Answer:
Time for the object to get h(max) s = 1.1875 sec
h (max) = 1272.57 feet
Down time for the object to hit the ground = 4.25 sec
Step-by-step explanation:
The relation
h(s) = - 16*s² + 38* s + 1250 (1)
Is equivalent to the equation for vertical shot
Δh = V(i)*t - 1/2g*t² (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.
The description of the movement is:
V(s) = V(i) - g*s ⇒ V(s) = 38 - 32*s
At h(max) V(s) = 0 38/32 = s
So the maximum height is at s = t = 1.1875 sec
The time for the object to pass for starting point is the same
t = 1.1875 sec
h(max) is
h(max) = - 16* (1.1875)² + 38 (1.1875) + 1250
h(max) = - 22,56 + 45.13 + 1250
h(max) = 1272.57 feet
Time for the object to hit the ground is
h(s) = - 1250 feet
-1250 = - 16 s² + 38*s + 1250
-16s² + 38s = 0
s ( -16s + 38 ) = 0
First solution for that second degree equation is x = 0 which we dismiss
then
( -16s + 38 ) = 0 ⇒ 16s = 38 s = 38/16
s = 2.375 sec and we have to add time between h (max) and to get to starting point ( 1. 1875 sec)
total time is = 2.375 + 1.875
Total time = 4.25 sec
Lee can purchase gas for his rental car for $3.25 per gallon. It will cost him $96 to rent the car. How much will it cost Lee if he purchases 160 gallons of gas? Write your answer in proper money form.
Answer:
It will cost him $616 for 160 gallons of gas.
Step-by-step EXPLANATION FIRST YOU HAVE TO MULTIPLY 3.25 BY 160 TO GET $520, THEN JUST ADD IT BY $96 TO GET $616.
It will cost Lee $520 to purchase 160 gallons of gas.
What are arithmetic operations?
The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division. The priority of these opeartors in a given expression can be determined by PEDMAS. Each letter represents one operation as P for Parenthesis, E for exponential, D for division, M for Multiplication, A for Addition and S for Subtraction.
The price of gas per gallon is $3,25.
The cost of 160 gallons can be calculated as follows,
Number of gallons × Price per gallon
⇒ 160 × 3.25
⇒ 520
Hence, the price of 160 gallons is given as $520.
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Robert's dog is 4 years older than Karen's cat. In 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. How old is Robert's dog right now?
Answer:
5.5 years old.
Step-by-step explanation:
Let D represent present age of Robert's dog and C represent present age of Karen's cat.
We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:
[tex]D=C+4...(1)[/tex]
We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be [tex]D+3[/tex] and [tex]C+3[/tex] respectively.
We can represent this information in an equation as:
[tex]D+3+C+3=13...(2)[/tex]
From equation (1), we will get:
[tex]C=D-4[/tex]
Upon substituting this value in equation (2), we will get:
[tex]D+3+D-4+3=13[/tex]
Combine like terms:
[tex]2D+2=13[/tex]
[tex]2D+2-2=13-2[/tex]
[tex]2D=11[/tex]
[tex]\frac{2D}{2}=\frac{11}{2}[/tex]
[tex]D=5.5[/tex]
Therefore, Robert's dog is 5.5 years old right now.
Suppose the expression a(b)n models the approximate number of people who visited an aquarium each day since an aquarium opened, where a is the initial number of people who visited, b is the rate of increase in the number of people who visited each day, and n is the number of days since the aquarium opened.
If the expression below models the number of visitors of a particular aquarium, what is the correct interpretation of the second factor?
54(1.3)^7
A.
There were 9.1 times as many people who visited the aquarium on the 7th day as on the first day.
B.
There were 1.3 times as many people who visited the aquarium on the 7th day as on the first day.
C.
There were 6.27 times as many people who visited the aquarium on the 7th day as on the first day.
D.
There were 10.2 times as many people who visited the aquarium on the 7th day as on the first day.
Answer:
C. There were 6,27 times as many people who visited the aquarium on the seventh day as on the first day.
Explanation:
[tex]\displaystyle 1,3^7 = 6,2748517 ≈ 6,27[/tex]
I am joyous to assist you anytime.
Need some help with these problems!
