Given data:
The given graph of the function.
In the given graph the dependent variable is the amount in saving.
Thus, the correct option is (C).
Give an equation for the graph of y=f(x) if we apply these transformations translate up 2 units vertical dilation by a factor of 3 translate right 2 units
SOLUTION:
Case: Equation of a graph
Method:
Let the equation be:
[tex]y=x^2[/tex]Transformation 1:
Translate 2 units up
[tex]y=x^2+2[/tex]Transformation 2:
Vertical dilation by a factor of 3
[tex]y=\frac{1}{3}x^2+2[/tex]Transformation 3:
[tex]y=\frac{1}{3}(x-2)^2+2[/tex]Final answer:
[tex]y=\frac{1}{3}(x-2)^2+2[/tex]In 1990, approximately 1,820,000 violent crimes were reported in the U.S. By 2019, this number had fallen to approximately 1,200,000.(a) Write a linear model to describe the number of violent crimes in the U.S. from 1990 onward.Pt =(b) Using this linear model, predict the number of violent crimes in 2032. Round your answer to the nearest whole number.violent crimes(c) When do you expect the number of violent crimes to reach 800,000? Give your answer as a calendar year (ex: 2020).During the year
Data:
• A,( 0, 1,820,000)
,• B,( 29, 1,200,000)
,• Year 2 - year 1 = 2019 - 1990 = 29
a)
Based on the point A and B, the linear model is as follows:
• Slope ( ,m ,)
[tex]m=\frac{1,200,000-1,820,000}{29\text{ -}0}=-\frac{620,000}{29}[/tex]• Parameter b
[tex]\begin{gathered} P(t)=mt+b \\ 1,200,000=-\frac{620,000}{29}\cdot29+b \\ 1,200,000=-620,000+b \\ b=1,200,000+620,000=1,820,000 \end{gathered}[/tex]Answer a) (linear model):
[tex]P(t)=-\frac{620,000}{29}t+1,820,000[/tex]b)
2032-1990 = 42
[tex]\begin{gathered} P(42)=-\frac{620,000}{29}\cdot42+1,820,000 \\ P(42)=922068.97 \end{gathered}[/tex]Answer of the number of violent crimes in 2032:
[tex]P(42)=922068.97[/tex]c)
[tex]\begin{gathered} 800,000=-\frac{620,000}{29}\cdot t+1,820,000 \\ 800,000-1,820,000=-\frac{620,000}{29}\cdot t \\ -1,020,000=-\frac{620,000}{29}\cdot t \\ t=\frac{-1,020,000}{-\frac{620,000}{29}}=47.71 \\ 1990+47.71=2037.71 \end{gathered}[/tex]Answer of c: 2037
At a basketball game, 21% we're supporting the visiting team. If total number of people attending the game was 1300, how many people were supporters of the home team?
The total number of people=1300
To find the number of people x, supporting the home team
[tex]\begin{gathered} x=1300-\frac{21}{100}1300 \\ x=1300-273 \\ x=1027 \end{gathered}[/tex]Hence the number of people supporting the home team is 1027
18 pt to quarts ? qt
This is a conversion problem
we need to convert 18 Pints to Quarts
since 1 pt = 0.5 qt , then:
[tex]18\cdot0.5=9[/tex]In summary
18 pt = 9 qt
The following table represents a good frequency distribution of the number of hours spent in class per week of. What is the class Widlth
The class width is the difference between the lower limits of any two consecutive classes. For context, the lower limit is the smallest value of a class, and the lower limit is the highest value of the class. All classes should have the same width.
In this case, we can consider the hour intervals as the classes, so if we focus on the 3.0 to 6.4 hours interval and on the 6.5 to 9.9 interval, we can determine the class width:
[tex]w=6.5-3=3.5.[/tex]If we do the same thing with any two consecutive classes, we'll see that the width is also 3.5 (10.0-6.5=3.5, for example).
In conclusion, the class width is 3.5.
Tell whether the table represents an exponential function. If so write a rule for the function X -1 0 1 2 3 Y 1 4 7 10 13
Ok, so
We got the next table:
First of all we're going to check if this represents an exponential function.
The table seems to be a linear function. It's not exponential. That's because if you see, the way that the values are changing is at a constant rate.
In x, we got one to one, and in y, three to three between each value.
7. The boxplot represents concert tickets sold on random days for a local venue. Identify the firstand third quartiles.245297323369388
The Solution:
Given the boxplot below:
Thus:
The first quartile = 297
The third quartile = 369
Therefore, the correct answer is [option 4]
- A desk is shaped like a rectangle.If the length is 2.6 feet, and thewidth is 1.3 feet, what is theperimeter of the desk?
Given:
A desk is shaped like a rectangle.
The length is l =2.6 feet,
The width is w = 1.3 feet.
Required:
We need to find the perimeter of the desk.
Explanation:
Consider the perimeter of the rectangle formula.
[tex]P=2(l+w)[/tex]Substitute l=2.6 and w =1.3 in the formula.
