circle, the product of the lengths of the segments of the chords are equal.
[tex](KL)(LZ)=(WL)(LP)[/tex]Substitute the given values into the equation and then solve for the value of x.
[tex]\begin{gathered} 2(3x-2)=x(5) \\ 6x-4=5x \\ 6x-5x=4 \\ x=4 \end{gathered}[/tex]Since the value of KZ is the sum of the length of KL and LZ, we must find the length of LZ. Substitute the value of x into the expression and then simplify.
[tex]\begin{gathered} LZ=3x-2 \\ =3(4)-2 \\ =12-2 \\ =10 \end{gathered}[/tex]To obtain the value of KZ, add the lengths of KL and LZ.
[tex]\begin{gathered} KZ=KL+LZ \\ KZ=2+10 \\ KZ=12 \end{gathered}[/tex]Which of the following is the rule for rotating the point with coordinates (x,y), 90° clockwise about the origin?A. (x,y)→(y,−x)B. (x,y)→(x,−y)C. (x,y)→(y,x)D. (x,y)→(−y,x)
Answers
To rotate the point with coordinates (x, y) 90° clockwise about the origin, we use the following transformation:
[tex](x,y)\rightarrow(y,x)[/tex]210 students were asked whether they want to go to a water park or a roller skating rink for a class party.50 students are girls who want to go to the water park.45 students are girls who want to go skating.60 students are boys who want to go to the water park.3. To the nearest hundredth, what is the relative frequency of boys who want to go to the water park?4. The probability that a student is in a category can be approximated by the relative frequency. To the nearest hundredth, what is the probability that a randomly selected student is a girl who wants to go skating?
Answers
3. We have to calculate the relative frequency of the class "boys who want to go to the water park".
We can calculate the relative frequency as the quotient between the absolute frequency, which in this case is 60, and the total sample size, which is 210.
[tex]f=\frac{60}{210}\approx0.29[/tex]4. We have to estimate the probability of selecting a girl who wants to go skating.
As this class has an absolute frequency of 45, we can approximate the probability as:
[tex]P(G\text{ and }S)=\frac{45}{210}\approx0.21[/tex]Answer:
3. The relative frequency is approximately 0.29.
4. The probability is approximately 0.21.
R=3(x-11)^8 solve for x
Answers
The expression we have is:
[tex]R=\frac{3(x-11)}{8}[/tex]And we need to solve this expression for the variable x.
Step 1. The first step will be to multiply both sides of the equation by 8 in order to cancel the 8 in the denominator on the right-hand side of the equation:
[tex]8R=8\times\frac{3(x-11)}{8}[/tex]On the left-hand side, we get 8R, and on the right-hand side we will be left with 3(x-11):
[tex]8R=3(x-11)[/tex]Step 2. We continue dividing both sides by 3:
[tex]\frac{8R}{3}=\frac{3(x-11)}{3}[/tex]This is in order to eliminate the three on the right-hand side and we will be left with x-11:
[tex]\frac{8R}{3}=x-11[/tex]Step 3. The final step is to add 11 to both sides of the equation:
[tex]\frac{8R}{3}+11=x-11+11[/tex]On the right-hand side, -11+11 is equal to 0, and thus we have solved for x:
[tex]\frac{8R}{3}+11=x[/tex]Answer:
[tex]x=\frac{8R}{3}+11[/tex]A researcher is interested in estimating the mean salary of firefighters in a certain area.She wants to be 95% sure her estimate is correct.If the standard deviation is $5500,how large a sample is needed to get the desired informationand to be accurate within $2500?
Answers
To calculate the sample size to determine a mean we use the following formula:
[tex]n=(\frac{Z\sigma}{E})^2[/tex]n is the population size. Z is the Z value for the confidence level (for a confidence level of 95%, Z = 1.96)
σ is the standard deviation ($5500 in this case) and E is the margin of error. ($2500 in this case). Replacing values in the formula:
[tex]n=(\frac{1.96\cdot5500}{2500})^2\approx18.59[/tex]Then, the sample size should be 19 to estimate the mean with 95% confidence.
Josiah measured a line to be 18.4 inches long. If the actual length of the line is 19.2
inches, then what was the percent error of the measurement, to the nearest tenth of a
percent?
Answers
Given:
The actual measurement is 19.2 inches.
The new measurement is 18.4 inches.
To find the percent error:
So, the formula is,
[tex]\begin{gathered} \frac{Actual-New}{\text{Actual}}\times100=\frac{19.2-18.4}{19.2}\times100 \\ =\frac{0.8}{19.2}\times100 \\ =\frac{80}{19.2} \\ =4.166667 \\ \approx4.2 \end{gathered}[/tex]Hence, the percent error is 4.2%.
