The translation we need to get f(x) is a translation of 7 units to the left and 6 units down.
Which shift do we have here?I assume we want to identify the transformation that we need to apply to the parent absolute value function |x| in order to get f(x).
Remember that a horizontal translation of N units and a vertical translation of M units is written as:
y = |x - N| + M
In this case we have:
f(x) = |x + 7| - 6
Comparing it with the formula above, we get:
N = -7
M = -6
This means that we have a translation of 7 units to the left, and 6 units down.
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Write a system of equations to describe the situation below, solve using substitution, and fillin the blanks.For her parents' anniversary party, Laura is considering using one of two venues. A hotel in Dayton will cost $693 for a reservation, plus $51 per person. A restaurant in the same city will cost $60 per person, in addition to $684 for the reservation. In order to make the best decision. Laura figures out how many attendees it would take to have the venues cost thesame amount. How many attendees would that be? What would the total cost be?
Answer:
• The number of attendees = 1
,• Total Cost = $744
Explanation:
Let the number of attendees = n
A hotel in Dayton will cost $693 for a reservation, plus $51 per person.
[tex]\text{ Hotel's Cost, H\lparen n\rparen}=693+51n\cdots(1)[/tex]A restaurant will cost $60 per person, in addition to $684 for the reservation.
[tex]\text{ Restaurant's Cost, R\lparen n\rparen}=684+60n\cdots(2)[/tex]We want to find the number of attendees(n) at which the venues cost the same amount.
Equate the cost equations (1) and (2) above:
[tex]693+51n=684+60n[/tex]Solve the equation for n:
[tex]\begin{gathered} \text{Subtract 51n from both sides of the equation.} \\ 693+51n-51n=684+60n-51n \\ 693=684+9n \\ \text{Subtract 684 from both s}\imaginaryI\text{des of the equat}\imaginaryI\text{on} \\ 693-684=684-684+9n \\ 9=9n \\ \text{ Divide both sides by 9} \\ \frac{9}{9}=\frac{9n}{9} \\ n=1 \end{gathered}[/tex]The number of attendees it would take for the cost to be the same amount is 1.
We determine the total cost using any of the equations:
[tex]\begin{gathered} \begin{equation*} 693+51n\cdots(1) \end{equation*} \\ Total\text{ Cost}=693+51(1)=\$744 \end{gathered}[/tex]The total cost will be $744.
I attached a picture with a practice problem from my prep guide, it has 5 questions that are included with the problem. You will find that below. I am having trouble doing this, and need help,Please note that this is complex and lengthy. 1. What is the balance of Albert’s $2000 after 10 years?2. What is the balance of Marie’s $2000 after 10 years??3. What is the balance of Han’s $2000 after 10 years??4. What is the balance of Max’s $2000 after 10 years?? Lastly, 5. Who is $10,000 richer at the end of this competition?
This is a question on present and
We are required to find out how much the future sums of the $2000 handed to them will amount to. This will test our knowledge on simple and compound interest.
Our approach is to take each one's case and analyse the appreciation or depreciation of the sums assigned using the appropriate formulae.
The compound interest formula goes thus:
[tex]F=P(1+\frac{i}{m})nm[/tex]Where:
F = future sum
P = Present sum / Principal
i = interest rate
n = no. of years
m = number of compounding periods in a year.
The simple interest rate formula goes thus:
[tex]F=Pi\text{n}[/tex]Albert:
Firstly, he had $1000 compounded monthly by 1.2%
[tex]\begin{gathered} F=1000(1+\frac{0.012}{12})^{10\times12} \\ F=\text{ \$1,127.43} \end{gathered}[/tex]He lost 2% of $500 over the course of the 10 years.