[tex]P=2(2.6+1.3)[/tex][tex]P=2(3.9)[/tex][tex]P=7.8\text{ feet.}[/tex]Final answer:
The perimeter of the desk is 7.8 feet,
Calculate the relative frequency of the second class determine the answer as a simplified fraction
Given: 1105,1180,1056,1102,1295,1313,1146,1248,1133,1059,1352,1317,1111,1025,1125,1270,1362,1103,1357,1062,1331
Find: relative frequency of second class.
Explanation: the second class varies from 1072-1131
1105,1102,1111,1125,1103. are the numbers lies from 1072-1131
these are 5 number so their frequency is 5.
and total numbers are 21 . so the relative frequency is
[tex]\frac{5}{21}=0.23[/tex]Final answer: the relative frequency of second class is 0.23
Create a third equation that could be added to the system so that this solution does not change the graph line on the coordinate plane above (PART C)
Given that the solution of the initial system of equations is (1,4), we need to find a third line such that it goes through (1,4); then,
[tex]\begin{gathered} y=ax+b \\ and \\ (1,4) \\ \Rightarrow4=a+b \end{gathered}[/tex]We can set any value for a; for example, a=1; thus,
[tex]\begin{gathered} a=1 \\ \Rightarrow4=1+b \\ \Rightarrow b=3 \end{gathered}[/tex]Therefore, one possible third line is
[tex]y=x+3[/tex]The green line is the one you need to graph, the others have already been plotted.
Identify each line or segment that intersects the given circle. Identify all thatapply to each name.TRVMmNwUse CAPITAL letters or your answer will be marked as wrong! Lines can berepresented as a NON-Capital letter.ONE Radius:Diameter:ONE Chord:Secant: line
The Solution.
The correct answers are:
One Radius = MT or MW
One Diameter = TW
One Chord = RV
Secant: Line = Line RV
Tangent: Line = Line m
1/3(3x-9)+2x=1/2(4x+ 8)????
1) Let's solve this expression 1/3(3x-9)+2x=1/2(4x+ 8)
2) Distribute the factor 1/3 and 1/2
[tex]undefined[/tex]True or False.To graph the line y = -4/5 x + 6, you would plot the y-intercept of 6 on they-axis and then move 4 units down and 5 units right from the y-interceptto plot the second point.
Given the instructions on the problem, we have the following:
which is the graph of the equation y = -4/5 x+ 6. Also, we have that the second point is (5,2)
Find x. Give your answer inthe simplest form.450 у845X = [?]ХEnter the number that belongs inthe green box
As you can see in the picture, the triangle is a Right triangle, because it has an angle that measures 90 degrees (also known as "Right angle").
Then, you can use the following Trigonometric function:
[tex]\tan \alpha=\frac{opposite}{adjacent}[/tex]In this case:
[tex]undefined[/tex]What are the terms in the expression,3 + 5 + 7b – 18a?
Given: An expression-
[tex]3+5+7b-18a[/tex]Required: To determine the terms in the expression.
Explanation: The terms in an expression are the variables, constants, or combination of variables and constants separated by a + or - operator.
Hence, the terms in the expression are-
[tex]3,5,7b,-18a[/tex]Final Answer: The terms are: 3, 5, 7b, and -18a.
13 Determine if the number is rational (R) or irrational (I)
13)
Answer:
Explanation:
A rational number can be written in the form of quotient of two integers
67.7148 1 cannot be written as a quotient f two integers. Thus, it is irrational
A company manufactures and sells shirts. The daily profit the company makes depends on how many shirts they sell. The profit, in dollars, when the company sells x shirts can be found using the function. f(x)=7x−80. Find and interpret the given function values and determine an appropriate domain for the function.
question below
interpretation answer key:
- makes sense
-does NOT make sense
Answer:
Step-by-step explanation:
i need help on this assignment an i was wondering if you can help me - number 2
Explanation:
Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
From the question, we can see that X, W, and Z do not lie on the same line. Therefore
Answer: False
3. If mAD = 85° and mBC = 31°, find the value of x.
Given that both secants are equal, we can deduct that arcs AB and DC are equal.
We know that the whole circumference is 360°.
[tex]\begin{gathered} 85+13x-21+31+13x-21=360 \\ 26x=360-74 \\ 26x=286 \\ x=\frac{286}{26} \\ x=11 \end{gathered}[/tex]Hence, x is equal to 11.
xP(x)00.210.320.230.3Find the mean of this probability distribution. Round your answer to one decimal place.
