"Match the expression and its value to the value of x that gives the expression its value by filling in the box in the correct column.
Evaluate the expression 4 n-5 r for n=-2 and r=3
(A) 23
(C) 7
(B) -7
(D) -23
The surface area for a rectangular prism with a square base is given the expression 2 s²+4 s h, where s is the side length of the square h is the height of the prism. What is the surface area in square feet rectangular prism when s=4 feet and h=6feet?"
Answers
Value of the expression 4n - 5r when n = -2 and r = 3 is -23.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
What do you mean by algebraic expression?
The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.
Given expression:
4n - 5r
When n = -2 and r = 3
The value of the expression become,
4(-2) - 5(3)
= -8 - 15
= -23
Hence, option D is correct.
Now, it is given that the surface area for a rectangular prism with a square base is given by the expression 2s²+4sh, where s is the side length of the square h is the height of the prism.
The surface area in square feet rectangular prism when s=4 feet and h=6feet is
2[tex](4)^{2}[/tex] + 4(4)(6)
= 2(16) + 96
= 32 + 96
= 128 square feet
therefore, the surface area in square feet rectangular prism when s=4 feet and h=6feet is 128 square feet.
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Related Questions
What is the distance between the points (-2,3) and (5, -1)?
Answers
Answer:
√65
Step-by-step explanation:
Compute the Euclidean distance between the following points:
p_1 = (-2, 3) and p_2 = (5, -1)
The Euclidean distance between points (x_1, y_1) and (x_2, y_2) is:
sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)
Substitute (x_1, y_1) = (-2, 3) and (x_2, y_2) = (5, -1):
= sqrt((-2 - 5)^2 + (--1 + 3)^2)
(-1)^2 = 1:
= sqrt((-2 - 5)^2 + (1 + 3)^2)
-2 - 5 = -(2 + 5):
= sqrt((-(2 + 5))^2 + (3 + 1)^2)
2 + 5 = 7:
= sqrt((-7)^2 + (3 + 1)^2)
Multiply each exponent in -7 by 2:
= sqrt((-1)^2×7^2 + (3 + 1)^2)
7^2 = 49:
= sqrt((-1)^2×49 + (3 + 1)^2)
(-1)^2 = 1:
= sqrt(49 + (3 + 1)^2)
3 + 1 = 4:
= sqrt(49 + 4^2)
4^2 = 16:
= sqrt(49 + 16)
| 1 |
| 4 | 9
+ | 1 | 6
| 6 | 5:
Answer: √65
Solve 5(2m + 1) − 3m = −16.
m equals negative 16 over 30
m equals negative 21 over 30
m = −3
m = −0.33
Answers
Answer:
m= -3
Step-by-step explanation:
5(2m+1)-3m=-16
5(2m)+5(1)-3m= -16
10m+5-3m= -16
7m+5= -16
-5. -5
7m= -21
/7. /7
m= -3
Hopes this helps please mark brainliest
And :-3
process:
5(2m + 1) - 3m = - 16
10m+5-3m=-16
7m=-16-5
m=-21/7
m=-3
You have $108,000 to invest in a portfolio containing Stock X and Stock Y. Your goal is to create a portfolio that has an expected return of 14.0 percent. Stock X has an expected return of 12.6 percent and a beta of 1.15, and Stock Y has an expected return of 9.8 percent and a beta of .86.
