Answer: (f)
Step-by-step explanation:
Given
The growth equation is [tex]y=50(1.05)^x[/tex]
When population becomes 1500
[tex]\Rightarrow 1500=50(1.05)^x\\\Rightarrow 30=(1.05)^x\\\text{Taking log both sides}\\\Rightarrow \ln (30)=x\ln (1.05)\\\\\Rightarrow x=\dfrac{\ln (30)}{\ln (1.05)}\\\\\Rightarrow x=69.71[/tex]
Thus, after 69.71 years of year 2015 i.e. [tex]2015+69.71=2084.71[/tex]. In year 2084, it becomes 1500.
option (f) is correct.
A restaurant charges large parties an amount that depends on the number of people
that are eating. The restaurant charges $650 for 25 people and $1,850 for 80 people.
What is the restaurant charging per person (unit rate)?
Answer:
$26 per person or $23.125 per person for the bigger group
Step-by-step explanation:
Software Solution (SOS) helps subscribers solve software problems. All transactions are made over the telephone. For the year 2018, 10 engineers, most of whom are recent graduates, handled 119,000 calls. The average yearly salary for software engineers was $58,000. Starting in 2019, the firm retained and hired only software engineers with at least 2 years of experience. SOS raised the engineers’ salary to $73,000 per year. In 2019, eight engineers handled 127,000 calls.
Required:
1. Calculate the partial operational productivity ratio for both years.
2. Calculate the partial financial productivity ratio for both years. (Round your answers to 4 decimal places.)
Answer:
a. 11900, 15875
b. 0.2052, 0.2175
Step-by-step explanation:
number of engineers in 2018 = 10
calls handled in 2018 = 119000
average salary in 2018 = 58000
number of engineers in 2019 = 8
calls handled = 127000
salary = 73000
a.) operational productivity = output/input
in year 2018 = 119000/10= 11900
in year 2019 = 127000/8 = 15875
b.) ratio for both years = output/amount spent
in year 2018 = 119000/10*58000 = 0.2052
in year 2019 = 127000/8*73000 = 0.2175
Records show that 12% of all college students are foreign students who also smoke. It is also known that 40% of all foreign college students smoke. What percent of the students at this university are foreign
Answer: the percent of the students at this university are foreign = 30%
Step-by-step explanation:
Given: Probability that college students are foreign students who also smoke: P(S|F)=0.12
Probability that foreign college students smoke P(S∩F)=0.4
The probability that the students at this university are foreign :
[tex]P(F)=\dfrac{P(S\cap F)}{P(S|F)}[/tex] [By conditional probability formula]
[tex]=\dfrac{0.12}{0.4}\\\\=0.3[/tex]
Hence, the percent of the students at this university are foreign = 30%
Find the distance from (4,2) to the line defined
by y = -2x + 5. Express as a radical or a number
rounded to the nearest hundredth.
Answer:
The desired distance is √5
Step-by-step explanation:
Recall that the distance from a point to a line is measured along a path perpendicular to the line. Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2: +1/2.
The line perpendicular to y = -2x + 5 and passing through (4, 2) is
y - 2 = (1/2)(x - 4), or
2y - 4 = x - 4, or 2y = x, or y = (1/2)x.
Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."
Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2. If x = 2, then y = (1/2)(2) = 1.
Finally, find the distance between (2, 1) and (4, 2):
Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5
The distance from (4, 2) to the line y = -2x + 5 is √5
PLEASE HELP!!! IM ALMOST DONE WITH THIS SEMESTER
Which choice describes symmetry?
A. When something is exactly the same on one side as it is on the
other side.
B. When something looks completely different on one side than
the other side.
C. When something has a spherical shape.
Answer: A. When something is exactly the same on one side as it is on the
other side
Step-by-step explanation: symmetry mean symmetrical: aka they look the same :) hope this helped!
plz answer if you know it....
Sales tax is charged on the subtotal (amount before tax).
First, find the subtotal by adding up all of the amounts.
4(675) + 2(110) + 5(41) + 6(135) + 230(2.50)
2700 + 220 + 205 + 810 + 575
Total = 4510
Next, we need to find 7% of 4510. That number is the sales tax.