Explanation:
Concept:
The mean of a probability distribution is calculated using the fomrula below
[tex]\mu=\sum_^xP(x)[/tex]By substituting the values, we will have
[tex]\begin{gathered} \mu=\sum_^xP(x) \\ \mu=(0\times0.2)+(1\times0.3)+(2\times0.2)+(3\times0.3) \\ \mu=0+0.3+0.4+0.9 \\ \mu=1.6 \end{gathered}[/tex]Hence,
The final answer is
[tex]1.6[/tex]
In a recent poll 590 people were asked if they liked dogs, and 66% said they did. Find the margin of error of this poll at the 90% confidence level. Give your answer to three decimals
SOLUTION
We will use the formula
[tex]\begin{gathered} p\pm_Z\sqrt{\frac{p(1-p)}{n}} \\ where\text{ p = 66\% = 0.66} \\ n=590 \\ Z_{90\%}=1.645 \end{gathered}[/tex]Plugging in we have
[tex]\begin{gathered} 0.66\pm_1.645\sqrt{\frac{0.66(1-0.66)}{590}} \\ 0.66\pm\sqrt{\frac{0.66\times0.34}{590}} \\ 0.66\pm0.0195022 \\ 0.67950,0.6404978 \end{gathered}[/tex]Hence the answer is
(0.640, 0.680)
Simplify the following expression:-9(3n+7) +10(n+3)
We want to simplify the expression:
[tex]-9(3n+7)+10(n+3)[/tex]First of all, w
find the surface area of a cone with slant height 10 cm and diameter 12 cm to the nearest hundredth
Given:
Slant height = 10 cm
Diameter = 12 cm
Let's find the surface area of the cone.
To find the surface area of the cone, apply the formula:
[tex]A=\pi rl+\pi r^2[/tex]Where:
L is the slant height = 10 cm
r is the radius = diameter/2 = 12/2 = 6 cm
Plug in the values into the formula and solve for surface area A:
[tex]\begin{gathered} A=(\pi *6*10)+(\pi *6^2) \\ \\ A=188.496+113.097 \\ \\ A=301.59\text{ cm}^2 \end{gathered}[/tex]Therefore, the surface area of the cone to the nearest hundredth is 301.59 cm².
ANSWER:
301.59 cm²
The time it takes duck eggs to hatch in a nursery is normally distributed with a meanof 42 days and a standard deviation of 3.8 days. What is the probability that arandomly selected duck egg takes between 34 and 43 days to hatch?
The time it takes duck eggs to hatch in a nursery is normally distributed with a mean
of 42 days and a standard deviation of 3.8 days. What is the probability that a
randomly selected duck egg takes between 34 and 43 days to hatch?
step 1
Find the z-scores
For x=34
z=(34-42)/3.8
z=--2.105
For x=43
z=(43-42)/3.8
z=0.263
step 2
using Standard Normal Distribution Table
we have
For z=-2.105 --------> P=0.4842
For z=0.263 -------> P=0.1026
therefore
the probability is
P=0.4842+0.1026=0.5868solve for x5x+7=9x-63
Given
[tex]5x+7=9x-63[/tex]To solve, we will collect
29 23/200 as a decimal
To transform 29 23/200 as a decimal, you have to divide 23 by 200
Then, 23/200 = 0.115 and 29 23/200 = 29.115
Question ID: 1190607The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.A triangle, A ABC, has angle measures of 82, 75, and 23* and no sides equal (congruent) in length. How wouldthis triangle be classified?
Given,
The measure of angles of triangle ABC is 82 degree, 75 degree, and 23 degree.
The side of triangle are not congruent.
As, the sides and angles of the triangle are not equal.
Hence, the triangle is scalene acute triangle.
A scarf that was originally $12 is now $15.Find the percent markup.
Markup is the difference between the scarf's selling price and it's original cost.
The scarf was originally $12, let
S1 = 12
The cost is $15, let
S2 = 15
Markup, M = S2 - S1
= 15 - 12
= 3
$3$
Markup Percent is now:
Markup divide by original cost, times one hundred
That is;
3/12 * 100
= 100/4
= 25 percent
For #1 - 4, use the given diagrams and what you have learned about similar polygons. Hint: use the radius of the circles.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
diagram
Step 02:
scale factor:
We must analyze the polygons to find the solution.
1. Circle A ===> Circle B
Circle A:
ra = 5
Circle B:
rb = 3
scale factor (k):
ra * k = rb
5 * k = 3
k = 3 / 5
k = 0.6
The answer is:
scale factor of dilation = 0.6
20Complete the proof.BFGiven: BAI ACDC I ACProve: ABFA ACFDStatementsReasons1. Given1. Given: BA I ACDC I AC2. BA|| DC2. If two lines are perpendicular to a third line,then the two lines are parallel.3. r11I-3. If two parallel lines are cut by a transversal,alternate interior angles are congruent.1- 4= nܘܢܩܫܙܩܬ .414. ABFA-ACED1:: ZDFC ~ ZBFA; ZDAB ~ ZBCD:: ZCBA ZADC; ZBAD ZDCB:: Angle-Angle (AA) postulate:: Side-Angle-Side (SAS) postulate):: ZCDA ~ ZBAD; ZCBA ~ ZBCD
3.- If two parallel lines are cut by a transversal, alternate interior angles are congruent. Therefore:
[tex]\measuredangle CBA\cong\measuredangle ADC;\text{ }\measuredangle BAD\cong\measuredangle\text{DCB}[/tex]4.-Angle-Angle Postulate states that two triangles are similar if they have two congruent angles.