Answers
The amount invested in Sock Y is - $126,000 and the Beta of the portfolio is 1.636.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Data provided in the question:
Total amount to be invested = $140000
Stock X Y
Expected return 14% 10%
Beta 1.42 1.18
Expected return of portfolio = 17.6%
Now,
let the weight invested n stock X be W
therefore,
Weight of Stock Y = 1 - W
thus,
( W × 14% ) + (1 - w) × 10% = 17.6 %
14W + 10% - 10W = 17.6%
4W = 7.6
W = 1.9
Therefore,
weight of Y = 1 - 1.9 = -0.9
Amount investment in Sock Y = Total amount to be invested × Weight
= 140,000 × ( - 0.9 )
= - $126,000 i.e short Y
Beta of portfolio = ∑ (Beta × Weight)
Beta of portfolio= [ 1.42 × 1.9 ] + [ 1.18 × (-0.9) ]
Beta of portfolio= 2.698 - 1.062
Beta of portfolio= 1.636
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Find a formula for the exponential function passing through the points(-1,4/5) and (1 , 20)
y=
Answers
The exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20) is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
How to derive the exponential function containing two given points
In this problem we must determine the exponential function that contains the points (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), whose formula is described below:
y = A · [tex]e^{B\cdot x}[/tex]
Where:
x - Independent variable.y - Dependent variable. A, B - Constants.If we know that (x₁, y₁) = (- 1, 4 / 5) and (x₂, y₂) = (1, 20), then the values of constants are:
4 / 5 = A · [tex]e^{-B}[/tex]
20 = A · [tex]e^{B}[/tex]
If we divide the latter expression by the former, then:
25 = [tex]e^{2\cdot B}[/tex]
㏑ 25 = 2 · B
B = (1 / 2) · ㏑ 25
B ≈ 1.609
And the value of A is:
A = 20 / [tex]e^{1.609}[/tex]
A ≈ 4.002
The exponential function is y = 4.002 · [tex]e^{1.609\cdot x}[/tex].
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HELP PLEASEEE
A party rental company has chairs and tables to rent. There were two customers who rented both chairs and tables last week. The table below shows the number of chairs, the number of tables, and the total cost (in dollars) for those two customers.
Answers
By setting up the equation, we get the system of linear equations are
9x + 7y = 77
3x + 5y = 49
solving these equation Cost to rent a chair = $1.75
cost to rent a table = $8.75
What is system of linear equation?A system of linear equations is a collection of one or more linear equations involving the same variables.
What are the method to solve system of linear equations?There are several methods for solving systems of linear equations, including:
Graphing: One way to solve a system of linear equations is to graph each equation on the same set of axes and look for the point of intersection. This method is useful when you want to visualize the solution, but it can be time-consuming if you have a large system of equations.
Substitution: The substitution method involves solving one of the equations for one of the variables and substituting this expression into the other equation. This will result in an equation with only one variable, which you can then solve.
Elimination: The elimination method involves adding or subtracting the equations in such a way that one of the variables is eliminated. This will result in an equation with only one variable, which you can then solve.
etc.
To solve the system of equations 9x + 7y = 77 and 3x + 5y = 49, you can use the substitution method.
First, solve the first equation for y:
9x + 7y = 77
7y = -9x + 77
y = (-9/7)x + 11
Now substitute this expression for y into the second equation:
3x + 5((-9/7)x + 5(11) = 49
3x - (45/7)x + 55 = 49
solving for x :
x = 1.75
Now substitute this value for x back into the first equation to find y:
y = 8.75
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Nina deposited $6,000 in a savings account with simple interest. Six months later, the
account held $6,270. What was the interest rate?
Answers
Answer:
Step-by-step explanation: 270
A transversal runs across two parallel lines, forming two angles. One measures 80 degrees. How large is the other angle
Answers
Answer:
100°
Step-by-step explanation:
180°- 80°= 100°
The angles are supplementary, meaning that they have to add up to 180.
Hope this helps!!! :)
If η. is an even positive integer, the double factorial notation represents the product of all the even integers from to η. For example 8! = 2 . 4. 6. 8 . What is the units digit of the following sum?
a. 0
b. 2
c. 4
d. 6
e. 8
Answers
The units digit of the double factorial notation is the units digit of the product of all the even integers from 2 to 8, which is 8! The units digit of 8! is 8, so the answer is 8.
What is meant by the term factorials?Factorials are mathematical operations symbolized by an exclamation point following a number. To find the factorial of a number, such as 5, write it down as 5! then multiply it by all the positive integers less than 5, including 1. Therefore, 5! is equivalent to 5 x 4 x 3 x 2 x 1, or 120. Factorials are frequently employed in mathematical equations and computations, especially in probability and statistics, where they are used to calculate the number of combinations or permutations that may be made from a given collection of numbers or variables. For example, if you had 5 distinct objects and want to determine how many various combinations , you used the factorial of 5.
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The function f(x) = -x + 2 can be formed by
shifting the function y = -2/3x in which way?