0.07 x 4510 = 315.70
Sales Tax = $315.70
Total Amount (with tax) = $4825.70
Hope this helps!! :)
 please helpppp!!! it’s timed!!!! thank u for helping!!!!!
Answer:
[tex]4 \pi {?}^{2} [/tex]
hope it is helpful to you
What are the coordinates of the vertex of the parabola described by the
equation below?
y= 2x+52-3
O A (-5.3)
0
B. (-3.-5)
C. (3.5)
O D. (5-3)
ANSWER ASAP!
Step-by-step explanation:
please type the question properly
Translate the phrase into an algebraic expression.
3 more than b
Answer:
b+3 or 3+b
Step-by-step explanation:
Which operation should you perform first in the expression 7x2^3?
Answer:
Below,
Step-by-step explanation:
The exponent part is done first
7 x 2^3
= 7 * 8
= 56.
You use the acronym PEMDAS:-
( E ( exponential) comes before M (multiply))
The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 42 ounces and a standard deviation of 10 ounces. Use the Empirical Rule.
a. 99.7% of the widget weights lie between _____ and _____.
b. What percentage of the widget weights lie between 26 and 66 ounces?
c. What percentage of the widget weights lie above 34?
Answer:
The answer is below
Step-by-step explanation:
The empirical rule states for a normal distribution, 68% of the data falls within one standard deviation, 95% falls within two standard deviations and 99.7% falls within three standard deviations.
z score is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Given that mean (μ) = 42 ounces, standard deviation (σ) = 10 ounces.
a) 99.7% falls within three standard deviations. Therefore:
99.7% falls within μ ± 3σ = 42 ± 3(10) = 42 ± 30 = (12, 72)
Therefore 99.7% falls within 12 ounce and 72 ounce.
b) For x > 26
[tex]z=\frac{26-42}{10}=-1.6\\[/tex]
For x < 66
[tex]z=\frac{66-42}{10}=2.4\\[/tex]
From the normal distribution table, P(26 < x < 66) = P(-1.6 < z < 2.4) = P(z < 2.4) - P(z < -1.6) = 0.9918 - 0.0548 = 0.937 = 93.7%
c) For x > 34
[tex]z=\frac{34-42}{10}=-0.8\\[/tex]
From the normal distribution table, P(x > 34) = P(z > -0.8) = 1 - P(z < -0.8) = 1 - 0.2119 = 0.7881 = 78.81%
Answer:
Step-by-step explanation:
Given that:
Mean [tex]\mu[/tex] = 42
standard deviation [tex]\sigma[/tex] = 10
Using Empirical Rule:
[tex]\mu[/tex] - [tex]\sigma[/tex] = 42 - 10 = 32 [tex]\mu[/tex] + [tex]\sigma[/tex] = 42 + 10 = 52
[tex]\mu[/tex] - 2[tex]\sigma[/tex] = 42 - 2(10) = 22 [tex]\mu[/tex] + 2[tex]\sigma[/tex] = 42 + 2(10) = 62
[tex]\mu[/tex] - 3[tex]\sigma[/tex] = 42 - 3(10) = 12 [tex]\mu[/tex] + 3[tex]\sigma[/tex] = 42 + 3(10) = 72
The curve is attached in the image below.
a). the widget of 99.7% lies between 12 and 72
b) 68 + 13.5 = 81.5%
c) 50 + 34 = 84%
What are the rational roots of f(d) = 5d - 6 + d-8?
What are the three plot points and is it over the x-axis or y-axis
Answer:
(-2,1), (0,1), and (2,0). its over the y axis
Step-by-step explanation:
Answer:
shift it 3 values right and 2 units up
Step-by-step explanation:
moving x-axis and moving y-axis
Examine the geometric relationships in the diagram below which option shows the correct value of x and y?
Answer:all of them
Step-by-step explanation:
Which equation represents a line that passes through (5, 1) and has a slope of ?
O y-5 = {(x-1)
Oy- } = 5(x –1)
Oy-1 = {(x–5)
Oy - 1 = 5(x-)
Answer:
y - 1 = 5(x - 5)
Step-by-step explanation:
Given the following data;
Points (x, y) = (5, 1)
Slope = ?
