x = number of 2 bedrooms units
y= number of 3 bedroom units
194 condominiums
x+y = 194 (a)
the total number of rooms in the entire complex is 494
2x + 3y = 494 (b)
We have the system of equations:
x+y = 194 (a)
2x + 3y = 494 (b)
Solve (a) for x
x = 194-y
Replace x on (b) and solve for y
2 (194-y ) + 3 y = 494
388 - 2y +3 y = 494
-2y+3y = 494-388
y= 106
Replace y on (a) and solve for x
x + 106 = 194
x = 194-106
x= 88
2-bedroom units = 88
3- bedrooms units = 106
Which of the following graphs represent the system of equations f(x) = x2 + 2x + 2 and g(x) = –x2 + 2x + 4?
The Solution:
Given:
[tex]\begin{gathered} f(x)=x^2+2x+2 \\ \\ g(x)=-x^2+2x+4 \end{gathered}[/tex]We are required to determine the graphs of the given functions.
Below is the graph of the function:
Thus, the correct answer is:
Evaluate the logarithmLog 6 1/36
Answer:
-2
Explanation:
By properties of logarithms, the logarithm of a fraction is equal to the difference of logarithms, so
[tex]\log _6(\frac{1}{36})=\log _61-\log _636[/tex]Now, log₆(1) = 0 and log₆36 = 2, so
[tex]\begin{gathered} \log _6(\frac{1}{36})=0-2 \\ \log _6(\frac{1}{36})=-2 \end{gathered}[/tex]Therefore, the answer is -2
The Oldest rocks on Earth are about 4 x 10^9 years old. For which of these ages could this be an approximation?
A. 3,862,100,000 years
B. 3.849999999x10^9 years
C. 0.000000004 years
D.4,149,000,000 years
E.3.45x10^9 years
4149000000 is the approximation age of oldest rock. The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest."
What is approximation age?The precise amount is not known with certainty. Similar to proximity or approximately, the word "approximation" is derived from the Latin Proximus, which meaning "nearest." The closest estimate you can make without knowing something's exact size or measurement is called an approximation.
Despite the fact that approximation is most usually used in relation to numbers, it is also regularly used in relation to mathematical functions, forms, and physical laws. In science, the term "approximation" can refer to using a less complex method or model when the proper one is challenging to use.
For this, sampling techniques like Markov chain Monte Carlo and significance sampling as well as variationally methods like mean-field approximations and assumed density filtering have been used.
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Josh wants to use Rockaway Hall, the Groove Guru Band, and PJ's Party Supplies. Josh has a total of
650 dollars and wants to invite 25 people. His friend told him he would be able to afford the band for 4 hours. Is that true?
1) Assume that x is the number of hours and that y is the total cost. To model, write an equation. 2) Tutoring his friend in geometry is the second way he can get money.
One of the first areas of mathematics is geometry, along with arithmetic.
What is the Bernoulli inequality?A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used. It contains a few helpful variations, including those for any integer r 0 and real number x > 1. If x 0 and r 2, the inequality is strictly true.A statement about raising a number to a natural power is made by the binomial inequality: and. It can be easily demonstrated by induction and is essentially a condensed version of the binomial theorem.A mathematical inequality that closely resembles the exponentiations of 1 + x is known as Bernoulli's inequality, named after Jacob Bernoulli. In actual analysis, it is frequently used.To learn more about Bernoulli inequality refer to:
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The ordered pairs represent a function. (0,-1), (1,0), (2,3), (3,8) and (4,15). Answer the questions in the picture.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
ordered pairs:
(0,-1), (1,0), (2,3), (3,8) and (4,15)
Step 02:
functions:
graph:
The function is nonlinear
x ==> increases by 1
y ==> increases by 2
y = x² - 1E-14x - 1
That is the full solution.
