we have the following equation
[tex]m(t)=430+430\cdot0.02\cdot t[/tex]where t is the time in years, as we have 9 months, we have to change to years
[tex]t=\frac{9}{12}=\frac{3}{4}=0.75[/tex]so after 9 months we get
[tex]430+430\cdot0.02\cdot0.75=430+6.45[/tex]So she will earn $6.45 in 9 month
A yogurt stand gave out 200 free samples of frozen yogurt, one free sample per person. The three sample choices were vanilla, chocolate, or chocolate & vanilla twist. 115 people tasted the vanilla and 137 people tasted the chocolate, some of those people tasted both because they chose the chocolate and vanilla twist. How many people chose chocolate and vanilla twist?
So we are to find x
[tex]137-x+x+115-x=200[/tex][tex]\begin{gathered} 137+115-x=200 \\ 252-x=200 \\ -x=200-252 \\ -x=-52 \\ x=52 \end{gathered}[/tex]The final answer52 people chose chocolate and vanilla twistestimate the product by rounding to the nearest ten: 28×51×76
To estimate each number by rounding it to the nearest ten, we will look at the unit digit,
If it is less than 5, then we replace it by 0 and keep the ten-digit as it
If it is 5 or more, then we will replace it by 0 and add the ten-digit by 1
Let us do that with every number
28, the unit digit is 8 which is greater than 5, then replace it by 0 and add 2 by 1
28 rounded to 30
51, the unit digit is 1 which is less than 5, then replace it by 0
51 rounded to 50
76, the unit digit is 6 which is greater than 5, then replace it by 0 and add 7 by 1
76 rounded to 80
Now let us multiply them
[tex]28\times51\times76=30\times50\times80=120,000[/tex]The product of the given numbers is 120,000
The ratio of a quarterback's completed passes to attempted passes is 5 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.
The ratio of a quarterback's completed passes to attempted passes is 5 to 8. If he attempted 16 passes, find how many passes he completed. Round to the nearest whole number if necessary.
Let
x -----> number of quarterback's completed passes
y -----> number of quarterback's attempted passes
so
x/y=5/8 -----> x=(5/8)*y -----> equation A
y=16 -----> equation B
substitute equation B in equation A
x=(5/8)*16
x=10
therefore
the answer is 10 completed passesQuestion 8 > Find the area of the trapezoid shown below 9 19 18 21 23 I Question Help ve
288 u²
1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:
[tex]\begin{gathered} S=\frac{(B+b)h}{2} \\ S=\frac{(23+9)18}{2} \\ S=288 \end{gathered}[/tex]2) So that trapezoid has an area of 288 u²
theres 2 fill in the blank boxes and 3 drop down menus, below i will list the options in the drop down menus.box 1 - apply quotient identities, apply Pythagorean identities, apply double-number identities, apply even-odd identities.box 2 - apply cofunction identities, use the definition of subtraction, apply even-odd identities, Write as one expresssion combine like terms.box 3 - apply cofunction identities, apply double-number identities, apply Pythagorean identities, apply even-odd identities.
Solution
Box 1 : Apply Quotient Identities
[tex]cotx-tanx=\frac{cosx}{sinx}-\frac{sinx}{cosx}[/tex]The answer for the first box is
[tex]\begin{equation*} \frac{cosx}{sinx}-\frac{sinx}{cosx} \end{equation*}[/tex]Box 2: Write as one expression
[tex]\begin{gathered} cotx-tanx=\frac{cosx}{s\imaginaryI nx}-\frac{s\imaginaryI nx}{cosx} \\ cotx-tanx=\frac{cosx(cosx)-sinx(sinx)}{sinxcosx} \\ cotx-tanx=\frac{cos^2x-sin^2x}{sinxcosx} \end{gathered}[/tex]The answer for the second box is
[tex]\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx}[/tex]Before the box 3, please note the identity
Note: Trigonometry I dentities
[tex]\begin{gathered} cos^2x-s\mathrm{i}n^2x=cos2x \\ 2sinxcosx=sin2x \end{gathered}[/tex]Box 3: Apply Double - Number Identities
[tex]\begin{gathered} cotx-tanx=\frac{cos^{2}x-s\imaginaryI n^{2}x}{s\imaginaryI nxcosx} \\ Applying\text{ the above trigonometry identities} \\ cotx-tanx=\frac{cos2x}{sinxcosx} \\ cotx-tanx=\frac{cos2x}{sinxcosx}\times\frac{2}{2} \\ cotx-tanx=\frac{2cos2x}{2sinxcosx} \\ cotx-tanx=\frac{2cos2x}{sin2x} \end{gathered}[/tex]Write the first 4 terms of the sequence defined by the given rule. f(n)=n^3-1
Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method.