A. vertical shift up 2
B. reflection over the x-axis
C. vertical shift down 2
D. horizontal shift to the left 2
Please Show the Work & thank u
Answers
Answer:
A) vertical shift up 2------------------------------
The difference of the functions is:
f(x) - y = - 2/3x + 2 - (- 2/3x) = 2The difference between functions is positive, therefore it is a vertical shift up by 2 units.
What is the correct to this answer ???????( answers only)
Answers
X is greater than or equal to 24 = x ≥ 24
X is less than 24 = x < 24
X is greater than 24 = x > 24
Answer:
x > 24 goes to the bottom
x < 24 goes to the 3rd slot
x ≤ 24 goes to the 1st slot
x ≥ 24 goes to the 2nd slot
Step-by-step explanation:
Hope this helps.
At a baseball game, a vender sold a combined total of 246 sodas and hot dogs. The number of hot dogs sold was 34 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Answers
Answer:
The vendor sold 212 sodas and 34 hot dogs.
Step-by-step explanation:
Subtract 34 from 246 for the number of sodas sold.
Choose the best answer. For a biology project, you measure the weight in grams (g) and the tail length in millimeters (mm) of a group of mice. The equation of the least-squares line for predicting tail length from weight is predicted tail length = 20 + 3
\times
×
weight. Which of the following is not correct? (a) The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length. (b) The predicted tail length of a mouse that weighs 38 grams is 134 millimeters. (c) By looking at the equation of the least-squares line, you can see that the correlation between weight and tail length is positive. (d) If you had measured the tail length in centimeters instead of millimeters, the slope of the regression line would have been 3/10 = 0.3. (e) One mouse weighed 29 grams and had a tail length of 100 millimeters. The residual for this mouse is -7.
Answers
The part (a) is not correct i.e. The slope is 3, which indicates that a mouse's weight should increase by about 3 grams for each additional millimeter of tail length.
What is Regression analysis ?
Regression analysis is the process of determining how one or more variables and the outcome variable relate to one another. Risk factors, co-founders, and the outcome variable are all referred to as predictors or independent variables. The result variable is sometimes referred to as the dependent or response variable. Regression analysis displays the dependent variable as "y" and the independent variables as "x".
Given, tail length = (3 × weight) + 20
(a) Here, The slope is 3 which indicates that a mouse's length is the sum of 3 times the weight and 20. So, the statement is not correct.
(b) If weight is 38 gm, then
tail length = 38 × 3 + 20
= 114 + 20 = 134mm.
So, the statement is correct.
(c) We've tail length = (3 × weight) + 20
we can see that the relationship between the two is positive because when the weight is increased, the tail length also increases.
So, the given statement is correct.
(d) The slope is 3 when the tail length is being measured in millimeters.
Now, If we measure it in centimeter = 3/10 = 0.3 cm
∵ 1 mm = 1/10 cm.
So, the given statement is correct.
(e) when a mouse has weight of 29 grams and tail length of 100 mm.
When the weight is 29 grams, it should have tail length as :
tail length = 29 × 3 + 20
= 107 mm.
but, tail length is given as 100 mm.
So, the residual for the mouse is -7 i.e. (100 - 107)
Hence, The given statement is correct.
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To test m for an x distribution that is mound-shaped using
sample size n 30, how do you decide whether to use the normal or the
Student’s t distribution?
Answers
To decide whether to use the normal or the Student’s t distribution, for an x distribution that is mound-shaped:
Use the normal distribution if the standard deviation is known. Use the Student's t - distribution when the standard deviation is not known.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.
It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution is depicted graphically as a bell curve.
What is t distribution?For small sample numbers or unidentified variances, population parameters are estimated using a form of probability function called a t-distribution.
Hence t-distribution is suitable when the variance which is standard deviation squared is unknown
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Find the value of x. Leave your answer in simplest radical form.
Answers
The value of x in simplest radical form is x = [tex]\sqrt{17}[/tex]
Explain Pythagoras theorem.
The Pythagorean Theorem (also known as the Pythagorean Theorem) is an important topic in mathematics that describes the relationship between the sides of a right triangle. The sides of a right triangle are also called Pythagorean numbers.