Answer:
h=12, w=24, t=8
Step-by-step explanation:
System of Linear Equations
We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.
We have the following data, being
w = price of a sweatshirt
t = price of a T-shirt
h = price of a pair of shorts
19.
The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as
[tex]\displaystyle w=2h[/tex]
The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as
[tex]\displaystyle t=h-4[/tex]
The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus
[tex]\displaystyle 3w+2h+5t=136[/tex]
This is the system of equations we need to solve for w,t,h
20.
To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so
[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]
Operating
[tex]\displaystyle 6h+2h+5h-20=136[/tex]
[tex]\displaystyle 13h=156[/tex]
Solving for h
[tex]\displaystyle h=12[/tex]
The other two variables are
[tex]\displaystyle w=2h=24[/tex]
[tex]\displaystyle t=12-4=8[/tex]
The length, L, of a rectangle is decreasing at the rate of 2cm/sec, while the width, W, is increasing at the rate of 2 cm/sec.When L = 12 cm and W = 5 cm, find the rates of change of :______________
A) The area
B) The Perimeter
C) The lengths of the diagonals of the rectangle
Answer:
A) 14 cm² per sec
B) 0 cm per sec
C) -28 cm per sec
Step-by-step explanation:
We know that,
If l = length of a rectangle and w = width of the rectangle
A) Area of a rectangle,
[tex]A=l\times w[/tex]
Differentiating with respect to t ( time )
[tex]\frac{dA}{dt}=l\frac{dw}{dt}+w\frac{dl}{dt}[/tex]
We have,
[tex]l=12\text{ cm}, w=5\text{ cm}, \frac{dw}{dt}=2\text{ cm per sec}, \frac{dl}{dt}=-2\text{ cm per sec}[/tex]
[tex]\frac{dA}{dt}=12\times 2+5\times -2[/tex]
[tex]\frac{dA}{dt}=24-10[/tex]
[tex]\frac{dA}{dt}=14\text{ square cm per sec}[/tex]
B) Perimeter of the rectangle,
[tex]P=2(l+w)[/tex]
Differentiating with respect to t ( time ),
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})=2(-2+2)=0[/tex]
C) Length of the diagonal,
[tex]D=\sqrt{l^2+w^2}[/tex]
[tex]D^2 = l^2 + w^2[/tex]
Differentiating with respect to t ( time ),
[tex]2D\frac{dD}{dt}=2l\frac{dl}{dt}+2w\frac{dw}{dt}[/tex]
Since, if l = 12 cm, w = 5 cm,
[tex]D=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\text{ cm}[/tex]
[tex]\implies 2\times 13 \frac{dD}{dt}=2(12)(-2)+2(5)(2)[/tex]
[tex]26\frac{dD}{dt}=-48+20=-28\text{ cm per sec}[/tex]
Using implicit differentiation, it is found that:
a) The rate of change of the area of the rectangle is: 14 cm²/sec.
b) The rate of change of the perimeter of the rectangle is: 0 cm/sec.
c) The rate of change of the lengths of the diagonal of the rectangle is: [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.
Item a:
The area of a rectangle of length l and width w is given by:
[tex]A = lw[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dA}{dt} = w\frac{dl}{dt} + l\frac{dw}{dt}[/tex]
For this problem, the values are:
[tex]w = 5, \frac{dl}{dt} = -2, l = 12, \frac{dw}{dt} = 2[/tex]
Then:
[tex]\frac{dA}{dt} = 5(-2) + 12(2)[/tex]
[tex]\frac{dA}{dt} = 14[/tex]
The rate of change of the area is of 14 cm²/sec.
Item b:
The perimeter is given by:
[tex]P = 2l + 2w[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dP}{dt} = 2\frac{dl}{dt} + 2\frac{dw}{dt}[/tex]
Then
[tex]\frac{dP}{dt} = 2(-2) + 2(2) = 0[/tex]
The rate of change of the perimeter is of 0 cm/sec.