We have the following:
[tex]s^2+7s+6[/tex]solving:
[tex]\begin{gathered} \text{step 1} \\ s^2+s+6s+6 \\ \text{step 2} \\ s\mleft(s+1\mright)+6\mleft(s+1\mright) \\ \text{step 3} \\ (s+1)(s+6) \end{gathered}[/tex]Which of the followingrepresents this inequality?|4x – 61 > 10
Solution:
Given the absolute inequality below:
[tex]\lvert4x-6\rvert>10[/tex]From the absolute law,
[tex]\begin{gathered} \lvert u\rvert>a \\ implies\text{ } \\ u>a\text{ } \\ or \\ u<-a \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6>10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6>10+6 \\ \Rightarrow4x>16 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}>\frac{16}{4} \\ \Rightarrow x>4 \end{gathered}[/tex][tex]\begin{gathered} When\text{ 4x-6<-10} \\ add\text{ 6 to both sides of the inequality,} \\ 4x-6+6<-10+6 \\ \Rightarrow4x<-4 \\ divide\text{ both sides by the coefficient of x, which is 4} \\ \frac{4x}{4}<-\frac{4}{4} \\ \Rightarrow x<-1 \end{gathered}[/tex]Plotting the solution to the inequality, we have the line graph of the inequality to be
Hence, the correct option is D.
An item is regularly priced at $65. Lena bought it on sale for 60% off the regular price. How much did Lena pay?
The regular price of an item is $65
Lena bought it on sale for 60% off the regular price.
Then it means that she paid only (100% - 60% = 40%) of the price.
Let us find the 40% of $65
[tex]\frac{40}{100}\times\$65=\$26[/tex]Therefore, Lena paid only $26 for the item.
How do you solve the system of equations by graphing? y=-3x/2 + 6y=5x - 7
The given system of equations are
y=-3x/2 + 6
y=5x - 7
We would substitute values for x into the equations and find the corresponding y values. These values would be plotted on a graph. Where the lines of both equations meet would represent the solution of the system of equations.
For the first equation,
y = - 3x/2 + 6
if x = 0, y = 3 * 0/2 + 6 = 6
If x = 1, y = - 3 * 1/2 + 6 = 4.5
if x = 2, y = - 3 * 2/2 + 6 = 3
We would plot these values on the graph
For the second equation,
y = 5x - 7
if x = 0, y = 5 * 0 - 7 = - 7
If x = 1, y = 5 * 1 - 7 = - 2
if x = 2, y = 5 * 2 - 7 = 3
We would plot these values on the graph
The diagram of the graph is shown below
Looking at the graph, at the point where both lines meet,
x = 2, y = 3
Thus, the solution is (2,3)
Which term is −20,155,392 for the following sequence, assuming that the pattern continues?
2, −12, 72, −432, …
a9
a10
a11
a12
The term that is the −20,155,392 in the sequence is a₁₀.
How to solve sequence?The sequence below is a geometric sequence.
Therefore, a geometric sequence can be represented as follows:
nth term = arⁿ⁻¹
where
a = first termn = number of termsr = common ratioTherefore, let's find which term is −20,155,392 for the sequence.
2, -12, 72, -432
r = -12 / 2 = 72 / -12 = -432 / 72 = -6
a = 2
Hence,
nth term = arⁿ⁻¹
−20,155,392 = 2 × -6ⁿ⁻¹
−20,155,392 / 2 = -6ⁿ⁻¹
- 10077696 = -6ⁿ⁻¹
6ⁿ⁻¹ = 10077696
6ⁿ⁻¹ = 6⁹
n - 1 = 9
n = 9 + 1
n = 10
Therefore, it's the 10th term.
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The term −20,155,392 is the tenth in the given geometric sequence.
The given sequence is below which is in a geometric pattern
2, -12, 72, -432
Here first term (a) = 2
The common ratio (r) = -12 / 2
The common ratio (r) = -6
We know that the nth term of the geometric sequence is
Tₙ = arⁿ⁻¹
Here Tₙ = −20,155,392
⇒ −20,155,392 = arⁿ⁻¹
Substitute the values of a and r in the above equation,
⇒ −20,155,392 = 2 × -6ⁿ⁻¹
⇒ −20,155,392 / 2 = -6ⁿ⁻¹
Apply the division operation,
⇒ - 10077696 = -6ⁿ⁻¹
⇒ 6ⁿ⁻¹ = 10077696
⇒ 6ⁿ⁻¹ = 6⁹
Equating exponents of the base
⇒ n - 1 = 9
⇒ n = 10
Therefore, the term −20,155,392 would be the tenth in the given sequence.
