In the given equation:
f(x) = 30x+ 10, where x is the number of days
We can see that at the beggining, when x = 0, then f (0) = 30 · 0+ 10 = 10
Then, renting a car costs at least $10, so $10 is the fixed fee
Each day that passes $30 is being multiplicated, then it cost $300 per day.
Then, the equation is expressed by
f(x)= daily rate · x + fixed fee
If the agency doubles the fixed fee, it would be that 2 · $10 = $20
If the agency increases the daily rate by $5, in addition, then $30 + $5 = $35 woul be the cost each day.
Then, with these new costs we reaplce our equation
f(x)= daily rate · x + fixed fee
f(x)= 35 · x + 20
Answer: D. f (x) = 35x + 207 1/5 - 6 2/5= ?
A. 1 4/5
B. 4/5
C. 1 1/5
D. 13 3/5
Hello!
So, we are given the following to solve:
[tex]7\frac{1}{5} -6\frac{2}{5}[/tex]
Convert the mixed numbers to improper fractions, then find the LCD and combine.
Exact Form of Solution:
[tex]\frac{4}{5}[/tex]
Hence, the correct choice is B. Hope this helps!
Answer:
B. 4/5
Step-by-step explanation:
7 1/5= to 36/5
6 2/5= to 32/5
subtract both numbers on top and keep the bottom, which equals to 4/5
41 points 3 games how many points 11 games
Answer:
33by 11
Step-by-step explanation:
in 41 3 games firstly we find 1 point it is 3by41
Select the correct operator for the following exponential expression.(-2)^4 ? 2^4 A. C. =
solve each of the expressions
[tex](2)^4=2\cdot2\cdot2\cdot2=16[/tex][tex](-2)^4=(-2)\cdot(-2)\cdot(-2)\cdot(-2)=16[/tex]the correct operator is =.
find they distance between poind A nada point B
We get that the distance is
[tex]d=\sqrt[]{(5-2)^2+(5-1)^2}=\sqrt[]{9+16}=\sqrt[]{25}=5[/tex]so the answer is 5
what is the product of [tex] ( - \frac{3}{4} ) \times ( - \frac{7}{8} )[/tex]
What is the product of
In the multiplication of fractions, you multiply the numerators with each other and the denominators with each other
( - 3/5) *(-7/8)
= -3*-7 / (5*8) = (positive)
= 21/40
_____________________
Answer
= 21/40
_____________________
Do you have any questions regarding the solution?
A person has a rectangular board 14 inches by 18 inches around which she wants to put a uniform border of shells. If she has enough shells for a border whose area is 320 square inches, determine the width of the border.
The width of the border will be 8 inches.
In the given question, it is stated that a rectangular board has dimensions of 18*14 around which a person has to put a border of shells. If there are enough shells for the border of an area of 320 square inches, we need to find out the Width of the border.
Firstly, we know the Area of Rectangle is l*b => Length*Breadth
So, now we calculate the area of the board with dimensions l = 18 and b = 14
=> A₁ = l*b
=> A₁ = 18*14
=> A₁ = 252 square inches
We get the Area of the Board as 252 Square inches.
Now, there are shells enough to cover a border area of 320 square inches.
So, the Board and Border area will be A₁ + A, where A₁ and A are the areas of the Board and border respectively.
So, Total Area = 252 + 320
Total = 572 Square inches.
Now, let 'w' be the width of the border. Then the dimensions for the board will be
l = (18 + w)
b = (14 + w)
Using the formula for the Area of the rectangle, we get
=> Total = l * b
=> Total = (18 + w)*(14 + w)
=> 572 = w² + 32m + 252
=> w² + 32m - 320 = 0
=> w² + 40w -8w -320
=> w(w + 40) -8(w + 40)
=> (w+40) (w-8)
We get factors as w = -40 and 8
Since Width can not be negative quantity, width w will be 8 inches.
Hence, the width will be 8 inches for the border.
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Decide which of the two given prices is the better deal and explain why.
You can buy shampoo in a 6-ounce bottle for $3.19 or in a 15-ounce bottle for $11.99
First person to help gets brainliest
The solution of the given equation w.r.t m is m = 3 ,i.e., option A
What are Algebraic equations?With one exception, algebraic equations are essentially algebraic expressions.