Item c:
The diagonal is the hypotenuse of a right triangle in which the sides are the length and the width, then, applying the Pythagorean Theorem:
[tex]d^2 = l^2 + w^2[/tex]
The value of the diagonal is:
[tex]d^2 = 5^2 + 12^2[/tex]
[tex]d^2 = 169[/tex]
[tex]d = \sqrt{169}[/tex]
[tex]d = 13[/tex]
The rate of change is:
[tex]2d\frac{dd}{dt} = 2l\frac{dl}{dt} + 2w\frac{dw}{dt}[/tex]
Then
[tex]26\frac{dd}{dt} = -48 + 20[/tex]
[tex]26\frac{dd}{dt} = -28[/tex]
[tex]\frac{dd}{dt} = -\frac{14}{13}[/tex]
The rate of change of the lengths of the diagonals of the rectangle is of [tex]\mathbf{-\frac{14}{13}}[/tex] cm/sec.
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The table shows the ages and weights of babies at a hospital. A 2-row table with 10 columns. The first row is labeled age (weeks) with entries 1, 2, 3, 3, 4, 4, 6, 8, 9, 9. The second row is labeled weight (pounds) with entries 7.5, 7.25, 8.2, 7.95, 8.0, 9.75, 9.25, 8.9, 9.85, 10.0. What is the correlation between age and weight as shown in the table? none positive negative constant
Answer:
Option (b) is correct.
The correlation between age and weight shown in the table is positive.
Step-by-step explanation:
According to the given values, it is found that there is a positive correlation between age and weight.
What is a correlation coefficient?It is an index that measures correlation between two variables, assuming values between -1 and 1.If it is positive, the relation is positive, that is, they are direct proportional. If it is negative, they are inverse proportional.If the absolute value of the correlation coefficient is greater than 0.6, the relationship is strong.In this problem, when the age increases, so does the weight, hence they have positive correlation.
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Eugene had 3 pies. He gave 1 4/5 to his friend. And kept the rest for himself. Who had more pie? How much more?
Answer:
Eugene friend will have more pie than Eugene.
Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Step-by-step explanation:
Given:
Amount of pie Eugene has = 3
Amount of Pie given to friend = [tex]1\frac{4}{5}[/tex]
[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]
We need to find who has pie and how much more.
We will first find the amount of pie Eugene is left with.
The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.
Framing the equation we get;
The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]
We will take LCM to solve the same.
The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]
Now [tex]\frac{9}{5} = 1.8[/tex] and [tex]\frac{6}{5} = 1.2[/tex]
Hence [tex]\frac{9}{5}[/tex] is greater than [tex]\frac{6}{5}[/tex]
Hence Eugene friend will have more pie than Eugene.
Now we will find amount more pie Eugene friend has.
Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.
Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]
Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.
Water pump A, B and c could empty a pool for 6 hours, a and b pump could empty a pool for 8 hours how long (to the nearest minute) will it take to drain the pool if both pumps are used simultaneously?
Answer:
3.4286 hours or 3 hours 26 minutes
Step-by-step explanation:
Well, it is considered that there are 5 different pumps (A, B, C, a and b). Pumps A and B are not same with pumps a and b.
Let us solve it. Well, it says a and b pump could empty a pool for 8 hours. So in 1 hour, pumps a and b empty 1/8 part of the pool.
And pumps A, B and C could empty a pool for 6 hours. Then A, B and C pumps empty 1/6 part of pool in 1 hour.
5 pumps (A, B, C, a and b) altogether can empty 7/24 parts (1/6+1/8=7/24) of a pool in 1 hour.
To drain whole pool, it will take 24/7=3.4286 hours or 3 hours 26 minutes.
Abigail"s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves. Write and expression two different ways to represent the amount for parents will pay Abigail and her sister from work you same amount of hours
Final answer:
To represent the total amount Abigail's parents will pay both Abigail and her sister for working the same number of hours, you could use the algebraic expressions 5h + 3h or (5 + 3)h, where h is the number of hours worked.
Explanation:
Abigail's parents pay her for weeding the yard and pay her little sister for raking leaves. If both of them work for the same amount of hours, we can represent the total amount their parents will pay using algebraic expressions. Let h be the number of hours they work.
One way to write the expression is: 5h + 3h, where 5 represents the dollars per hour for Abigail and 3 represents the dollars per hour for her sister.
Another way to represent this is: (5 + 3)h, which simplifies the expression by adding the hourly wages first and then multiplying by the number of hours worked, h.
Both expressions will give us the total amount paid to Abigail and her sister for the same number of hours worked, h.