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what is the sum of -1 1/3 + 3/4
Here, we want to add two fractions
What we have to do here is to make the mixed fractin an improper one
To do this, we multiply the denominator by the standing number, and add to the numerator, then we place the value over the denominator
Thus, we have it that;
[tex]\begin{gathered} 1\frac{1}{3}\text{ = }\frac{4}{3} \\ -\frac{4}{3}+\frac{3}{4}\text{ = }\frac{-16+9}{12}=\text{ }\frac{-7}{12} \end{gathered}[/tex]Which describes a number that cannot be irrational?A. a number that represents the ratio of the circumference to the diameter of a circle B. a number that can be written as the ratio of two integers C. a number that can be used to solve an algebraic equation D. a number that represents the length of the diagnostic of a square
a number that can be written as the ratio of two integers (option B)
Explanation:Irrational number cannot be written in the fractional form
Rational numbers can be written in the form of fraction
Checking the options:
a) Circumference = πd
where d = diameter
π = Circumference/diameter
π is an irrational number
b) A number written as ratio of two intergers can be written in the form of fraction
Hence, it is rational
c) A number that we can use in solving an algebraic equation can be any real number.
From a real number, we have rational and irrational numbers. So, there is the likelihood we get an irrational number
d) side of a square = a
diagonal² = a² + a²
length of diagonal of a square = √(a² + a²) = √2a²
This can also yield either irrational or rational numbers.
A number that cannot be irrational means a number that is rational.
From the option, the only one without doubt that it is rational is a number that can be written as the ratio of two integers (option B)
Point S is on line segment \overline{RT} RT . Given RT=3x,RT=3x, RS=3x-5,RS=3x−5, and ST=3x-1,ST=3x−1, determine the numerical length of \overline{RT}. RT .
The numerical length of the line segment RT is 6.
Length:
Length is the measuring unit used to identifying the size of an object or distance from one point to the other.
Given,
There is a point on the line segment RT.
And the values of the pots are,
RT = 3x, RS = 3x - 5 and ST = 3x - 1.
Now we need to find the length of the line segment RT.
To find the line of the line segment RT,
We have to add the length of the segments,
That can be written as,
=> RT = RS + ST
Now, we have to apply the values of the point to the equation, then we get,
=> 3x = 3x - 5 + 3x - 1
=> 3x = 6x - 6
=> 6x - 3x - 6
=> 3x - 6
=> 3x = 6
=> x = 2
If the value of x is 2, then the length of the line segment RT is,
RT = 3x => 3 x 2 = 6
Therefore, the length of the line segment RT is 6.
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In Abc,AB=5 feet and BC=3 feet.Which inequality represents all possible values for the length of AC,in feet?
The smallest value of length AC would be 5 ft - 3 ft = 2 ft while the largest length would be 5 ft + 3 ft = 8ft. The answer will be
2 < Ac < 8
Describe the difference on table, graph and equation between discrete and continuous functions.
REmember that
A continuous function allows the x-values to be ANY points in the interval, including fractions, decimals, and irrational values
A discrete function allows the x-values to be only certain points in the interval, usually only integers or whole numbers.
Discrete functions have scatter plots as graphs and continuous functions have lines or curves as graphs
image
Determine the value of x.
Question 17 options:
A)
x = 20°
B)
x = 45°
C)
x = 4.5°
D)
x = 90°
The value of the x in the rectangle is 4.5°
Rectangle:
A rectangle is a two-dimensional shape (2D shape) in which the opposite sides are parallel and equal to each other and all four angles are right angles
Given,
Here we have the rectangle with one angle as 90°.
Here we have to find the value of x.
We know that, we we divide the rectangle as two distinct right angled triangle.
We know that, the right triangles are triangles in which one of the interior angles is 90 degrees, a right angle.
So,
20x = 90
x = 90/20
x = 4.5°
Therefore, the value of x is 4.5°.
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Had someone explain it and I didn’t get it still
From the question:
Let f(x) = 2x² + 2x - 8
g(x) = √x - 2
We are aske to write f(g(x))
f(x) = 2x² + 2x - 8, g(x) = √x - 2
g(x) = √x - 2
= f(√x - 2)
f(√x - 2): 2x + 2√x - 2 - 12
f(g(x)) = 2x - 12 + 2√x - 2.
Select the correct answer.