From the question, the value of the slope is missing. Hence, let's assume a value of 5.
Mathematically, the equation of a straight line is given by the formula;
y = mx + c
Where;
m is the slope.
x and y are the points
c is the intercept.
To find the equation of line, we would use the following formula;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - 1 = 5(x - 5)
y - 1 = 5x - 25
y = 5x - 25 + 1
y = 5x - 24 = mx + c
evaluate g(x)=x/x-3, if g(1/2)
Answer:
-1/5
Step-by-step explanation:
g(x) = x/(x-3)
Substituting x = 1/2 in g(x),
g(1/2) = 1/2/(1/2-3)
= 1/2/(1/2-6/2)
= 1/2/(-5/2)
= 1/2 ÷ - 5/2
= 1/2 x -2/5
= - 1/5
Step-by-step explanation:
here is your answer
here is your answer
Evaluate the function at the given values of x. Round to 4 decimal places, if necessary. =fx7x
Step-by-step explanation:
what are the given values of x ?
there is nothing visible.
and what is the function itself ? f(x) = 7x ?
it is not clear.
The cost, in dollars, of a gym membership for n months can be described by the explicit equation Pn = 70 + 30n. What does this equation tell us?
Answer:
30 plus 70 equals 100
Step-by-step explanation:
it tells the gum explicit equation
Choose the conditional statement that can be used with its converse to form the following biconditional statement: "It is a leap year if and only if the year has 366 days."
A. If it is not a leap year, then it does not have 366 days.
B. If it is a leap year, then the year has 366 days.
C. If a leap year has 366 days, then this is a leap year. D. If a year does not have 366 days, then it is not a leap year
Given the biconditional statement: "It is a leap year if and only if the year has 366 days.", the converse to form it is "If the year has 366 days, then this is a leap year". (Right choice: C)
How to determine the propositional form of a sentence
According to logics, propostions are truth bearers that makes sentences true or false. In linguistics, propositions are the meaning of declarative sentences. There are simple and composite propositions, the latter are formed by one simple proposition at least and logic connectors. There are five logic connectors:
Conjuction X ∧ Y ("and" operator)Disjunction X ∨ Y ("or" operator)Negation ¬ X ("not" operator)Implication/Conditional X ⇒ Y ("if-then" operator)Double implication/Biconditional X ⇔ Y ("if-only if" operator)By logic rules we know that the double implication/biconditional is commutative operator:
(X ⇔ Y) ⇔ (Y ⇔ X)
In addition, a double implication/biconditional has the following equivalence:
(X ⇒ Y) ∧ (Y ⇒ X)
Where Y ⇒ X is the converse of X ⇒ Y.
Therefore, the converse to form the statement "It is a leap year if and only if the year has 366 days" is Y ⇒ X: "If the year has 366 days, then this is a leap year".
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Simplify -4 + (-3) + 6.
Answer:3/6 in simplest fraction form is 1/2.
Step-by-step explanation:EASY and my chanel is FireFlameZero if u can check dat out
A rectangular garage is 12 yards long and 8 yards wide. It costs $1.00 per square yard to put in a new concrete floor. How much would it cost to put a new concrete floor in the garage?
===========================================================
Explanation:
Compute the area to get 12*8 = 96 square yards
We can think of it like having 96 squares and each square costs $1. So naturally the total cost is 96*1 = 96 dollars.
15
Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth.
The vertices of ABC are Al-2, 2), B6, 2), and 90, 8). The perimeter of ABC is
units, and its area is
square units.
9514 1404 393
Answer:
perimeter: 22.81 unitsarea: 24 square unitsStep-by-step explanation:
The lengths of the sides can be found using the distance formula.
d = √((x2 -x1)^2 +(y2 -y1)^2)
AC = √((0 -(-2))^2 +(8 -2)^2) = √(4+36) = 2√10
BC = √((0 -6)^2 +(8 -2)^2) = √(36+36) = 6√2
The distance AB is the difference of the x-coordinates of the points: 6-(-2) = 8.
Then the perimeter is ...