A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29
which is the solution of 3(t + 1) = 6 - 13.5?A <-5.5B t2-5.5Ci< 5.5D (>55
Let's begin by identifying key information given to us:
[tex]\begin{gathered} 3\mleft(t+1\mright)\le6t-13.5 \\ 3t+3\le6t-13.5 \\ \text{Put like terms together, we have:} \\ 3+13.5\le6t-3t \\ 16.5\le3t \\ \frac{16.5}{3}\le\frac{3t}{3} \\ 5.5\le t\Rightarrow t\ge5.5 \\ \therefore t\ge5.5 \end{gathered}[/tex]Therefore, D is the correct answer
2/___=4/18What is the answer to the problem
Explanation:
These are equivalent fractions, we have to find the missing denominator from the fraction on the left. Since the numerator of the fraction on the right is 4 and the numerator of the fraction on the left is 2, we can see that we have to divide by 2. Therefore 18 divided by 2 is 9. This is the numerat
Answer:
a machine can stamp 36 bottle caps in 10 seconds copy and complete the table. At this rate, how many bottle caps can the machine stamp in 5 minutes? At this rate, how many minutes will it take to stamp 24,408 bottle caps?
SOLUTION
1. From the question the machine stamps 36 caps in 10 seconds
In 5 minutes it will cap
[tex]\begin{gathered} 5\text{ minutes = 5 }\times\text{ 60 seconds } \\ =300\text{ seconds } \\ 36\text{ }\rightarrow\text{caps in 10 seconds } \\ x\text{ }\rightarrow\text{caps in 300 seconds } \\ \text{cross multiplying we have } \\ 36\times300=10\times x \\ 10800=10x \\ x=\frac{10800}{10} \\ x=1080 \end{gathered}[/tex]So in 5 minutes, it would stamp 1080 bottle caps
2. Minutes it would take to stamp 24,408 bottle caps?
[tex]\begin{gathered} 1080\text{ }\rightarrow\text{caps in 5 minutes } \\ 24,408\rightarrow caps\text{ in }x\text{ minutes } \\ \text{cross multiplying we have } \\ 1080\times x=24,408\times5 \\ 1080x=122040 \\ x=\frac{122040}{1080} \\ x=113\text{ minutes } \end{gathered}[/tex]Hence it would take 113 minutes to stamp 24,408 bottle caps
Use the distributive property and simplify: 3n+4-5(n+6)
By distributing the number -5 into the parentheses, we have
[tex]3n+4-5n-30[/tex]Now, by collecting similar terms, we get
[tex]-2n-26[/tex]Therefore, the answer is: -2n-26
Identify all points and line segments in the picture below.Points: A, B, C, DLine segments: AB, BC, CD, AD, BD, ACPoints: A, B, C, DLine segments: AD, AC, DC, BOPoints: A, B, C, DLine segments: AB, AD, AC, DC, BCPoints: A, BLine segments: AB, AC, DC, BC
Option C
Points: A, B, C, D
Line segments: AB, AD, AC, DC, BC
In a test of the effectiveness of garlic for lowering cholesterol, 48 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes (before−after) in their levels of LDL cholesterol (in mg/dL) have a mean of 5.3 and a standard deviation of 19.6. Construct a 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
1) The 95% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment is 5.3 ± 5.6.
2) Regarding the effectiveness of garlic in reducing LDL cholesterol, the confidence interval suggests A. The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
What is the confidence interval estimate?The confidence interval estimate shows us the mean estimate plus or minus the margin of error (or variation in the estimate).
On the other hand, the margin of error is the difference between the actual and projected results in a random sample.
The number of subjects treated with garlic, n = 48
The mean changes in LDL cholesterol level = 5.3
The standard deviation = 19.6
The 95% confidence interval gives a Z-score of 1.96
The margin of error = Z-score x standard deviation/√n
= 1.96 x 19.6/√48
= 1.96 x 19.6/6.9
= 1.96 x 2.84
= 5.6
Lower Limit = Mean - Margin of Error
= 5.3 - 5.6
= -0.3
Upper Limit = Mean + Margin of Error
= 5.3 + 5.6
= 10.9
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Question Completion with Answer Options:2. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
A.The confidence interval limits contain 0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
B.The confidence interval limits do not contain0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
C.The confidence interval limits do not contain0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
D.The confidence interval limits contain 0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
HELP PLEASEEEEE!!!!!!