Baby Kana's parents measure her height every month. H(t)H(t)H, left parenthesis, t, right parenthesis models Kana's height (in centimeters) when she was ttt months old. What does the statement H(160)=150H(160)=150H, left parenthesis, 160, right parenthesis, equals, 150 mean?
Answer:
H(160)=150 means that Kana's height is 150 cm when she is 160 months old
Step-by-step explanation:
According to the model described in the question:
H(t)=X where
X is the measure of Kana's height in centimeterst is Kana's lifetime in months when Kana's parents measure her height.Thus H(160)=150 states
150 as Kana's heights as centimeters160 as Kana's lifetime in months when her height was measured as 150 cmAnswer:
When Kana was 160 months old, her height was equal to 150 centimeters.
Step-by-step explanation:
The manager of the Danvers-Hilton Resort Hotel stated that the mean guest bill for a weekendis $600 or less. Amember of the hotel’s accounting staff noticed that the total chargesfor guest bills have been increasing in recent months. The accountant will use a sample ofweekend guest bills to test the manager’s claim.a. Which form of the hypotheses should be used to test the manager’s claim? Explain.$H0:μ≥600Ha:μ<600H0:μ≤600Ha:μ>600H0:μ=600Ha:μ≠600$b. What conclusion is appropriate when H0 cannot be rejected?c. What conclusion is appropriate when H0 can be rejected?
Answer:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Step-by-step explanation:
We are given the following in the question:
Manager's claim: The mean guest bill for a weekend is $600 or less.
A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months.
A sample of weekend guest bills were collected to test the manager’s claim.
We design the null and alternate hypothesis in the following manner:
[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]
Conclusion when null hypothesis cannot be rejected:
When we fail to reject the null hypothesis and accept the null hypothesis, thus, we have enough evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
Conclusion when null hypothesis can be rejected:
When the null hypothesis is rejected, we accept the alternate hypothesis.
Thus, there are not sufficient evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.
A price fixed above equilibrium that change the incentives that both buyers and sellers face is called price
Answer:
floor
Step-by-step explanation:
price floor is a situation when the price changed is greater or leave than the equilibrium price determined by the force of demand and supply. For a price floor to be effective, the minimum price has to be higher than the equilibrium price. It must be set above the equilibrium price. The opposite of price floor is price ceiling.
Property A initially sold for $412,500. The property sold a second time 12 months later for $430,500. What was A's monthly rate of change? (Round the final calculation to four decimal places.)
i got 1.0436 on my calculation hope this helps...
GASB requires a budget to actual comparison in the financial statements for the general fund and the ________.
Answer: Major special revenue funds with legally adopted budgets.
Step-by-step explanation: GASB ( Governmental accounting standards board) is a private organization based in Norwalk,that tries to regulates Government accounting process in the United States of America by giving specific standards to ensure proper accounting.
Governmental accounting standards board (GASB) requires a budget to actual comparison in the financial statements for the general fund and major special revenue funds with legally adopted budgets.
A postal worker counts the number of complaint letters received by the United States Postal Service in a givenday. Identify the type of data collected.
A) quantitative
B) qualitative
Answer:
A) quantitative
Step-by-step explanation:
A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.
PLLLZ HELP HAVE A DEADLINE 30 POINTS Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cot θ= - 3/7 . Find the exact values of the five remaining trigonometric functions of θ.
Answer:
answer is the first option
Step-by-step explanation:
The ratio of corresponding side lengths of two similar MP3 players is 4:3. The area of the larger MP3 player is 8 square inches. What is the area of the smaller MP3 player?
The area of smaller mp3 player is 4.5 square inches
Solution:
Given that ratio of corresponding side lengths of two similar MP3 players is 4:3
The area of the larger MP3 player is 8 square inches
To find: area of the smaller MP3 player
If two MP3 players are similar, then their corresponding sides are proportional.