[tex]F=500(100\text{ \% - }2\text{ \%) = 500(0.98)= \$490}[/tex]Firstly, he had $500 compounded monthly by 0.8%
[tex]F=500(1+\frac{0.008}{1})^{10}=541.47[/tex]Total sum he gained over the course of the 10 years:
[tex]1127.43+490+541.47\text{ = \$2,158.90}[/tex]Marie:
Firstly, she had $1500 compounded quarterly by 1.4%
[tex]\begin{gathered} F=1500(1+\frac{0.014}{4})^{10\times4} \\ F=\text{ \$1,724}.99 \end{gathered}[/tex]She lost $500 by 4% over the course of the 10 years.
[tex]F=500(100\text{ \% + 4 \%) = 500(1.04)= \$}520[/tex]Total sum gained by Marie over the course of the 10 years:
[tex]\text{ \$1724.99 + \$520 = \$2,244.99}[/tex]Hans
He had $2000 compounded annually by 0.9%
[tex]\begin{gathered} F=2000(1+\frac{0.009}{1})^{10} \\ F=\text{ \$}2187.47 \end{gathered}[/tex]Total sum gained by Hans over the course of the 10 years:
[tex]\text{ \$2187.47}[/tex]Max:
$1000 decreased in value exponentially at a rate of 0.5% annually.
[tex]1000(1-\frac{0.005}{1})^{10}=\text{ \$951.11}[/tex]He had $1000 compounded biannually by 1.8%
[tex]\begin{gathered} F=1000(1+\frac{0.018}{2})^{10\times2} \\ F=\text{ \$}1196.25 \end{gathered}[/tex]Total sum gained by Max over the course of the 10 years:
[tex]\text{ \$9}51.11+\text{ \$1196.25=\$2,147.36}[/tex]
Determine a series of transformations that would map Figure F onto Figure G. 12 11 10 9 8 Figure G7 6 4 3 1 2 3 4 5 6 7 8 9 10 11 12 -12-11-10-9-8-7 -6 -5 -4 -3 -2 -1 -2 -3 -4 -6 N . Figure F -8
To find the series of transformations that would map Figure F onto Figure G
We will choose one side to figure out the transformations
So, Look at the vertical side of the figure F which has the end points (1 , -3) and (1 , -5)
The image of this side will be the horizontal side of figure G with the end points ( -3 , 1 ) and (-5,1)
so, we need to rotate it
So, the series of transformation will be :
Reflection
To find the rule of reflection
Note ( 1 , -3 ) → (-3 , 1)
this mean ( x , y ) → (y,x)
Which mean reflection over y = x
The same can obtained by translation 2 units up then rtation 90 clockwise
2a + 3b when a=2 and b=4
Answer:
16
Step-by-step explanation:
[tex]2a+3b \\ \\ =2(2)+3(4) \\ \\ =4+12 \\ \\ =16[/tex]
Answer:
Step-by-step explanation:
2a+3b when a=2 and b=4
2a 2*2 =4
3b 3*4=12
=12+4=16
=2a+3b= 16 :)
Mena is making a hamster house. She cuts a hole for a window that has side lengths of 5 inches and 3 inches. Which drawing plan shows the correct rectangular opening? On these graphs, each unit represents 1 inch. 10 B(1,8) C (48) A. 6 5 4 3 2 1 A (1,2) D (4.2) 1 2 3 4 5 6 7 8 9 10 F (7.8) 10 9 E (3.8) 8 7 B. N00 1 H (3,2) G (7.2) 1 2 3 4 5 6 7 8 9 10
We need a rectangle with one side 5 units long and another side 3 units long
The correct option is:
Can you help me with circumference and rotations?A Bicycle tire has a diameter of 62 cm, What is the distance the bicycle travels in 10 revolutions, round your answer to the nearest cm
Given:
[tex]\begin{gathered} D_{\text{iamteter of the tire}}=62cm \\ N_{\text{umber of revolution}}=10revolutions \end{gathered}[/tex]To Determine: The distance travelled
The distance travel in 1 revolution is the circumference of the tire.