An = sign is required in all algebraic equations.
No matter what kind of equation it is, all equations use the = sign.
The next topic is algebraic expression, which lacks the operators =,,, >, and.
To put it simply, there is no comparison between two terms in an algebraic statement.
Algebraic expressions frequently use terms like polynomial and square root.
So you now recognize the distinction between the two?
1) An algebraic equation has the symbol =, and 2) an algebraic expression lacks any comparison symbols (such as > and =).
As per the question:
[tex]6\frac{1}{9} + 3\frac{1}{3} =28\frac{1}{3}[/tex]
55/9 + 10/3 = 85/3
(55m+30m)/9 = 85/3
85m/9 = 85/3
85m = (85*9)/3
85m = 85*3
m = (85*3)/85
∴ m = 3
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Calculate the final price. Round all answers to the hundredths place and make sure to write your answer in the form of $12.34. Book: $14.99. Discount: 15%
We will determine the final price as follows:
[tex]p=14.99-(14.99)(0.15)\Rightarrow p\approx12.74[/tex]So, the final price is approximately $12.74.
The half-life of a radioactive kind of copper is 3 hours. if you start with 2,352 grams of it, how much will be left after 9 hours??
Answer:
294 grams
Explanation:
The amount of radioactive material left after t hours given that the half-life is to hours is
[tex]A=P(0.5)^{\frac{t}{t_0}}[/tex]Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives
[tex]A=2352(0.5)^{9/3}[/tex][tex]A=294g[/tex]which is our answer!
Hence, the amount of radioactive copper left after 9 hours is 294 grams.
Find the coordinates of the vertex of the following parabola algebraically. Writer answer as an (x,y) point y=-x² - 7
The expression we have is:
[tex]y=-x^2-7[/tex]We need to compare this equation of our parabola, with the general equation of a parabola in vertex form:
[tex]y=a(x-h)^2+k[/tex]Where (h,k) is the vertex of the parabola, and a indicates if the parabola opens up or opens down (if a is positive the parabola opens up, and if a is negative the parabola opens down).
We take our equation:
[tex]y=-x^2-7[/tex]And we arrange the terms so that it looks like the vertex form:
[tex]y=(-1)(x-0)^2+(-7)[/tex]And we can find the values of a, h, and k:
[tex]\begin{gathered} a=-1 \\ h=0 \\ k=-7 \end{gathered}[/tex]We only need h and k for the vertex:
[tex](h,k)=(0,-7)[/tex]Answer: the vertex is at (0,-7)
There are 8 1/2 cups of fruit punch shared equally among 4 friends. How many does each friend get?
Answer:
17/8 or 2 and 1/8 cups
Step-by-step explanation:
turn the 8 and 1/2 into one fraction :
17/2
then divide that by 4:
17/8
What is the arc length of CD in the circle below?
Solution
[tex]\begin{gathered} \theta=35^0 \\ r=8ft \end{gathered}[/tex]The formula for arc length is;
[tex]\begin{gathered} A=\frac{\theta}{360}\times2\pi r \\ \\ \Rightarrow A=\frac{35}{360}\times2\pi\times8=4.88\text{ feet} \end{gathered}[/tex]The monthly mortgage payment on the Flynn's home is $634.8. Additionally, they pay $1,785.13 in annual real estate taxes and $726 per year in homeowner's insurance.
What is the total amount of their entire monthly payment?
State your answer in terms of dollars, rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Answer: 695.30
Step-by-step explanation: We know that 634.8 is what the monthly mortgage is, then we use the value of $726 and divide it by 12 which represents the 12 months in a year. So 726 ÷ 12 = 60.5 therefore monthly he will additionally need to pay that amount. I don't think the annual real estate taxes are going to be used for this problem. So after this, we do the following equation. 634.8 + 60.5 = 695.3. We round this value to the nearest cent and we get 695.30. When the digit to the right is less than 5 we round toward 0... 695.3 was rounded down toward zero to 695.30
Write the given expression as an algebraic expression in x.