To find the area ratios, raise the side length ratio to the second power
[tex]\frac{\text {area of larger mp3}}{\text {area of smaller mp3}}=\left(\frac{4}{3}\right)^{2}[/tex]
From given information,
area of larger mp3 = 8 square inches
Let the area of smaller mp3 = x
So the above ratio becomes,
[tex]\frac{8}{x}=\left(\frac{4}{3}\right)^{2}\\\\\frac{8}{x} = \frac{16}{9}\\\\16x = 9 \times 8\\\\16x = 72\\\\x = 4.5[/tex]
Thus the area of smaller mp3 player is 4.5 square inches
Final answer:
The area of the smaller MP3 player is 128/9 square inches.
Explanation:
The area of the larger MP3 player is 8 square inches and the ratio of corresponding side lengths of the two MP3 players is 4:3. To find the area of the smaller MP3 player, we need to use the ratio of the side lengths squared. Since the ratio is 4:3, the area ratio will be (4/3)^2 = 16/9. Given that the area of the larger MP3 player is 8 square inches, we can find the area of the smaller MP3 player by multiplying 8 by the area ratio: (8) * (16/9) = 128/9 square inches.
question 1. Enter the ratio equivalent to sin(B)
question 2. Consider this a right triangle. enter the measure of angle CAB to the nearest hundredth degree.
question 3. Suppose angle A is an angle such that angle cosA < sinA. select ALL angle measures that are possible values for angle A. 25, 35, 45, 55, 66, 75.
Answer:
The three questions about the given triangle has been answered below.
Step-by-step explanation:
We are given a right angled triangle whose sides are of length 20, 21 and 29.
(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]
= [tex]\frac{21}{29}[/tex]
= 0.72
(2) sin(A) = [tex]\frac{20}{29}[/tex]
sin(A) = 0.689
∠CAB = [tex]sin^{-1}(0.689)[/tex]
∠CAB = 43.551°
(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.
From the given options the angles that satisfy this are 55 , 66 and 75.
45 is not included as then sinA = cosA and that condition is not there.
We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
Given that:AB = 29 unitsBC = 20 unitsCA = 21 unitsUsing definitions of specific trigonometric ratios:A: The ratio equivalent to sin(B) is:
[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]
B: The measure of angle ∠CAB is calculated as:
[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]
C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:
55, 65 and 75:
The reason for the angles possible are 55, 66 ,75 is that:
[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]
Thus, we have:
A: The ratio equivalent to sin(B) is [tex]\dfrac{21}{29}[/tex]
B: The measure of angle ∠CAB is [tex]43.6^\circ[/tex]
C: The possible measures of angle A can be: 55, 66 or 75
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Sales variances may be computed in a manner similar to cost variances–that is, computing both price and volume variances.
Answer:
The answer is True.
Step-by-step explanation:
Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if
A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then
Material price varaince = 500 (5-4) = 500,
This gives us favourable price variance of 500 dollars. However in sales price variance if
A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then
Sale price varaince = 500 (5-4) = (500)
This gives us unfavourable sales price variance of 500 dollars.
This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.
The number of representatives is 160 less than five times the number of senators. There are a total of 560 members. Find the number of senators and the number of representatives
Answer:
The number of Senators are 120 and number of Representatives are 440.
Step-by-step explanation:
Given,
Total number of members = 560
Solution,
Let the number of Senators be 'x'.
Since, the number of representatives is 160 less than five times the number of senators.
Framing the above sentence in equation form,we get the number of Representative.
So, number of Representative = [tex]5x-160[/tex]
Now, Total number of members is the sum of total number of Senators and total number of representative.
Total number of members = Total number of Senators + Total number of representative
On substituting the values, we get;
[tex]x+5x-160=560\\\\6x=560+160\\\\6x=720\\\\x=\frac{720}{6}\\\\x=120[/tex]
Total number of Senators = 120
So, number of Representative = [tex]5\times120-160=600-160=440[/tex]
Thus the number of Senators are 120 and number of Representatives are 440.
The function f is f of x= √4-x
What is the xcoordinate of the point on the functions graph that is closest to the origin?
Answer:
0.5
Step-by-step explanation:
We assume your function is
[tex]f(x)=\sqrt{4-x}[/tex]
The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:
d^2 = (x)^2 + (f(x))^2 = x^2 + (4 -x)
Written in vertex form, this is ...
d^2 = (x -1/2) + 3.75
This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.
In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.
Explanation:The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.
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Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which statement best describes triangle P′Q′R′?A. It is similar to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).B. It is congruent to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).C. It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).D. It is congruent to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
Answer:
Option C.