The two rational number D and point R are found as 2/7 and 4/7 respectively.
What is meant by the term rational number?Rational numbers are those that can be specified in the type p/q, for which p and q are integers and q≠0 is a negative number. The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the denominator and numerator of a fraction were all numbers (denominator q≠0), whereas the denominator and the numerator of rational numbers are integers.For the given question.
The number line is given with the rational number D and R to be plotted.
There are 7 units between the points 4 and 5.
D point is 2 units right of 4.
Thus, D = 2/7
R point is 4 units right of point 4.
Thus, R = 4/7
Thus, the two rational number D and R are found as 2/7 and 4/7 respectively.
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used to name a point
Answer:
It is represented by a dot and named by a capital letter
Step-by-step explanation:
Hello! I need a little bit of help with this question please. (This information is not from an open test, it is a book as I'm studying for the ASVAB I am going to take later on.)
Given:
[tex]\sqrt{100}-\sqrt{64}[/tex]To find:
We need to solve this sum and find the final answer
Step-by-step solution:
To solve this problem, we need to know the square root of 100 and 64.
√100 = 10
√64 = 8
[tex]\begin{gathered} =\sqrt{100}-\sqrt{64} \\ \\ =10\text{ - 8} \\ \\ =2 \end{gathered}[/tex]Final answer:
Thus 2 (Option A) is the correct answer.
Find the length of AC
The rule of the length of an arc is
[tex]L=\frac{x}{360}\times2\pi\text{ r}[/tex]Where L is the length of the arc
x is the central angle subtended by the arc
r is the radius of the circle
∵ BC = r
∵ BC = 16 ft
∴ r = 16
∵ < ABC is a central angle subtended by the arc AC
∴ ∵ < ABC = 51 degrees
∴ x = 51
→ Substitute the values of x and r in the rule above to find The length of arc AC
[tex]\begin{gathered} AC=\frac{51}{360}\times2\times3.14\times16 \\ AC=14.23466667 \end{gathered}[/tex]→ Round it to 2 decimal places
∴ AC arc = 14.23 ft
Karen wants to buy a new car but needs money for the down payment. Her parents agree to lend her money at an annual rate of 4%, charged as simpleInterest. They lend her $8000 for 6 years. She makes no payments except the one at the end of that time.Answer the following questions. If necessary, refer to the list of financial formulas.х5?(a) How much total interest will Karen have to pay?s0(b) What will the total repayment amount be (including Interest)?s[]
Answer:
a) $1,920
b) $9,920
Explanation:
Step 1. Gather all of the information.
The amount borrowed will be the principal or starting amount P:
[tex]P=8,000[/tex]The interest rate will be r:
[tex]r=4\text{ percent}[/tex]We will need the interest rate in decimal form, for that, divide the percentage amount by 100:
[tex]\begin{gathered} r=\frac{4}{100} \\ \downarrow \\ r=0.04 \end{gathered}[/tex]And the time of the loan is 6 years, this will be the value of t:
[tex]t=6[/tex]Step 2. To solve part a, we use the following formula to calculate the interest:
[tex]I=p\times r\times t[/tex]Substituting all of the known values:
[tex]I=8,000\times0.04\times6[/tex]The result is:
[tex]I=1,920[/tex]The total interest that Karen will have to pay is $1,920.
Step 3. To solve part b, we need to find the total repayment amount.
To find this, we add the interest and the principal amount:
[tex]T=P+I[/tex]Where T represents the total amount.
Substituting P and I:
[tex]\begin{gathered} T=8,000+1,920 \\ \downarrow \\ T=9,920 \end{gathered}[/tex]The total amount she will have to repay is $9,920.