cos(2 taninverse (x))
Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives
How to write given expression: cos(2 tan inverse (x)) as algebraic expressionData given in the question are as follows:
cos(2 tan inverse (x))
Using trigonometry (double angle formula)
cos 2x = 1 - 2sin² x
when x = tan inverse (x)
cos(2 tan inverse (x)) = 1 - 2sin² tan inverse (x) (1)
cos² x + sin² x = 1
cos² x = 1 - sin² x
cos x = √(1 - sin x)
tan x = sin x / cos x
[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]
squaring all parts of the trigonometry expression and clearing the fraction
[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]
[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]
[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]
[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]
[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]
[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]
since tan (tan inverse) (x) = x
[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]
[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]
[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]
Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)
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Equation 1: A [-4x+7y=4]
Equation 2: B [3x-3y=6]
Think about using the elimination method to solve this system.
Question 1: If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be ______ and the value of B must be ______.
Question 2: If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be ______ and the value of B must be _____.
Using the elimination method, the value of A and B must 3 and 4 respectively to eliminate x in the equation. The value of A and B must be 3 and 7 respectively to eliminate y.
How to solve system of equation?System of equation can be solved using elimination method, substitution method of graphical method.
But we are asked to use elimination method.
Therefore, the system of equation are as follows:
Equation 1: A [-4x + 7y = 4]
Equation 2: B [3x - 3y = 6]
Therefore,
If you wanted to eliminate the x variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 4.
If you wanted to eliminate the y variables with the lowest common value by multiplying each equation by numbers A and B, the value of A must be 3 and the value of B must be 7.
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You flip a coin twice what is the probability of getting tails and then getting tails
The probability a single event A occurs is:
[tex]P(A)=\frac{\text{ number of favorable outcomes to A}}{\text{ number of total outcomes}}[/tex]The probability P two consecutive events A and B occurs is:
[tex]P=P(A)*P(B)[/tex]So, let's consider the probability of the first event: getting tails.
Favorable outcomes: Tail
Number of favorable outcomes: 1
Total outcomes: Tail, Head
Number of total outcomes: 2
So, the probability of getting a tail is:
[tex]P(A)=\frac{1}{2}[/tex]So, let's consider the probability of the second event: getting tails in the second time.
Favorable outcomes: Tail
Number of favorable outcomes: 1
Total outcomes: Tail, Head
Number of total outcomes: 2
So, the probability of getting a tail is:
[tex]P(B)=\frac{1}{2}[/tex]Finally, let's calculate the probability of getting a tail twice.
[tex]\begin{gathered} P=P(A)*P(B) \\ P=\frac{1}{2}*\frac{1}{2} \\ P=\frac{1}{4} \end{gathered}[/tex]Answer: The probability is 1/4.
Geometry ?Use the photo to help me solveTriangle DEF is shown. What is the coordinate of D if triangle D E F is created by dilating DEF with a scale of 0.5 about the origin
Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).
Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).
The original coordinates of D are
[tex](3,0)\text{.}[/tex]Multiplying them by the scale factor, we get
[tex]0.5\cdot(3,0)=(0.5\cdot3,0.5\cdot0)=(1.5,0)\text{.}[/tex]AnswerThe coordinates of D after the given dilation is
[tex](1.5,0)\text{.}[/tex]help I'm practicing
Answer:
The total surface area is;
[tex]336\text{ }ft^2[/tex]Explanation:
Given the square pyramid as show in the attached image.
The total surface area is the sum of the area of the base square and the area of the four triangles.
[tex]A=l^2+4(\frac{1}{2}lh)[/tex]Given;
[tex]\begin{gathered} l=12\text{ ft} \\ h=8\text{ ft} \end{gathered}[/tex]substituting the given values;
[tex]\begin{gathered} A=l^2+4(\frac{1}{2}lh) \\ A=12^2+4(\frac{1}{2}\times12\times8) \\ A=144+192 \\ A=336\text{ ft}^2 \end{gathered}[/tex]Therefore, the total surface area is;
[tex]336\text{ }ft^2[/tex]How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Whereas working with laws of exponents, when splitting the exponential equations with the same base, the exponents ought to be subtracted.
