A house is on a 60,000-squarefoot lot. Rounded to the nearest tenth, approximately how many acres are inthe lot?Note: There are 43,560 square feet in an acre.A 1.3 acresB 1.0 acres1.7 acres1.4 acres
Given:-
[tex]60,000\text{sqfeet}[/tex]To find the given area in acre.
So now we use the formula,
[tex]1\text{acre}=43560[/tex]So now we get,
[tex]\frac{60000}{43560}=1.3774[/tex]So rounding to the nearest tenth we get,
[tex]1.4[/tex]So the required solution is 1.4acres.
Which pair of functions are inverse functions?()=3+5f(x)=3x+5and()=−3−5g(x)=−3x−5 ()=−+57f(x)=−x+57and()=−7+5g(x)=−7x+5 ()=−3−57f(x)=−3x−57and()=3+57g(x)=3x+57 ()=3−5f(x)=3x−5and()=−53
1) Let's examine the f(x) functions and find the inverse function of f(x), in the first pair of functions:
a) At first, let's swap x for y in the original function
[tex]\begin{gathered} f(x)=3x+5 \\ y=3x+5 \\ x=3y+5 \\ -3y=-x+5 \\ 3y=\text{ x-5} \\ \frac{3y}{3}=\frac{x-5}{3} \\ y=\frac{x-5}{3}\text{ } \\ f^{-1}(x)=\frac{x-5}{3} \end{gathered}[/tex]Note that after swapping x for y, we can isolate y on the left side. So as regards g(x) this is not the inverse function of f(x)
2) Similarly, let's check for f(x)
[tex]\begin{gathered} f(x)=\frac{-x+5}{7} \\ y=\frac{-x+5}{7} \\ x=\frac{-y+5}{7} \\ 7x=-y+5 \\ y=-7x+5 \\ f^{-1}(x)=-7x+5 \end{gathered}[/tex]Note that in this case, we can state that these are inverse functions
[tex]f^{-1}(x)=g(x)[/tex]3) Finally, let's find out the last pair of functions.
[tex]\begin{gathered} f(x)=\frac{-3x-5}{7} \\ y=\frac{-3x-5}{7} \\ x=\frac{-3y-5}{7} \\ 7x=-3y-5 \\ 3y=-7x-5 \\ f^{-1}(x)=\frac{-7x-5}{3} \end{gathered}[/tex]So in this pair, g(x) is not the inverse function of f(x).
4) Hence, the answer is following pair:
[tex]\begin{gathered} f(x)=\frac{-x+5}{7}\text{ } \\ g(x)=f^{-1}(x)=-7x+5 \end{gathered}[/tex]Can I get help on 22. I don’t understand what I did wrong
From the problem, we have an inequality :
[tex]-6x+1<7[/tex]Subtract 1 to both sides of the equation :
[tex]\begin{gathered} -6x+1-1<7-1 \\ -6x<6 \end{gathered}[/tex]Divide both sides by -6 :
[tex]\begin{gathered} -6x<6 \\ x<\frac{6}{-6} \\ x<-1 \end{gathered}[/tex]The solution is x < -1
Which of the following is the following measure of angle BOC
The tangent of a circle always form 90 degree angle with the radius. So measure of angle ABO and angle ACO is 90 degrees each.
The sum of angles of a quadilateral is 360 degrees. So,
[tex]\angle BOC+\angle ABO+\angle ACO+\angle BAC=360[/tex]Substitute the measures of angles in the equation to obtain the measure of angle BOC.
[tex]\begin{gathered} \angle BOC+90+90+90=360 \\ \angle BOC=360-270 \\ =90 \end{gathered}[/tex]Thus, measure of angle BOC is 90 degrees.
5. The picture below showsthe number of pages in 3textbooks.424 pages 290 pages286 pagesMarc has 10 days to finish allthree before exams. He plansto read an equal amounteach day. How many pagesshould he read the first day?
The number of pages in 3 textbooks are ; 424 pages, 290 pages, and 286 pages.
The total number of pages in the three books is;
[tex]N=424+290+286=1000\text{ pages}[/tex]To complete the three books in ten days ( before the exam), Marc must read one-tenth of the total pages daily.
Since, He plans to read an equal amount each day.
The number of pages P he should read in the first day is;
[tex]P=\frac{1000}{10}=100\text{ pages}[/tex]He should read 100 pages in the first day.