What is the value of this logarithmic e ession?
log2 16 - log₂ 4
Answer:l og2(16)=x log 2 ( 16 ) = x in exponential form using the definition of a logarithm. If x x and b b are positive real numbers and b b does not equal ...
Step-by-step explanation:
Graph the inequality on a plane. Shade a region below or above. Y < - 1
In order to graph the inequality on the coordinate plane, we first need to find it's border, which is delimited by the line below:
[tex]y=-1[/tex]This line is a straight line parallel to the x-axis and that passes through the y-axis at the point (0, -1). Since the original inequality has a "less" sign, we need to make this boundary line into dashes.
Now we can analyze the inequality:
[tex]y<-1[/tex]Since the signal is "<", we need to shade all the region of the coordinate plane for which y is below -1, this means that we have to paint the region below the line. The result is shown below:
find the point that is symmetric to the point (-7,6) with respect to the x axis, y axis and origin
Answer:
[tex]\begin{gathered} a)(-7,-6)\text{ } \\ b)\text{ (7,6)} \\ c)\text{ (7,-6)} \end{gathered}[/tex]Explanation:
a) We want to get the point symmetric to the given point with respect to the x-axis
To get this, we have to multiply the y-value by -1
Mathematically, we have the symmetric point as (-7,-6)
b) To get the point that is symmetric to the given point with respect to the y-axis, we have to multiply the x-value by -1
Mathematically, we have that as (7,6)
c) To get the point symmetric with respect to the origin, we multiply both of the coordinate values by -1
Mathematically, we have that as:
(7,-6)
23. At a company employing 140 people, 40% of the employees took the bus to work,and 5 % lived close enough to walk. The others drove cars. How many employeesdrive cars to work?Answer
Since the total percent of the employees is 100%
Since 40% of them took the bus
Since 5% walk
Add them and subtract the sum from 100% to get the percentage of who take the car
[tex]\begin{gathered} 40+5=45 \\ 100-45=55 \end{gathered}[/tex]Then 55% of the employees use cars
Since the total number of employees is 140, then
Let us find 55% of 140
Change 55% to a number by divide it by 100, then multiply it by 140
[tex]\begin{gathered} N=\frac{55}{100}\times140 \\ N=77 \end{gathered}[/tex]There are 77 employees who use cars
please help 50 points!
What is the solution to the equation below? √x+9 = 11 O A. x= 2 O B. X= √ O C. x = 42 D. x = 4
answer: D. x = 4
When 8 is subtracted from a number and that difference is doubled, the result is 10. What is the number?
A) 6
B) 5
C) 18
D) 13
Answer:
n = 13
Step-by-step explanation:
Find the number
8 is subtracted from a number
(n-8)
that difference is doubled
2(n-8)
the result is 10
2(n-8) = 10
Solve the equation by dividing each side by 2
2(n-8)/2 = 10/2
n-8 = 5
Add 8 to each side
n-8+8 = 5+8
n = 13
Exponential Regression
The table below shows the population, P. (in thousands) of a town after 12 years.
0
72
P 2400
3
2801.27
7
3608.71
12
14
4974.15 5426.17
19
6898.37
(a) Use your calculator to determine the exponential regression equation P that models the set of
data above. Round the value of a to two decimal places and round the value of b to three decimal
places. Use the indicated variables.
P =
(b) Based on the regression model, what is the percent increase per year?
96
(c) Use your regression model to find P when n = 13. Round your answer to two decimal places.
The population of the town after
P =
thousand people
(d) Interpret your answer by completing the following sentence.
years is
thousand people.
Considering the given table, it is found that:
a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.
b. The yearly percent increase is of 5.9%.
c. P(13) = 5075.
d. The population of the town after 13 years is of 5075.
How to find the exponential regression equation?The exponential regression equation is found inserting the points into a calculator.
The points are given as follows:
(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).
Using a calculator, the function is:
2408.80(1.059)^t.
The yearly percent increase rate is calculated as follows:
1 + r = 1.059
r = 1.059 - 1
r = 0.059
r = 5.9%.
Then in 13 years, the population will be given as follows:
P(13) = 2408.80(1.059)^13 = 5075.
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The length is twice the sum of its width 3. What are the dimension of the rectangle if it’s area 216 square inches?