Basically, the Quotient of Powers rules is used to decrease the number of terms when parts like terms with exponents. In order to get the solution, just remove the exponents while dividing the terms with the same base, it is applicable to exponents with the same bases. when powers are multiplied, for two whole numbers of the same bases the exponents are added, whereas when powers are divided for two whole numbers of the same bases, exponents are subtracted. The zero exponent rule basically states that when any number is raised to the power of zero it results in 1.
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Money set aside to pay for small, unforeseen expenses is called a(n) _____.
A.
down payment
B.
emergency fund
C.
mutual fund
D.
equity fund
Answer:
B. Emergency fund.
Step-by-step explanation:
What is the area of triangle ADC is ? Square units?
Given:
The triangle ADC is formed by reflecting the triangle ABC across the line segment AC
So, the triangles ABC and ADC are congruent
The area of the triangle ADC = Area of the triangle ABC
The area of the triangle = 1/2 * base * height
Base = AC = 4 units
Height = BE = 3 units
So, the area will be as follows:
[tex]Area=\frac{1}{2}*AC*BE=\frac{1}{2}*4*3=6[/tex]So, the answer will be:
Area of the triangle ADC is 6 square units
2. A ladder rises 20 feet for every horizontal change of 4 feet. What is the slope of the ladder?A. O 5C. O 20D.OChoose
The slope is defined as rise/run - in other words, for every step you take horizontally, how many steps you should take vertically to get to a point on the same line.
In our case, the ladder rises 20 feet for every horizontal change of 4 feet; therefore, the slope is
[tex]\frac{\text{rise}}{\text{run}}=\frac{20ft}{4ft}[/tex]dividing 30 ft by 4 ft gives 5; therefore,
[tex]\frac{\text{rise}}{\text{run}}=5.[/tex]Hence, the correct answer to choose is A. 5.
I’m confused on this drag and drop assignment can someone please help me out? I’ll give brainliest
The most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.What is the similarity of the figures?Two figures are said to be similar if the corresponding angles are equal and the corresponding sides are in the same ratio.So,
(A) HIJK∼WXYZ [Given].
HJ/WX = KJ/ZY6/5 = 24/ZY6 × ZY = 24 × 5ZY = 24×5/6ZY = 20(B) The two triangles are similar [Given].
2/2+4.5 = x/396.5x = 39×2x = 39×2/6.5x = 12(C) 5cm on the drawing represented 2 miles on the ground.
Let 22.5 cm on the drawing represent x miles on the ground.
The problem:
5/22.5 = 2/x5x = 22.5 × 25x = 45x = 45/5x = 9 miles22.5 cm on the drawing represented 9 miles on the ground.
Therefore, the most appropriate choice for the similarity of figures will be given by:
(A) ZY = 20(B) x = 12(C) 22.5 cm on the drawing represented 9 miles on the ground.To learn more about the similarity of figures, refer to the link:
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What is the value of the following sum: 1+2+3+…+397+398+399+400?
Answer:
80,200
Step-by-step explanation:
There is a formula for the sum of a series of numbers from a_1 to a_n.
S = (a_n * a_n+1)/2
This formula means: multiply the last number of the series by what would be the next number, and divide by 2.
The last number you have is 400. The next number would be 401.
Multiply 400 by 401 and divide by 2. That is the sum of the 400 numbers.
S = (401 * 402)/2
S = 160400/2
S = 80200
Answer: The sum is 80,200
Here's a way to understand the formula.
You are adding 400 numbers, from 1 to 400.
Write the first 200 numbers on a line:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... 198 199 200
Now write the next 200 numbers, from 201 to 400 under these numbers, but start from 400 and go down 1 each number to the right.
You end up with these two lines:
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
Now add every two numbers in the same column.
1 2 3 4 5 6 7 8 9 ... 198 199 200
400 399 398 397 396 395 394 393 392 ... 203 202 201
------------------------------------------------------------------------------------------------------
401 401 401 401 401 401 401 401 401 ... 401 401 401
Now you have 200 times the number 401.
200 * 401 = 80,200
A random sample of n = 50 teachers was selected from a Local Government and it has been established that 30% of the entire teachers are ghost workers and 70% are real workers. Determine the expected number of the real workers in any sample of size 50?
The expected number of the real number in any sample size is 150.