Step-by-step explanation:
The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).
It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.
We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′
If a figure dilated by factor k about the origin then
[tex](x,y)\rightarrow (kx,ky)[/tex]
PQR dilated by a scale factor of 3, so
[tex](x,y)\rightarrow (3x,3y)[/tex]
Using this rule we get
[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]
[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]
[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]
The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).
Therefore, the correct option is C.
Answer:
C
Step-by-step explanation:
If point D is placed on AC, how will the measure of DAB relate to the measure of CAB?
Answer:angle DAB will be equal to angle CAB
Step-by-step explanation:
AC is a straight line and forms one of the sides of triangle ABC. If point D is placed on line AC, angle DAB would remain equal to angle CAB since they are on the same line the angle formed with line AB remains the same.
The measure of angle DAB will be congruent to angle CAB if AB and CD are parallel and right angles to AC and AD. The relationship changes as point D moves along AC, with angle DAB diminishing if DE remains parallel to AB.
Explanation:If point D is placed on AC, the measure of ∠DAB will relate to the measure of ∠CAB based on several geometric principles. If AB is parallel to CD and D moves along AC, with DE remaining constantly parallel to AB, the angle at D (∠DAB) will diminish as D moves away from A. If AB and CD maintain parallels and AC makes equal angles with them, then accordingly ∠DAB will also equal ∠CAB at the point where the two angles are bisected by AC.
Moreover, if AB and CD are right angles to AC and AD, as described by the circle theorem stating that angles inscribed in the same arc are congruent, then ∠DAB will be congruent to ∠CAB.
Kendal bought x boxes of cookies to bring to a party. Each box contains 12 cookies. She decides to keep two boxes for herself. She brings 60 cookies to the party. Which equation can be used to find the number of boxes, x, Kendal bought?
Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
Let x represent the number of boxes of cookies bought by Kendal.
Each box has 12 cookies, hence:
number of cookies = 12x
Kendal brings 60 cookies to the party. She keeps 2 boxes for herself. To find the number of boxes we use:
12x = 60 + 12(2)
12x = 84
x = 7
Therefore Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.
Find out more at: https://brainly.com/question/21105092
Final answer:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. The equation (x - 2) * 12 = 60 can be used to find the number of boxes Kendal bought.
Explanation:
To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. Kendal initially buys x boxes of cookies. Each box contains 12 cookies. She decides to keep two boxes for herself and brings 60 cookies to the party.
The number of cookies Kendal brings to the party can be calculated by multiplying the number of boxes she bought minus the number of boxes she kept for herself by the number of cookies in each box. So, the equation to find x would be:
(x - 2) * 12 = 60
Solving this equation will give us the value of x, which represents the number of boxes Kendal bought.
A circle has a radius of 5 inches (What is the measure, in radians, of this central angle?
Answer:
Step-by-step explanation:
Given
Circle has radius [tex]r=5 in.[/tex]
Area of the sector is given by
[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]
if [tex]A_s[/tex] is one-sixth of area of circle then
[tex]A_s=\frac{\pi r^2}{6}[/tex]
[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]
[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]
If [tex]A_s[/tex] is one-fourth of area of circle then
[tex]A_s=\frac{\pi r^2}{4}[/tex]
[tex]\theta =\frac{2\pi }{4}[/tex]
[tex]\theta =\frac{\pi }{2}[/tex]
Roddy Richards invested $12014.88 in Wolverine Meat Distributors (W.M.D.) five years ago. The investment had yearly arithmetic returns of minus9.7%, minus8.1%, 15%, 7.2%, and 15.4%. What is the arithmetic average return of Roddy Richard's investment?
Answer:
The arithmetic average return would be 3.96%
Step-by-step explanation:
Given,
The returns in 5 years are,
-9.7%, -8.1%, 15%, 7.2%, and 15.4%
We know that,
[tex]\text{Arithmetic average}=\frac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]
Hence,
The arithmetic average return of the investment = [tex]\frac{-9.7-8.1+15+7.2+15.4}{5}[/tex]
[tex]=\frac{19.8}{5}[/tex]
= 3.96%
Two trains leave a town at the same time heading in opposite directions. One train is traveling 12 mph faster than the other. After two hours, they are 232 miles apart. What is the average speed of each train?