Answer:
a) $1,920
b) $9,920
drag the location of each ordered pair after a reflection over the x axis stated. then, drag the correct algebraic representation of the reflection to the white box. answer choices: (y, x), (-2,-6),(x,-y),(-3,-2),(5,8),(-5,-8),(-x, y),(-6,-6),(-6,-1),(2,-6),(6,-1),(3,2),(-x, -y),(-7,-2),(6,-6),(7,2)
Reflection over the x-axis transform the point (x, y) into (x, -y)
Applying this rule to the vertex of the triangle ABC, we get:
A(-6, 6) → A'(-6, -6)
B(-2, 6) → B'(-2, -6)
C(-6, 1) → C'(-6, -1)
Algebraic representation: (x, -y)
kmarks Solve the following system of equations graphically on the set of axes below 1 y 22 - 4 y = -X – 7 Plot two lines by clicking the graph. Click a line to delete il. y 10 9 8 7 6 5 4 3 2. 1 5 6 7 8 9 10
Explanation:
For the first line :
1. Draw a line which has a slope of 1 /2
2. Adjust the line so that it has a y-intercept of -4.
For the second line:
1. Draw a line which has a slope of -1
2. Adjust this line so that it has a y-intercept of -7.
Finally, find the point where the two lines intersect.
The coordinates of the point of intersection are the solution to our system.
To get a line which has a slope 1/2, you start from (0, -4 ) and then move 2 units to the right and then 1 unit up.
Solve the inequalities|4x + 5| + 2 > 10
We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
write the function below in slope. Show ALL the steps and type the answer.
This is a simple question to solve. First, let's take a look at a slope-intercept form equation as follows:
Once we know how a slope-intercept form looks like all we need to do is to simplify our equation to find that as follows:
And that is our slope-intercept form:
Based on the diagram below, which statement is true? b a C 110° 115° d 60° e 120° Oь || с Oa || ь alle Odlle
we have that
Verify each statement
1) b parallel to c
If b is parallel to c then
115+60=180
175=180 ----> is not true
2) a parallel to b
If a is parallel to b
then
110+60=180
170=180 -----> is not true
3) a parallel to c
If a is parallel to c
then
110=115 -----> is not true
4) d parallel to e
If d is parallel to e
then
60+120=180
180=180 -----> is true
therefore
the answer is
d parallel to ePart 2
In this problem
If n and m are parallel
then
the interior angles of the triangle are
30, 80 and x degrees
so
30+80+x=180
110+x=180
x=180-110
x=70 degreesAt the end of 2008, the number of text messages sent one month was
110.4 billion. If 270.3 million people used text messaging, about how
many did each person send that month? Round to the nearest whole
number.
The average number of text messages sent during the month by each person was 408.
What is the average?The average is the total number of a data set divided by the number of items on the data set.
The average is the same as the mean, which is a central value of a data set.
The total number of text messages sent in a month in 2008 = 110.4 billion
(110,400,000,000)
The total number of people using text messaging = 270.3 million (270,300,000)
Average text messages per person = 408. 44 (110,400,000,000/270,300,000)
Thus, we can conclude that, on average, each person in the population texted 408 messages per month in 2008.
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I need help solving this and figuring out the plotting points.
SOLUTION
It is gien that the monthly salary is $2200
It is given that Keren receives additional $80 for every copy of English is fun she sells.
Let the number of English is fun she sells be n and let the total amount earned in the month be s
Thus the equation representing the total amount earned is:
[tex]s=2200+8n[/tex]The graph of the equation is shown:
The dimensions of a rectangular prism are shown below length 1 1over2 width 1 foot hight 2 1over2
Solution
Given the dimensions of a rectangular prism as
length: 1.5 ft
width: 1 ft
Height: 2.5 ft
Part A.
Volume of a rectangular prism =
[tex]\begin{gathered} V_{RP}=l\times w\times h \\ \\ l\text{ is the length} \\ \\ w\text{ is the width} \\ \\ h\text{ is the height} \end{gathered}[/tex][tex]V_{RP}=1.5\times1\times2.5=3.75\text{ ft}^3[/tex]Volume of small cubes
[tex]V_{SC}=0.5^3=0.125\text{ ft}^3[/tex]Number of small cubes that can be packed in a rectangular prism is 30
[tex]N=\frac{V_{RP}}{V_{SC}}=\frac{3.75}{0.125}=30[/tex]Hence, there are 30 small cubes that can be packed in the rectangular box.
Part B.