The circumference of a circle is calculated by the formula below
[tex]\begin{gathered} C_{\text{ircumference of a circle }}=2\pi r \\ 2r=d \\ \text{Therefore} \\ C_{\text{ircumference of a circle }}=\pi d \end{gathered}[/tex]Substituting for diameter in the formula to get the distance travelled in 1 revolution as below
[tex]D_{is\tan ce\text{ travelled in 1 revolution}}=\pi\times62cm=62\pi cm[/tex]Therefore the distance in 10 revolution would be
[tex]\begin{gathered} D_{is\tan ce\text{ travelled in 10 revolutions}}=10\times62\pi cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}=620\pi cm=1947.787cm \\ D_{is\tan ce\text{ travelled in 10 revolutions}}\approx1948cm \end{gathered}[/tex]Hence, the distance travelled by the bicycle in 10 revolutions to the nearest cm is 1948cm
How long will it take for an investment to triple if interest is compounded continuously at 7%
Step-by-step explanation:
Question:
How long will it take an investment to triple, if the interest is
7
%
and compounded quarterly?
Future Value:
You have to find time that will it take an investment to triple. The amount is compounded quarterly so, n=4. Substitute all values into the formula,
A
(
t
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=
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1
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and simplify to get your desired result.
Answer and Explanation:
You have Given
A
=
3
P
n
=
4
t
=
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m
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r
=
0.07.
Substitute all values into the formula and you have
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(use intergrated format)
Chip Ahoy
The number of chocolate chips in an 18-ounce bag of
Chips Ahoy! chocolate chip cookies is approximately
normally distributed with a mean 1262 chips and a
standard deviation of 118 chips according to a study
by cadets of the U.S. Air Force Academy. (Why are
they studying chocolate chip cookies?}
What percent of bags has between 1026 and 1380 chocolate chips? Write your percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains fewer than 1144 chocolate chips? Write the percent without the percent sign.
What percentage of the 18-ounce bags of chips ahoy! Cookies contains more than 1498 chocolate chips? Write the percent without the percent sign.
Using the normal distribution, it is found that:
81.85% of bags has between 1026 and 1380 chocolate chips.15.87% of the bags contain fewer than 1144 chocolate chips.2.28% of bags contain more than 1498 chocolate chips.Normal Probability DistributionThe z-score of a measure X of a variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the fraction presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation of the number of chips are given as follows:
[tex]\mu = 1262, \sigma = 118[/tex]
The proportion of bags that has between 1026 and 1380 chocolate chips is the p-value of Z when X = 1380 subtracted by the p-value of Z when X = 1026, hence:
X = 1380:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1380 - 1262)/118
Z = 1
Z = 1 has a p-value of 0.8413.
X = 1026:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1026 - 1262)/118
Z = -2
Z = -2 has a p-value of 0.0228.
0.8413 - 0.0228 = 0.8185.
Hence the percentage is 81.85%.
The proportion that has fewer than 1144 chips is the p-value of Z when X = 1144, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1144 - 1262)/118
Z = -1
Z = -1 has a p-value of 0.1587.
Hence the percentage is of 15.87%.
The proportion that has more than 1498 chips is one subtracted by the p-value of Z when X = 1498, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (1498 - 1262)/118
Z = 2
Z = 2 has a p-value of 0.9772.
1 - 0.9772 = 0.0228
Hence the percentage is of 2.28%.
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If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get?
The factored form of function does not affect the trajectory of the graph.
Given that,
If we graph the terms of a factored form of a quadratic equation individually, what type of graphs do you get is to be discussed?
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
here,
The graph of a quadratic equation is a parabolic structure, when structuring the graph of the factor of the quadratic function it outcome same as the graph of the quadratic function itself.
Thus, the factored form of function does not affect the trajectory of the graph.
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A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words.
The random variable X is the ounces of water in the bottle.
What is a random variable?The mathematical formalization of a number or object that is subject to chance events is known as a random variable. It is a function or mapping between a sample space of potential outcomes to a measured space, frequently the real numbers.
A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. A random variable is a numerical representation of the result of an experiment in statistics. Discrete random variables are those that can only take on a finite number or an infinite series of values.