The Pythagorean theorem is basically used to find unknown side lengths and triangle angles. Using this theorem, we can derive the formulas for the base, perpendicular and hypotenuse.
Using Pythagoras theorem in both the triangles,
Find the hypotenuse in above triangle
[tex]h^2=P^2+B^2[/tex]
[tex]h^2=4+4=8[/tex]
h = [tex]2\sqrt{2}[/tex]
Now, using Pythagoras theorem in below triangle,
[tex]h^2=P^2+B^2[/tex]
[tex]5^2 = x^{2} + 8[/tex]
25 = [tex]x^{2}[/tex] + 8
[tex]x^{2}[/tex] = 25 - 8 = 17
x = [tex]\sqrt{17}[/tex]
Therefore, x = [tex]\sqrt{17}[/tex]
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Mugs can be packed with up to 6 mugs in each box how many boxes are needed to pack 1528
Answers
X box = 1528 mugs
Cross multiplying, we get:
(1)(1528) = (6)(x)
1528/6 = x
254 = x
So, 254 boxes needed to pack 1528 mugs
Select all that apply.
Which of the following are proportions?
2/8=3/12
3/4=8/10
25/10=5/2
3/4=15/20
Answers
In the following proportions:-
A. [tex]\frac{2}{8} =\frac{3}{12}[/tex]
C. [tex]\\\\\ \frac{25}{10} =\frac{5}{2}[/tex]
D. [tex]\\\\ \frac{3}{4} =\frac{15}{20}[/tex] Are Equal
What are proportion?
A part, share, or quantity that is compared to a total is referred to as a proportion. According to the concept of proportion, two ratios are in proportion when they are equal. Two ratios or fractions are equal when an equation or a declaration to that effect is utilised.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
When two ratios are equal, they are said to be in proportion.For instance, the time it takes a train to go 50 kilometers per hour is equal to the time it needs to travel 250 kilometres in 5 hours. e.g., 250km/5 hours at 50 km/h.
[tex]A) \\\\\frac{2}{8} =\frac{3}{12} =\frac{1}{4}\\\\(B) \\\\\frac{3}{4} \ !=\frac{8}{10}= \frac{4}{5}\\\\\ (C)\\\\\frac{25}{10} =\frac{5}{2}\\\\(D)\\\\ \frac{3}{4} =\frac{15}{20}[/tex]
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Help me thank u very much
Answers
Answer:
y = 3x + 2
y = 1/2 x -1
Step-by-step explanation:
The slope intercept form of a line is
y = mx + b You substitute in the slope for m and the y intercept for b
Find an angle θ with 0∘ < θ < 360∘ that has the same:
sine as 30°:∅= degrees
cosine as 30°:∅= degrees
Answers
Angle θ with 0∘ < θ < 360∘ that has the same: sine as 30°:∅= degrees
cosine as 30°:∅= degrees are 150 and 330 degrees.
What is trigonometric function?
Trigonometric functions are referred to as Circular Functions may be merely outlined because the functions of an angle of a triangle
Main Body:
We have to find an angle θ with 0° < θ < 360° that has the same:
(a) sin(30∘)
We know that sin(θ) is positive in 2nd quadrant and in the 2nd quadrant θ lies between 90∘ and 180∘.
sin(30∘)=sin(180∘−30∘)
[∵sin(180∘−θ)=sin(θ)]=sin(150∘)
Thus:
sin as 30∘:θ=150 degrees
(b) cos(30∘)
We know that cos(θ) is positive in the 4th quadrant and in the 4th quadrant θ lies between 270∘ and 360∘.
cos(30∘)=cos(360∘−30∘)
[∵cos(360∘−θ)=cos(θ)]=cos(330∘)
Thus:cos as 30∘
:θ=330 degrees
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Write this number in scientific notation.
.0000149
Answers
Answer: 1.49 x [tex]10^{-5}[/tex]
Step-by-step explanation:
Choose the slope-intercept form of 3x + 2y = 5. y =
Answers
Answer: [tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Given: [tex]3x + 2y = 5[/tex]
We are needed to find the slope-intercept form.