P = a + b + c = 6√2 +2√10 +8 = 8.49 +6.32 +8 = 22.81 . . . units
__
The height of the triangle is the difference in y-values between vertex C and line AB: 8 -2 = 6. The area is given by the formula ...
A = 1/2bh
A = 1/2(8)(6) = 24 . . . square units
Suppose a certain state university's college of business obtained the following results on the salaries of a recent graduating class:
Finance Majors Business Analytics Majors
n1 = 140 n2 = 30
x1 = $48,237 x2 = $55,417
s1 = $19,000 s2 = $10,000
Required:
a. Formulate hypotheses so that, if the null hypothesis is rejected, we can conclude that salaries for Finance majors are significantly lower than the salaries of Business Analytics majors. Use α = 0.05. (Let μ1 = the population mean salary for Finance majors, and let μ2 = the population mean salary for Business Analytics majors.
b. What is the value of the test statistic?
c. What is the p-value? (Round your answer to four decimal places.)
d. What is your conclusion?
Answer:
Following are the responses to the given choice:
Step-by-step explanation:
For point a:
[tex]H_0: \mu_1 - \mu_2 = 0\\\\ H_1: \mu_1 - \mu_2 < 0[/tex]
For point b:
[tex]t = -2.953[/tex]
For point c:
[tex]\to p- value = 0.0021[/tex]
For point d:
Reject [tex]H_o[/tex]. It could deduce that the pay of higher banking is considerably lower than the pay of higher project management.
Kevin paid $2.52 for 6 juice boxes. How much should Kevin expect to pay for 18 juice boxes?
Answer:
7.56
Step-by-step explanation:
Kevin should expect to pay approximately $7.56 for 18 juice boxes based on the given information.
To find out how much Kevin should expect to pay for 18 juice boxes based on the given information, we can set up a proportion using the number of juice boxes and the cost:
In general, an expression refers to a combination of symbols, numbers, variables, and operators that represent a specific computation or value. Expressions are a fundamental concept in mathematics, programming, and logic.
Let "x" be the cost of 18 juice boxes.
We have the proportion:
6 juice boxes / $2.52 = 18 juice boxes / x
To solve for "x," we can cross-multiply:
6x = 18 x $2.52
6x = $45.36
Now, divide both sides by 6 to isolate "x":
x = $45.36 / 6
x ≈ $7.56
Therefore, According to the data provided, Kevin should budget about $7.56 for 18 juice cartons.
To know more about an expression follow
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The solution set for -18 < 5x - 3 is _____.
3 > x
3 < x
-3 < x
-3 > x
Answer:
[tex]-3 < x[/tex]
Step-by-step explanation:
Given
[tex]-18 < 5x-3[/tex]
Required
The solution
[tex]-18 < 5x-3[/tex]
Add 3 to both sides
[tex]3-18 < 5x-3+3[/tex]
[tex]-15 < 5x[/tex]
Divide both sides by 5
[tex]-3 < x[/tex]
3 tons of topsoil cost $2,040.00. What is the price per pound?
Answer:
$0.34/pound
Step-by-step explanation:
1 ton = 2000 pounds
3 tons = 6000 pounds
-------------------------
2040/6000 = $0.34/pound
Help me complete this
Answer:
x = 9.9 in.
Step-by-step explanation:
area of triangle = base * height /2
49 = x*x /2
49*2 = x^2
98 = x^2
[tex]\sqrt{98}[/tex] = x
[tex]7\sqrt{2}[/tex] = x
9.9 = x
Question 5
Refer to the data that you recorded in part D. In each row, compare the slope of ABto the slope of the perpendicular line. What is the
relationship between the two slopes? What conclusion can you draw about the relationship between the slopes of any two perpendicular lines?
Ok
Answer:
Step-by-step explanation:
Answer:
The product of the slopes of and the line perpendicular to through C is -1 in all cases. So, I can conclude that any two perpendicular lines have slopes that are negative reciprocals of each other.
Step-by-step explanation:
its correct
x/4 - 3 = -7
what is x equal to?
Answer:
x=-16
Step-by-step explanation:
x/4-3=-7
x/4=-4
x=-16