Answer:
Step-by-step explanation:
I'm going to paint you a picture in words of what this looks like on paper. We have a train leaving from a point on your paper heading straight west. We have another train leaving from the same point on your paper heading straight east. This is the "opposite directions" that your problem gives you.
Now let's make a table:
distance = rate * time
Train 1
Train 2
We will fill in this table from the info in the problem then refer back to our drawing. It says that one train is traveling 12 mph faster than the other train. We don't know how fast "the other train" is going, so let's call that rate r. If the first train is travelin 12 mph faster, that rate is r + 12. Let's put that into the table
distance = rate * time
Train 1 r
Train 2 (r + 12)
Then it says "after 2 hours", so the time for both trains is 2 hours:
distance = rate * time
Train 1 r * 2
Train 2 (r + 12) * 2
Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r. The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24. The distance between them (which is also the length of the whole entire arrow) is 232. Thus:
2r + 2r + 24 = 232 and
4r = 208 so
r = 52
This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph
Answer: its A ^3^❤
Step-by-step explanation:
that guy above me probably got yall confused
The price of a ceryain item js P dollars. The sales tax on the item is 7%. Which expressio.N represents the total cost if the itsm , in dollars, -aftee the tas has been applied
Answer:
The expression representing the Total Cost of the item is [tex]P + 0.07P[/tex].
Step-by-step explanation:
Given:
Price of Certain item = 'P' dollars
Sales tax =7%
We need to find the expression for Total Cost of the item when tax is applied.
we will first find the Amount deducted in tax;
Amount deducted in Tax is equal to Percentage of sales tax multiplied by Price of Certain item and then divide by 100
Framing in equation form we get;
Amount Deducted in Tax = [tex]\frac{7}{100}\times P = 0.07P[/tex]
Now Total Cost of the item is equal to sum of Price of Certain item and Amount deducted in tax.
Expressing in expression form we get;
Total Cost of item = [tex]P + 0.07P[/tex]
Hence The expression representing the Total Cost of the item is [tex]P + 0.07P[/tex].
Six hundred chances are sold at $3 apiece for a raffle. There is a grand prize of $700, two second prizes of $200, and five third prizes of $50. First calculate the expected value of the lottery. Determine whether the lottery is a fair game. If the game is not fair, determine a price for playing the game that would make it fair.
Answer:
Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.
Step-by-step explanation:
There is 1 in 600 chance to win the grand price (1/600)
There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)
There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)
We can use these probability to calculate the expected gain from this game
[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]
Since the cost to play is $3, the expected net gain from this game is
$2.25 - $3 = -$0.75
So this game is not fair as the player is losing money. The appropriate price should instead be $2.25
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Calculate the total amount collected from selling all tickets: 600 tickets × $3 = $1800.Calculate the expected value by taking into account the probabilities of winning and the respective prizes: ($700 × 1/600) + ($200 × 2/600) + ($50 × 5/600) = $1.91.Determining Fairness:
The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.
Which sentence below represents the number of test questions in the problem below?
A test is worth 80 points. Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. If the test has 25 questions, how many multiple choice questions are there?
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
B. The number of multiple-choice questions times the number of short-answer questions is 25.
C. The number of multiple-choice questions minus the number of short-answer questions is 80.
D. The number of multiple-choice questions plus the number of short-answer questions is 80.
Answer: there are 10 multiple choice questions and 15 short-answer questions
Step-by-step explanation:
Let x represent the number of multiple choice questions in the test.
Let y represent the number of short-answer questions in the test.
If the test has 25 questions, it means that
x + y = 25
Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that
2x + 4y = 80 - - - - - - - -1
Substituting x = 25 - y into equation 1, it becomes
2(25 - y) + 4y = 80
50 - 2y + 4y = 80
- 2y + 4y = 80 - 50
2y = 30
y = 30/2 = 15
x = 25 - y = 25 - 15 = 10
A. The number of multiple-choice questions plus the number of short-answer questions is 25.
Answer:
A makes the most sense
Step-by-step explanation:
as if you don't get tricked and notice that C and D are not true but between A and B are two answers but B isn't correct if you go over what it means without getting tricked and A is to be the right answer