What is sample size?
In statistics, the sample size refers to the group of people whose data is analyzed during calculation. Depending upon the constraints, the data is analyzed for the measurement. The analysis of samples is perform with the help of Binomial distribution.
According to the question, the given random sample can be solved with the help of Binomial distribution:
The sample size of teachers: n = 50
Percentage of ghost workers: 30%
Percentage of real workers: 70%
For ghost workers: n = 50 and p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69
Now, to calculate the expected number of the real workers as per given samples:
For real workers: n = 50 and p = 0.70 and q = 1 - p = 1 - 0.70 = 0.30
Expected number is: (n)(q) = (50)(0.30) = 150
Hence, the expected number of the real number in any sample size is 150.
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Solve |3x + 7 = 4x for x.A) Infinitely many solutionsB) 7 and -7C) No solutionOD) -7 or 1
The given equation is
[tex]\lvert{3x+7}\rvert=4x[/tex]We will solve it in this way
[tex]3x+7=4x,3x+7=-4x[/tex]For the 1st equation
[tex]3x+7=4x[/tex]Subtract 7 from each side
[tex]\begin{gathered} 3x+7-7=4x-7 \\ 3x=4x-7 \end{gathered}[/tex]Subtract 4x from both sides
[tex]\begin{gathered} 3x-4x=4x-4x-7 \\ -x=-7 \\ x=7 \end{gathered}[/tex]For the 2nd equation
[tex]3x+7=-4x[/tex]Subtract 3x from both sides
[tex]\begin{gathered} 3x-3x+7=-4x-3x \\ 7=-7x \end{gathered}[/tex]Divide both sides by -7
[tex]\begin{gathered} \frac{7}{-7}=\frac{-7x}{-7} \\ -1=x \end{gathered}[/tex]The solutions are
7, -1
The answer should be B
Which expression evaluates to 2048?
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
The expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
What is meant by exponent rule?Exponent rules include: Rule of the product of powers: When multiplying like bases, add the powers together. Rule of the quotient of powers: When splitting like bases, take the powers out. Power of powers rule: When increasing a power by another exponent, multiply all the powers together.
A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.
Let the value be 2048
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex]
simplifying the above expression we get
[tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3=512 \\[/tex]
[tex]$&=512\left(\frac{1}{2^{-1}}\right)^2[/tex]
By using exponent rule, we get
[tex]$&\left(\frac{1}{2^{-1}}\right)^2=\frac{1^2}{\left(2^{-1}\right)^2} \\[/tex]
[tex]$&=512 \cdot \frac{1^2}{\left(2^{-1}\right)^2}[/tex]
1² = 1
[tex]$&=512 \cdot \frac{1}{\left(2^{-1}\right)^2}[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}$$[/tex]
[tex]$\left(2^{-1}\right)^2=\frac{1}{4}$$[/tex]
[tex]$=512 \cdot \frac{1}{\frac{1}{4}}[/tex]
[tex]$&\frac{1}{\frac{1}{4}}=4 \\\pi[/tex]
= 512 × 4
= 2048
By simplifying the expression [tex]$&\left(\frac{\left(\frac{1}{2}\right)^{-1}}{\left(\frac{1}{2}\right)^2}\right)^3\left(\frac{1}{2^{-1}}\right)^2 \\[/tex], we get 2048.
Therefore, the correct answer is option (b).
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Select the GCF of these numbers. 2^5 · 5· 11 and 2^3· 5^2 · 7
The greatest common factors of 2^5 · 5· 11 and 2^3· 5^2 · 7 is equivalent to 2^3 * 5
What are greatest common factors?The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor.
This factor must be able to divide all the terms of the expression withour remainder.
Given the numbers 2^5 · 5· 11 and 2^3· 5^2 · 7. Find the factors;
2^5 · 5· 11 = 2^3 * 2^2 * 5 * 11
2^3· 5^2 · 7= 2^3 * 5 * 5 * 7
Since the number 2^3 * 5 is common to both factors, hence the GCF of these numbers 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 * 5
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I have watched 32% of the episodes of my favorite show. I have watched 8 episodes. How many episodes are there?
Answer:
There are 35 episodes in the show