3 5 6 Question 1 What is your answer? The speed vs. time graph shows the motion of a person driving a car Why is this your answer? 60 speed (m/min) 20 time (min) -20 Which is the correct answer? 20 30 Why is this the correct answer? How much did the car's speed change in the time interval from 15 and 20 minutes? The speed increased by 40 m/min. B The speed decreased by 40 m/min c The speed increased by 20 m/min. The speed decreased by 20 m/min.
Answers
From the graph, the speed of the car at t=15m is 60 m/min, and the speed of the car at t=20m is 40 m/min. The change in velocity is given by:
[tex]\begin{gathered} \Delta v=40m/\min -60m/\min \\ =-20m/\min \end{gathered}[/tex]Therefore, the speed decreased by 20 m/min.
Rob had a test average of 85.6 last semester. His first four test grades were 78, 92, 94, and 80. Use the formula x‾=x1+x2+…+xnn to find his score on the fifth test.
Answers
Given the equation:
[tex]\bar{x}=\frac{x_1+x_2+x_3+x_4+x_5}{n}[/tex]In this question:
x- = 85.6
x₁ = 78
x₂ = 92
x₃ = 94
x₄ = 80
x₅ = missing
n = 5
Substitute the values and then solve for x₅.
[tex]\begin{gathered} 85.6=\frac{78+92+94+80+x_5}{5} \\ 85.6=\frac{344+x_5}{5} \\ \text{ Multiplying both sides by 5:} \\ 85.6*5=\frac{344+x_5}{5}*5 \\ 428=344+x_5 \\ \text{ Subtracting 344 from both sides:} \\ 428-344=344-344+x_5 \\ 84=x_5 \end{gathered}[/tex]Answer: 84.
Which of the following best defines the sequence shown? 7, 16, 25, 34....f(1) = 7, f(n) = f(n-1) - 9f(1) = 7, f(n) = f(n-1) - 16f(1) = 7 f(n) = f(n-1) + 16 f(1) = 7 f(n) = f(n-1) + 9
Answers
The general form of an arithmetic sequence can be written as:
[tex]a(n)=a+(n-1)d[/tex]Where
a is the first term
d is the common difference [difference between a term and its preceeding term]
• The first term is 7
Thus,
a = 7
• The common difference between the terms is:
16 - 7 = 9
25 - 16 = 9
34 - 25 = 9
Thus,
common difference is 9
d = 9
Plugging into the equation we have:
[tex]\begin{gathered} a(n)=7+(n-1)(9) \\ a(n)=7+9n-9 \\ a(n)=9n-2 \end{gathered}[/tex]This question gives the information in a different notation, that's all.
We match it with our solution.
a(1), or f(1) is the first term, which is 7.
The formula given is in terms of f(n-1).
f(n-1) is the term before it
So, we have:
f(n) = term before it + WHAT???
We know that to get the next term [ f(n) }, we have to ADD 9 to the term before it [ f(n-1) ].
Thus,
f(n) = f(n-1) + 9
Looking at the answer choices, the last one is correct.
Correct Answer:
f(1) = 7; f(n) = f(n-1) + 9A dilation with a scale factor < 1choose your answer...the size of the pre-image.
Answers
Answer
1) A dilation with a scale factor < 1 will reduce/decrease the size of the pre-image.
2) A dilation with a scale factor > 1 will enlarge/increase the size of the pre-image.
Step-by-step Explanation
Dilation refers to enlarging or reducing the size of an image. And the scale factor determines how much the image is reduced or enlarged.
- A scale factor of 1 means the image is neither enlarged or reduced.
- A very large scale factor (greater than 1) indicates that the size of the image is enlarged compared to the size of the original image.
- A very small scale factor (less than 1) indicates that the size of the image is reduced compared to the size of the original image.
So, for the question,
1) A dilation with a scale factor < 1 will reduce/decrease the size of the pre-image.
2) A dilation with a scale factor > 1 will enlarge/increase the size of the pre-image.
Hope this Helps!!!
1. Describe the transformations shown in the function 3f(x+2)-1 * A. Vertical Stretch of 3, Left 2, Down 1 B. Vertical Compression of 1/2, Left 2, Down 1C. Vertical Stretch of 3, Right 2, Up 1 D. Vertical Stretch of 3, Right 2, Down 1
Answers
First of all this is a linear function, and the basic function f(x) has now been translated to become
3f(x + 2 ) - 1
This means the basic function has been stretched by 3 units, moved two units to the right (which is x + 2) and one unit down (- 1)
The option D, describes the transformation that occured which is;
D: Vertical stretch of 3, Right 2, Down 1.