According to the provided information, it is known that a bottle of water contains 12.05 fluid ounces; hence it is clear that the random variable X will be the ounces of water.
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a grain silo has a cylindrical shape. its radius is 9ft, and height is 52ft. what is the volume of the silo?use the value of 3.14 for pieround to the nearest whole number
Given:
Radius = 9 ft
Height = 52 ft
Volume of cylindrical (silo) is:
[tex]\text{Volume}=\pi r^2h[/tex][tex]\begin{gathered} r=9 \\ h=52 \\ \pi=3.14 \end{gathered}[/tex][tex]\begin{gathered} \text{Volume}=\pi r^2h \\ =3.14\times(9)^2\times52 \\ =3.14\times81\times52 \\ =254.34\times52 \\ =13225.68 \end{gathered}[/tex]Nearst whole number is 13226
Nikhil sells digital cameras. He bought a DSLR camera for 24,000. He sold the camera for
€25,500.
What is Nikhil's profit per 100?
Answer:
He makes €100,000
Step-by-step explanation:
First, subtract 25,000- 24,000= 1000
Then, multiply 1000*100
€100,000 is how much he makes
PLEASE HELP!! pleaseAlthough she's only in middle school, Tameka loves to drive go-carts! Her favorite place to drive go-carts, Drivers Delight, has 3 circular tracks. Track 1 has a radius of 60 feet. Track 2 has a radius of 85 feet. Track 3 has a radius of 110 feet. A. Compute the circumference of Track 1. B. Compute the circumference of Track 2. C. Compute the circumference of Track 3.D. Driver's Delight is considering building a new track. They have a circular space with a diameter of 150ft. Compute the circumference of the circular space
A. Circumference of Track 1 = 2π r
= 2 x 3.14 x 60
=376.8 feet
B.Circumeference of track2 = 2π r
= 2 x 3.14 x 85
=533.8 feet
C.Circumference of track3 = 2π r
=2 x 3.14 x 110
=690.8 feet
D.Circumference of the circular space = 2π r
Diameter was given to be 150 ft
but radius(r) is half the diameter. Hence radius = 150ft/2 = 75 ft
Circumference of the circular space = 2x 3.14 x 75
=471 feet
The rabbit population in Logan County, which is currently at 6,516 rabbits, is increasing by 15% each year. How many rabbits will there be in 7 years?If necessary, round your answer to the nearest whole number.
Given data;
The current rabbit population in the Logan country = 6516.
the increse in the population each year = 15 %.
to find the population of rabbit after 7 years.
so, 15 % of 6516 is,
use the formula,
[tex]\begin{gathered} A=p_0(1+\frac{1}{n})^{nt}_{} \\ \end{gathered}[/tex][tex]\begin{gathered} p(t)=6516(1+\frac{0.15}{1})^t \\ p(t)=6516(1.15)^t \\ p(7)=6516(1.15)^7 \\ p\mleft(t\mright)=6516\mleft(2.66\mright) \\ =17332.68 \end{gathered}[/tex]there will be 17333 rabbits will there be in 7 years
Thus, the answer is 17333.
A twelve-foot ladder is leaning against a wall. If the ladder reaches 8 ft. high on the wall, what is the angle the ladder forms with the ground to the nearest degrees?
Solution
Recall: SOHCAHTOA
[tex]\begin{gathered} sin\theta=\frac{8}{12} \\ \\ \theta=sin^{-1}0.6667 \\ \theta=41.81^0 \\ \end{gathered}[/tex]The final answer
[tex]\theta=42^0[/tex]Graph the line with the equation y = 2x - 1.
A line is uniquely defined by two points.
Since the points (0, -1) and (1, 1) lie on the graph (since they satisfy the equation), you can draw the line through these points.
At an important meet, rosalba won the 200 meters in 26.39 seconds. Rosalba ran at an average rate of?
We have to find the average rate of meters per second (also known as average speed).