The volume is given as
[tex]\sqrt[3]{30}=3.12[/tex]What is an equation of a parabola with the given vertex and focus? vertex: (-2, 5)focus: (-2, 6)show each step
Explanation
the equation of a parabola in vertex form is give by:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \text{where} \\ (h,k)\text{ is the vertex} \\ and\text{ the focus is( h,k}+\frac{1}{4a}) \end{gathered}[/tex]Step 1
so
let
a) vertex
[tex]\begin{gathered} vertex\colon(h.k)\text{ }\rightarrow(-2,5) \\ h=-2 \\ k=5 \end{gathered}[/tex]and
b) focus
[tex]\begin{gathered} \text{( h,k}+\frac{1}{4a})\rightarrow(-2,6) \\ so \\ h=-2 \\ \text{k}+\frac{1}{4a}=6 \\ \end{gathered}[/tex]replace the k value and solve for a,
[tex]\begin{gathered} \text{k}+\frac{1}{4a}=6 \\ 5+\frac{1}{4a}=6 \\ \text{subtract 5 in both sides} \\ 5+\frac{1}{4a}-5=6-5 \\ \frac{1}{4a}=1 \\ \text{cross multiply } \\ 1=1\cdot4a \\ 1=4a \\ \text{divide both sides by }4 \\ \frac{1}{4}=\frac{4a}{4}=a \\ a=\text{ }\frac{1}{4} \end{gathered}[/tex]Step 2
finally, replace in the formula
[tex]\begin{gathered} y=a(x-h)^2+k \\ y=\frac{1}{4}(x-(-2))^2+5 \\ y=\frac{1}{4}(x+2)^2+5 \\ \end{gathered}[/tex]therefore, the answer is
[tex]y=\frac{1}{4}(x+2)^2+5[/tex]I hope this helps you
What is the answer and how do I solve this
A parent absolute value function f(x) = |x| is plotted as
We can change the appearance of this absolute value function based on what we add to the absolute value function and the constant accompanied by it.
Let's start with shifting the plot from |x| to |x+1|. If we add +1 to x inside an absolute value function, the parent absolute value function will shift one unit to the left. This shifting is represented by the red dotted plot on the figure below.
We now multiply a constant -3 on the absolute value function |x+1|. Multiplying a negative number to the absolute value function results in mirroring the absolute value function via the x-axis. Then, the plot will be compressed by a factor of 1/3. We now have
Hence, the final plot for the given absolute value function y = -3|x+1| is
please help me with this problem this question asks for the angle measure and if the lines are tangent
step 1
we have that
44=(1/2)[180-arc} ------> by exterior angle
solve for arc
88=180-arc
arc=180-88
arc=92 degrees
give me a minute to draw a figure with letters to better understand the problem
we have that
x+?=180 degrees -------> by form a linear pair (supplemenatry angles)
x=arc=92 degrees ------> by central angle
so
?=180-92
?=88 degrees
therefore
the missing angle is 88 degreesSystems of 2 Equations Word Problems
Let x and y be the two numbers
x + y = 72 ------------------------------(1)
x - y = 4 ----------------------------------(2)
Add equation (1) and equation (2)
2x = 76
Divide both-side of the equation by 2
x = 38
substitute x = 38 into equation (1) and then solve for y
38 + y = 72
subtract 38 from both-side of the equation
y = 72 - 38
y = 34
The two numbers are 34 and 38
Not sure on how to do this. Could really use some help.
We will have the following:
We will recall that the surface area of a sphere is given by:
[tex]A_s=4\pi r^2[/tex]So, the surface area of the given sphere will be:
[tex]\begin{gathered} A_s=4\pi(\sqrt{\frac{7}{3.14}})^2\Rightarrow A_s=4(3.14)\ast\frac{7}{3.14} \\ \\ \Rightarrow A_s=4\ast7\Rightarrow A=28 \end{gathered}[/tex]So, the surface area of the sphere will be 28 yd^2.
*The reason we can use "mental math" is that we are using an approximation of pi, which makes it so it cancels with the 3.14 in the denominator after a point; leaving a simple multiplication at the very end.