Please help with this problem:Solve for b.16 = a^2 + b^2A. b = 16 − a2B. b = ±16−a^2−−−−−−√C. b = ±16+a^2−−−−−−√D. b = 4−a
Answers
SOLUTION
We want to solve for b in the equation
[tex]16=a^2+b^2[/tex]Solving we have
[tex]\begin{gathered} 16=a^2+b^2 \\ we\text{ will move a}^2\text{ to meet 16, we have } \\ 16-a^2=b^2 \\ b^2=16-a^2 \\ move\text{ the square to the other side, it becomes square root, we have } \\ b=\pm\sqrt{16-a^2} \end{gathered}[/tex]Hence the answer is the second option
may anyone help me with this? im confused and would love an explanation!
Answers
Answer
Angle PQR = 82°
Explanation
Tosolve this, we just need to note one thing about the properties of a rhombus;
The diagonals of a rhombus bisects its angles into two equal parts.
So, this means that
4x - 27° = 2x + 7°
4x - 2x = 27° + 7°
2x = 34°
Divide both sides by 2
(2x/2) = (34°/2)
x = 17°
We are then asked to solve for Angle PQR
Angle PQR = 4x - 27° + 2x + 7°
Angle PQR = 6x - 20°
Recall that x = 17°
Angle PQR = 6x - 20°
Angle PQR = 6(17°) - 20°
Angle PQR = 102° - 20°
Angle PQR = 82°
Hope this Helps!!!
Select the correct answer.Select how this number is read.19.05A. one and nine hundred five thousandthsB. nineteen and five tenthsC. nineteen and five hundredthsD. nineteen point zero five
Answers
Given number:
[tex]19.05[/tex]When reading decimals we should identify the place value of the number after the decimal point. In this case, the place value of 5 is the hundredth.
Hence, the number is read as : nineteen and five hundredths
Answer:
Option C
Which ordered pair is included in the solution set to the following system?y > x2 + 1y < x2 – x + 1 (–3, 4) (–2, 6) (0, 2) (2, 4)
Answers
Explanation
We are given the following system of inequalities:
[tex]\begin{gathered} y>x^2+1 \\ yWe are required to determine the ordered pair that is included in the solution of the system of inequalities.We can get that by graphing the inequalities.
Using a graphical calculator, we have:
Hence, the answer is (-2, 6).
Answer:
(–2, 6)
Step-by-step explanation:
I got it right on the test.
1 point You are testing two different fertilizers on identical plants A and B. Plant Als 6 inches tall and growing at a rate of 4 inches per day. Plant Bis 10 inches call and growing at a rate of 2 inches per day. How would you write the equations? y = 4 +63 Y = 2 + 10.2 2 y=4 – 62 y = 2 – 10.2 Y = = 42 + 6 y = 2x + 10 y = – 42+6 y = -2x + 10
Answers
We have to find the equation that relate height y with time x.
In the case of Plant A, it starts with a height of 6 inches, so y(0)=6. It grows 4 inches per day, so we will have:
[tex]\frac{y(1)-y(0)}{1-0}=4=\text{slope m}[/tex]Then, as the slope is constant, we have a linear function, with y-intercept b=y(0)=6 and slope m=4, which equation can be written as:
[tex]y=4x+6[/tex]If we apply the same analysis to plant B, we have that the y-intercept is y(0)=10 and the slope is m=2 inches per day.
Then, the equation for B is:
[tex]y=2x+10[/tex]Answer:
Plant A: y = 4x + 6
Plant B: y = 2x + 10
Two recreational tennis teams, Westside and Eastside, wanted to compare the ages of their players. The ages of the Westside players are 20, 21, 21, 22, 23, 24, and 24. The mean age of the Westside players is 22 The ages of the Eastside players are 22, 23, 23, 24, 24, 26, and 26. The mean age of the East side players is 24 Which statement is true? The range of Team Westside's players ages is greater than the range of Team Eastside's players ages. Team Eastside's players ages vary more than Team Westside's players ages. Team Westsides's players ages vary more than Team Eastsides's players ages. Team Eastside's players ages vary the same amount as Team Westside's players ages
Answers
We have two sets of values: the ages of Westside players and the ages of Eastside players.
Ages of the Westside players = [20, 21, 21, 22, 23, 24, 24]
Ages of the Eastside players = [22, 23, 23, 24, 24, 26, 26]
We can evaluate the mean of each set as:
could you help with
Answers
By thales theorem we have that:
[tex]\frac{4x}{32}=\frac{84}{24}[/tex]then:
[tex]4x=112\Rightarrow x=28[/tex]Then the answer is that x=28
Given AGHJ - AXYZ, find each missing measure.H18 ftzXa) GJ =d) mZH =27 fte) m =38b) XY=c) ZY =f) mZJE
Answers
Lisa, Felipe, and Justin have a total of $120 in their wallets. Lisa has $6 more than Justin. Felipe has 4 times what Justin has. How much does each have?