We can calculate it as the quotient between the distance and the time:
[tex]v=\frac{d}{t}=\frac{200\text{ m}}{26.39\text{ s}}\approx7.58\text{ m\textbackslash s}[/tex]Answer: the average rate is approximately 7.58 m/s.
I can only send this at first. I will send you a picture of the work problem with the choices for the blanks.
Concept
Area of the shaded part
= Area of the outer square - Area of the inner square
Next,
Area of the outer square = Length x Length = 5 x 5 = 25
Area of the inner sqaure = Length x Length = 2 x 2 = 4
Final answer
The area of the shaded part = 25 - 4
= 21 inches square
two 5 in by 1.5 in and two 2 in by 1.5 in
1.5
2 in and 5 in
The graph shows the earnings of two employees working at the same company both earn money at constant rates please help me figure out which table the unit rate that matches each graph thank you so much
On the first graph, when x moves 1 unit, that is, from x = 2 to x = 3, the change in y is
[tex]\begin{gathered} \Delta y=y_2-y_1 \\ =87-58 \\ =29 \end{gathered}[/tex]Unit rate of the first graph is $29 per hour.
On the second graph, when x moves 1 unit, that is, from x = 0 to x = 1, the change in y is
[tex]\begin{gathered} \Delta y=y_2-y_1 \\ =22-0 \\ =22 \end{gathered}[/tex]Unit rate of the second graph is $22 per hour.
Can someone help me with this geometry question? I am pretty sure it’s 67
Solution
Step 1:
The angle at the center is twice the angle at the circumference.
Step 2:
[tex]\begin{gathered} m\angle PMN\text{ = 134} \\ m\angle PON\text{ = ?} \\ m\angle PMN\text{ = 2m}\angle PON \\ 134\text{ = 2m}\angle PON \\ m\angle PON\text{ = }\frac{134}{2} \\ m\angle PON\text{ = 67} \end{gathered}[/tex]Answer
m
Hans paid $37.51 Employment Insurance (El) on his monthly income of $2168.21.
What was the El rate?
The EI rate is 17.3%
How to calculate the EI rate ?The first step is to write out the parameters given in the question
Hans employment insurance is $37.51
Hans monthly income is $2168.21
The EI rate can calculated as follows
37.51/2168.21 × 100
= 0.0173 × 100
= 17.3%
Hence the EI rate is 17.3 %
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which is the best estimate of the amount of interest you will save if if you take the 5% of loan instead of the 6% loan?
For the 5% loan, you will pay a total of:
[tex]219\cdot25=5475[/tex]For the 6% loan, you will pay a total of:
[tex]221\cdot25=5525[/tex]if if you take the 5% of loan instead of the 6% loan you will save:
[tex]5525-5475=50[/tex]Answer:
$50
For her phone service, Ashley pays a monthly fee of $19, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is$72.15.What are the possible numbers of minutes she has used her phone in a month?Use m for the number of minutes, and solve your inequality for m.
Given:
Ashley pays a monthly fee of $19, and she pays an additional $0.05 per minute of use. The least she has been charged in a month is $72.15.
Required:
Find the possible numbers of minutes she has used her phone in a month.
Use m for the number of minutes, and solve your inequality for m.
Explanation:
The initial amount paid by Ashley = $19
The additional amount per minute = $0.05
Let the number of minutes used in the phone = m
The least amount that is charged in a month = $72.15
Now by using the given information
[tex]19+0.05m\ge72.15[/tex]Solve for m as:
[tex]\begin{gathered} 0.05m\ge72.15-19 \\ 0.05m\ge53.15 \\ m\ge\frac{53.15}{0.05} \\ m\ge1063 \end{gathered}[/tex]Thus at least 1063 minutes were used on Ashley's phone in a month.
Final Answer:
The least possible minutes are 1063.
two sets of 5 different numbers that have the same standard deviation but different mean
The sets of 5 different numbers with same standard deviation but different mean are {2,4,6,8,10} and {20,22,24,26,28}.