We know that the slope-intercept form of an equation is given by
[tex]y = mc + c[/tex]
[tex]3x + 2y = 5[/tex]
[tex]2y = 5 -3x[/tex]
[tex]2y = -3x + 5[/tex]
[tex]y = \frac{-3}{2} x + \frac{5}{2}[/tex]
Thus, the answer is [tex]y = \frac{-3} {2} x + \frac{5}{2}[/tex]
Regroup to express the number in a different way.
71{,}83071,83071, comma, 830 ==equals 7\text{ ten thousands}7 ten thousands7, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus 1\text{ thousand}1 thousand1, start text, space, t, h, o, u, s, a, n, d, end text ++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens3, start text, space, t, e, n, s, end text
71{,}83071,83071, comma, 830 ==equals 6\text{ ten thousands}6 ten thousands6, start text, space, t, e, n, space, t, h, o, u, s, a, n, d, s, end text ++plus
++plus 8\text{ hundreds}8 hundreds8, start text, space, h, u, n, d, r, e, d, s, end text ++plus 3\text{ tens}3 tens
Answers
Answer:
11 thousands---------------------------------
Given number is 71830.
The last part: 830 is same on both lines.
We need to represent 71000 in different way, instead of 7 ten thousands and 1 thousands we have 6 ten thousands then we need:
71000 - 60000 = 11000It is 11 thousands.
Answer:
11,000 (or) 11 thousands
Step-by-step explanation:
Now we have to,
→ find the missing number.
→ Let the number be x.
Forming the equation,
→ 60,000 + x + 800 + 30 = 71,830
Then the value of x will be,
→ 60,000 + x + 800 + 30 = 71,830
→ x + 60,830 = 71,830
→ x = 71,830 - 60,830
→ [ x = 11,000 ]
Hence, the value of x is 11,000.
Write an explicit formula for a_n, the n^{\text{th}}n th term of the sequence 6, -24, 96, ...
Answers
The explicit formula for the geometric sequence 6, -24, 96, ... is
6 * -4^(n - 1)How to find the formula for the geometric sequenceEvery term in a geometric series is obtained by multiplying the term before it by the same number called the common ratio
The common ratio is denoted by the number r. It can be calculated by dividing any term in the sequence by the term before it.
For the given sequence the first term is a = 6
The common ratio is solved as follows
a * r = second term
6 * r = -24
r = -24/6
r = -4
check
-24 * -4 = 96 correct
The nth term of a geometric sequence
= ar^(n - 1)
= a * -4^(n - 1)
checking for the third term
= a * -4^(n - 1)
= 6 * -4^(3 - 1)
= 6 * -4^(2)
= 6 * 16
= 96
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Use the formula A=(1+r/n)^nt to solve the compound interest problem.
Find how long it takes for 900$ to double if it is invested at 6% interest compounded monthly.
The money will double in value in approximately ? years.
(Do not round until the final answer. Then round to the nearest tenth as needed.)
Answers
In 11.56 years the given amount of $ 900 will be double.
What is Compound interest:The interest charged on a loan or deposit is known as compound interest which depends on both the principal amount and rate of interest.
The formula used for
Amount, A = P(1+r/n)^ntwhere P = Principal amount
r = Rate of interest in decimal
n = Number of compounds per year
t = Time period
Here from the given data,
Principal amount, p = $ 900
Rate of interest, r = 6% = 6/100 = 0.06
Number of compounds, n = 12 [ ∵ compounded mothly ]
Here we need to find the time period
Assume that after 'n' years the amount will be doubled i.e $ 1800
From the given problem,
Amount, A = 900(1+0.06/12)¹²ⁿ
= 900(1+0.06/12)¹²ⁿ
= 900(1 + 0.005)¹²ⁿ
= 900 (1.005)¹²ⁿ
As we assumed after 'n' years the amount is $ 1800
=> 900 (1.005)¹²ⁿ = 1800
=> (1.005)¹²ⁿ = 2
Apply to log on both sides
=> log (1.005)¹²ⁿ = log 2
=> 12n log(1.005) = log 2
=> 12n = log 2/log(1.005)
[ use calculator for log (1.005) and log 2]
=> 12n = 0.301029996/ 0.00216606176
=> 12n = 138.975722
=> n = 11.5813102
=> n = 11.56
Therefore,
In 11.56 years the given amount of $ 900 will be double.