Assume that the width of the rectangle = x
Since the length is twice the sum of the width and 3, then
[tex]\begin{gathered} L=2(x+3) \\ L=2x+6 \end{gathered}[/tex]Since the area of the rectangle is 216 square inches, then
Multiply the length and the width, then equate the product by 216
[tex]\begin{gathered} (x)(2x+6)=216 \\ 2x^2+6x=216 \end{gathered}[/tex]Divide all terms by 2 to simplify
[tex]\begin{gathered} \frac{2x^2}{2}+\frac{6x}{2}=\frac{216}{2} \\ x^2+3x=108 \end{gathered}[/tex]Subtract 108 from both sides
[tex]\begin{gathered} x^2+3x-108=108-108 \\ x^2+3x-108=0 \end{gathered}[/tex]Now, let us factorize the trinomial into 2 factors
[tex]\begin{gathered} x^2=(x)(x) \\ -108=(-9)(12) \\ (x)(-9)+(x)(12)=-9x+12x=3x \end{gathered}[/tex]Then the factors are
[tex]x^2+3x-108=^{}(x-9)(x+12)[/tex]Equate them by 0
[tex](x-9)(x+12)=0[/tex]Equate each factor by 0, then find the values of x
[tex]x-9=0[/tex]Add 9 to both sides
[tex]\begin{gathered} x-9+9=0+9 \\ x=9 \end{gathered}[/tex][tex]x+12=0[/tex]Subtract 12 from both sides
[tex]\begin{gathered} x+12-12=0-12 \\ x=-12 \end{gathered}[/tex]Since the width can not be a negative number (no negative length)
Then the width of the rectangle = 9
Let us find the length
[tex]\begin{gathered} L=2(9)+6 \\ L=18+6 \\ L=24 \end{gathered}[/tex]Then the dimensions of the rectangle are 9 inches and 24 inches
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
The company’s equivalent markup on selling price is 26%.
What is markup?The markup is the gap between the selling price and the cost of a good or service. It is frequently represented as a percentage of the total cost. To cover the costs of doing business and generate a profit, a markup is added to the overall cost borne by the manufacturer of a good or service.
The following can be deduced based on the information:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price will be:
= (0.35/1.35 x 100)
= 26%
Therefore, the value is 26%.
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Read the following scenario and write two equations we could use to solve to find for the number of cars and trucks washed. Use the variables C for cars washed and T for trucks washed. (Hint: both equations should have T and C). SCENARIO: Western's eSports Team raised money for charity by organizing a car wash. They washed a total of 80 vehicles and raised a total of $486. They charged $5 to wash a car and $7 to wash a truck.
Let:
C = Number of cars washed
T = Number of trucks washed
They washed a total of 80 vehicles, so:
[tex]C+T=80[/tex]They raised a total of $486. They charged $5 to wash a car and $7 to wash a truck. so:
[tex]5C+7T=486[/tex]Let:
[tex]\begin{gathered} C+T=80_{\text{ }}(1) \\ 5C+7T=486_{\text{ }}(2) \end{gathered}[/tex]From (1) solve for T:
[tex]T=80-C_{\text{ }}(3)[/tex]Replace (3) into (2):
[tex]\begin{gathered} 5C+7(80-C)=486 \\ 5C+560-7C=486 \\ -2C=486-560 \\ -2C=-74 \\ C=\frac{-74}{-2} \\ C=37 \end{gathered}[/tex]Replace the value of C into (3):
[tex]\begin{gathered} T=80-37 \\ T=43 \end{gathered}[/tex]They washed 37 cars and 43 trucks
Out of 441 applicants for a job 235 have over five years of experience and 106 have over five years of experience and have a graduate degreeWhat is the probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience enter a fraction or round your answer to four decimal places if necessary
Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience = 106/441
Explanation:Total number of applicants, n(Total) = 441
Number of candidates that have over five years of experience, n(5 yrs) = 235
Probability that a randomly chosen applicant has over 5 years experience
[tex]\begin{gathered} P(5yrs)=\frac{n(5yrs)}{n(Total)} \\ \\ P(5yrs)=\frac{235}{441} \end{gathered}[/tex]Number of applicants that have over five years of experience and have a graduate degree, n(5 n g) = 106
Probability that a randomly selected applicant has over five years of experience and have a graduate degree
[tex]\begin{gathered} P(5\text{ n g\rparen = }\frac{n(5\text{ n g\rparen}}{n(Total)} \\ \\ P(5\text{ n g\rparen = }\frac{106}{441} \end{gathered}[/tex]Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience
[tex]\begin{gathered} P(g\text{ /5yrs\rparen = }\frac{P(5\text{ n g\rparen}}{P(5yrs)} \\ \\ P(g\text{ /5yrs\rparen = }\frac{106}{441}÷\frac{235}{441} \\ \\ P(g\text{ /5yrs\rparen=}\frac{106}{441} \end{gathered}[/tex]