The standard deviation is a statistic that describes the degree of volatility or dispersion in a set of numerical values.
Values having a low standard deviation are more likely to be within a narrow range of the mean (also known as the anticipated value) of the collection than values with a high standard deviation.The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is equal to the square root of that variable's variance. It is more algebraically straightforward than the average absolute deviation, but being less reliable in practice. The standard deviation is a useful statistic because, unlike the variance, it is expressed in the same unit as the data.Let us consider two data sets :{2,4,6,8,10} and {20,22,24,26,28}
Now for the first set:{2,4,6,8,10}
Mean = (2+4+6+8+10)÷5 = 30÷5 = 6
Standard deviation = 3.16
Now for the second set:{20,22,24,26,28}
Mean = (22+24+26+28+20)÷5 = 120÷5 = 24
Standard deviation = 3.16
Therefore these two data sets have same standard deviation but different mean.
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help meeeeeeeeeeeeeeeeeeeeeee
thank you
The function notation f(-5) has a value of -6
How to solve the function?From the question, we have the function definition to be f(-5)
Also, we have the graphs to be f(x) and g(x)
The equation of the first graph is illustrated by the blue curve f(x), while the second is illustrated by the red curve
Because the function is f(x), we make use the blue curve
On the blue curve, we have
f(-5) = -6
The interpretation of the above equation is that
When x = -5, the blue curve has a value of -6
This means that the function f(-5) has a value of -6
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4. What is the discount and special sale price of a pair of shoes regularly priced $120 when the store has a 33% off sale /(round to the nearest dollar)? 5.a retailer purchase a $3 toy in as a markup rate of 150%. determine the markup and the regular retail price of the toy. 6. Jody received a 30% Commission on the profit when he sells over 20 cars in a month . if he sold 23 cars in October, resulting in $15000 profit for the dealership , how much did Joe earn in commission ?7.how much would be in an account when you turn 18 if, on the day you were born, 1000 were disposed into the account which returned 6% simple interest, and no longer disposes or withdrawals were made ?
Let's begin by identifying key information given to us:
Shoe Price = $120
Discount rate = 33% = 0.33
The Discount price of the shoe is calculated below:
[tex]\begin{gathered} DiscountPrice=ShoePrice-(ShoePrice\cdot DiscountRate) \\ DiscountPrice=120-\lbrack120\cdot(0.33)\rbrack=120-39.6 \\ DiscountPrice=80.40 \end{gathered}[/tex]Therefore, the discount price is $80.40
Please help me graph and answer this question
The graph of the inequality is attached below
Graph of InequalityTo solve this problem, we need to solve the inequality and then plot the graph on a number line.
What is Inequality?
inequality, In mathematics, is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions
Applying absolute rule;
[tex]-4\leq x-2\leq 4\\x - 3\geq -4 and x - 2 \leq 4\\x - 2 \leq 4; \\x \leq 6\\x \geq -2[/tex]
Combining the overlapping intervals;
[tex]-2\leq x\leq 6[/tex]
Kindly find the attached image as the graph on a number line below.
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write the following equation in a function form.3x+4y=0
You have the following equation:
[tex]3x+4y=0[/tex]To write the previous equation in a function form consists in solving for y, just as follow:
3x + 4y = 0 subtract 3x both sides
4y = -3x divide by 4 both sides
y = -3/4 x
Hence, the function for of the given equation is:
y = -3/4 x
PLS HELP FAST!! Question due in 5 minutes!!!
Answer:
hypotenuse 3 leg 1 =1 leg2=
if i walked to my parents house for Thanksgiving and lived 25.6 miles away, and it took me 4 hrs to get there is it true tht my constant speed would be 4.6 mph?
Distance walked over time
25.6 miles away, are going to walk
lets find if
25.6/ 4 = 4.6?
Then 25.6 = 24 + 1.6 =
so. 25.6/4= 24/4 + 1.6/4 = 6 + 0.4 = 6.4
So its NOT TRUE that constant speed is 4.6 mph