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If f(x) = 4x - 5 and g(x) = 6 - 3x, what is f (x) + g(x)?
Answers
If f(x) = 4x - 5 and g(x) = 6 - 3x then f(x) + g(x) = x + 1.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
We know f(x) + g(x) = (f + g)(x).
Given, f(x) = 4x - 5 and g(x) = 6 - 3x.
∴ f(x) + g(x) = (4x - 5) + (6 - 3x).
f(x) + g(x) = 4x - 3x - 5 + 6.
f(x) + g(x) = x + 1.
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Answer to these required:
Answers
Answer to question 2 is = 25 cm^2
Step by step
Question 1
Using Pythagorean theorem
a^2 + b^2 = c^2 to prove a right triangle
We are Given the c^2 - find the square root and match with the diagram triangles hypotenuse or diagonal
A) √82 = 9.06 ❌
B) √25 = 5 ✅
C) √180 = 13.4 ❌
D) √80 = 8.9 ❌
So B) is your answer it is the one that is true
Question 2
We know the box labeled 16 cm^2 will have a side of 4 because √16 = 4
We know the box labeled 9 cm ^2 will have a side of 3 because √9 = 3
So we have two sides of a right triangle we can use Pythagorean theorem to find the hypotenuse or diagonal
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
√25 = c
c = 5 is the hypotenuse or diagonal and also the unknown side of the square
So your square has an area of 25 cm^2
Because LxW is 5 x 5 = 25
Graph this line y+4=1/4(x+10)
Answers
Answer:
goes from(6,0),(10,1),(14,2) in +ve
Please help ASAP I've been stuck on this question
Answers
The coordinate of the vertices of △A'B'C' are A'(3,6), B'(9,-3), and C'(-12, 6). Since the scale factor is 3.
What is coordinate of a point?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph.
The coordinate of △ABC are A(1,2), B(3,-1) and C(-4,2).
The scale factor is k = 3.
The x-coordinate of A is 1.
The y-coordinate of A is 2.
The x-coordinate of B is 3.
The y-coordinate of B is -1.
The x-coordinate of C is -4.
The y-coordinate of C is 2.
To find the vertices of △A'B'C', multiplying x-coordinate and y-coordinate by 3.
The x-coordinate of A' is 1 × 3 = 3.
The y-coordinate of A' is 2 × 3 = 6.
The x-coordinate of B' is 3 × 3= 9.
The y-coordinate of B' is -1 × 3 = -3.
The x-coordinate of C' is -4 × 3 = -12.
The y-coordinate of C' is 2 × 3 = 6.
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Write a function describing the relationship of the given variables.
A, varies directly with, r, and when r = 4, A = 8
A=______
Answers
The relation between a and r is 2r
How to write a function describing the relationship of the given variables?According to the given information
a varies directly with r
a = 8
r = 4
a is directly proportional to r
a ∝ r
a = k r
where k is constant of proportionality
k = [tex]\frac{a}{r}[/tex]
k = [tex]\frac{8}{4}[/tex]
k = 2
so,
a = k r
putting the value of k in the above equation
we get
a = 2r
The relation between a and r is 2r
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A water tank initially contained 65 liters of water. It is being drained at a constant rate of 2.5 liters per minute.
How many liters of water are in the tank after 109 seconds? Round answers to the nearest whole liter.
Answers
The number of liters in the tank after 109 seconds is 60.5 liters.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
2.5 liters = 1 minute
2.5 liters = 60 seconds
Multiply 109/60 on both sides.
109/60 x 2.5 liters = 109 seconds
4.5 liters = 109 seconds
This means,
4.5 liters is drained after 109 seconds
Now,
The liters of water in the tank.
= 65 - 4.5
= 60.5 liters
Thus,
There are 60.5 liters in the tank.
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Aspen incorrectly converted 15/8 to a decimal using long division. Check her work carefully to find the error. Select the digit where she first made a mistake.
Answers
The mistake happens when computing 70-64. The result is not 4, but should be 6 instead.
The correct long division is shown below.
This means [tex]\frac{15}{8} = 1.875[/tex] in which you can use your calculator to verify this.