Answers
Let
x -----> Lisa's amount
y -----> Felipe's amount
z -----> Justin's amount
we have that
x+y+z=120 --------> equation A
x=z+6 ------> equation B
y=4z -----> equation C
substitute equation B and equation C in equation A
so
(z+6)+4z+z=120
solve for z
6z+6=120
6z=120-6
6z=114
z=$19
Find the value of x
substitute the value of z in equation B
so
x=19+6
x=$25
Find the value of y
substitute the value of z in equation C
y=4(19)
y=$76
therefore
Lisa's amount is $25
Felipe's amount is $76
Justin's amount is $19
Line AB is parallel to line CD. What is the measure of ∠1?
Answers
∠1 = 100° (option E)
Explanation:∠5 and 80 degrees are supplementary angles.
Their sum is equal to 180 degrees
∠5 + 80° = 180° (sum of angles on a line)
∠5 = 180 - 80
∠5 = 100°
The angle at the top of the first line corresponds to the the angle at the top of the 2nd line
∠5 corresponds to ∠1
Corresponding angles are equal
∠5 = ∠1
Hence, ∠1 = 100° (option E)
A septic tank has the shape shown to the right. How many gallons does it hold? (1 ft3 ≈ 7.48 gallons) Round to the nearest tenth
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The rate traveling upriver is ____(Write it as an expression)
Answers
in 9 hours 22 against current, and 22 with current
the rate of the current is 4
22 / a + 22/ b
identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.) Square root -81
Answers
√-81 = -9i Pure imaginary - complex
Suppose that 25% of the time Danny eats out twice a month, 30% of the time he eats out once a month, and 45% of the time he doesn't eat out at all in a given month. What is the expected value for the number of times Danny eats out during a month?
Answers
Express percentages in decimal form ( dividing by 10)
25 % = 25 / 100 = 0.25 (twice)
30% = 30/100 = 0.3 (once)
45%= 45/100= 0.45 (zero)
2*0.25 + 1*0.3 + 0*0.45 =
0.5 + 0.3 + 0 =
0.8
Expected value = 0.8
A car costs $5,100.00 with a tax rate of 6.5%, and the percent of down payment was 10%. You are trading in a vehicle worth $600.00. How much will the amount of the down payment be?
Answers
The cost of the car is originally $5100. The tax rate is given as 6.5%. Therefore, the total cost of the car would be;
[tex]\begin{gathered} \text{Cost}+\text{Tax}=\text{Total cost} \\ 5100+(5100\times0.065)=\text{Total cost} \\ 5100+331.5=\text{Total cost} \\ \text{Total cost}=5431.5 \end{gathered}[/tex]The percent of down payment was 10%. This means at the point of making your down payment you would pay;
[tex]\begin{gathered} \text{Down payment}=0.1\times(Total\text{ cost}-\text{Trade-in)} \\ \text{Down payment}=0.1\times(5431.5-600) \\ \text{Down payment}=0.1\times4831.5 \\ \text{Down payment}=483.15 \end{gathered}[/tex]Note that, the amount due would be cost of the car plus tax. Then after that, we can deduct the amount of the car traded in for the new one. The difference is now the amount to be paid for the car altogether. Since the down payment is 10%, we can now calculate the 10% of this final figure.
ANSWER:
The down payment would be $483.15
8. Determine the area of the shaded region
in the rectangle.
4 yd
2 yd
5 yd
5 yd
4 yd
3 yd
Answers
Answer: 49 yd
Subtract the unshaded region from the total area to find the shaded region.
Total Area:
[tex](4+3)*(4+5)=Area\\7*9=63[/tex]
The unshaded area consists of 2 triangles, so we have to find the area of each triangle.
[tex]\frac{1}{2}(2*4)=4\\\\\frac{1}{2}(4*5)=10\\\\4+10=14\\[/tex]
The combined area of the unshaded region is 14 yd^2
Now subtract the unshaded from the total to find the shaded:
[tex]63-14=49[/tex]
The shaded region is 49 yd^2
Write the slope-intercept form of the equation of the line described. 10.) through: ( 5 , 5 ) , perpendicular to Y= -5x +3
Answers
To find the line equation perpendicular to the line equation y = -5x + 3, we need to know that the product of the slopes of two linear equation must be = -1. Then, the slope of the line perpendicular to y = -5x + 3 is:
m1 = -5x ---> m2 = 1/5, so m1 * m2 = -5 * 1/5 = -1.
As we can see, the new slope is the inverse and the reciprocal of the original slope.
Then, we have that passes through the point (5, 5). For this, we can use the Point-Slope Form of the line:
[tex]y-y_1=m(x-x_{1)}[/tex]Where, x1 = 5, and y1 = 5. Hence:
[tex]y-5=\frac{1}{5}(x-5)\Rightarrow y-5_{}=\frac{1}{5}x-1\Rightarrow y=\frac{1}{5}x-1+5[/tex]Therefore, the line is:
[tex]y=\frac{1}{5}x+4[/tex]