Higher Order Thinking The bakery had
84 muffins. Ms. Craig bought 5 packs of
6 muffins. Did she purchase an even or an
odd number of muffins? Is the number of
muffins left even or odd? Explain.
shi
Answer:
Even and 54
Step-by-step explanation:
Based on the given conditions, formulate: 84-6x5
Calculate the product or quotient: 84-30
Calculate the sum or difference: 54
Mayra bought x grams of rice.Anika boughtmore than Mayra bought.Select ALL of the equations that represent therelationship between the amount of rice that Mayrabought, x, and the amount of rice that Anika bought, y.#1. y=4/3x #2.Y=2/3x 3#.Y=1/3x #4.y=x+1/3x #5.Y=X-1/3x
Given that the amount of rice Anika bought is
more than Mayra bought and Mayra bought x grams while Anika bought y grams then considering the options
#1. y=4/3x - this is true
#2.Y=2/3x - this is not true as this means that the value of y is less than that of x
3#.Y=1/3x - this is not true as this means that the value of y is less than that of x #4.y=x+1/3x - this is same as #1
#5.Y=X-1/3x - this is same as #2
Hence th
Hi I’ve been struggling with these two problems for sometime now
Answer
The answer is Distributive property
SOLUTION
Problem Statement
We are given the mathematical statement below:
[tex]5(x-3)=5x-15[/tex]We are asked to find the property that justifies the above statement.
Solution
To solve this problem, we need to understand what the distributive property is.
The distributive property states:
[tex]A(B+C)=AB+AC[/tex]If A = 5, B = x and C = -3
Thus, applying the Distributive property on the left-hand side of the mathematical equation given:
[tex]\begin{gathered} A(B+C)=AB+BC \\ 5(x-3)=5(x)+5(-3)_{} \\ =5x-15 \end{gathered}[/tex]This conforms to the Distributive property
Final Answer
The answer is Distributive property
1. Patty is arranging the chairs for an awards ceremony. She wants to put the 36 chairs into a rectangular array. Choose the ways that Patty can arrange the chalrs. 1. Select all the expressions that have a product of 640. 16 x 40 (4 x 4) * (4 x 10) 40 = 16 (4 x 4) * (8 x 6) (2 x 5) * (8 x 2) x (2 x 2)
The pieces of construction paper ordered can be determined as,
[tex]\begin{gathered} N=22\times64 \\ =1408 \end{gathered}[/tex]Thus, the required pieces of construction paper is 1408.
x is inversely proportional to y, and x = 18 when y = 4. a. Write an equation relating x and y b. Find x when y = 30
Here, we want to solve a proportional relationship problem
a) We have the proportion as follows;
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \\ k\text{ as constant} \\ \\ k\text{ = xy} \\ \\ \text{for x = 18 and y = 4} \\ \\ k\text{ = 18}\times4\text{ = 72} \\ xy\text{ = 72} \end{gathered}[/tex]b) X, when y = 30
[tex]\begin{gathered} xy\text{ = 72} \\ x\text{ = }\frac{72}{y} \\ x\text{ = }\frac{72}{30} \\ x\text{ = 2.4} \end{gathered}[/tex]on Core Math 6 A What is the greatest common factor of 16 and 24? O4 X 6 O 8 O 10
The Greatest Common Factor
The greatest common factor (or divisor) (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers of that set.
For example, we have the numbers 16 and 24. One common divisor is 2 because 16/2=8 and 24/2=12. Both divisions are exact.
But 2 is not the greatest common divisor. To find the GCF, the procedure is:
* Write the prime factor of each number:
16 = 2*2*2*2
24 = 2*2*2*3
Select the maximum number of common prime factors from the numbers, even if they repeat.
We can select the product of 2*2*2 = 8 as the GCF, thus:
Answer = 8
Allison spent $7.80 on lunch. That represents 6% of her daily net income. What is Allison's daily net income? Round your answer to the nearest penny if needed.
we get that the net income of Alison is:
[tex]\frac{7.8}{6}\cdot100=130[/tex]so her net income is $130
Find the circumference of a circular swimming pool with a diameter of feet. Use as an approximation for . Round your answer to the nearest foot. Enter only the number.
To determine the circumference of any circle we need to use the following formula:
[tex]C=2\cdot\pi\cdot r[/tex]Where r is the radius, which is half of the diameter. For this problem we have a pool with diameter equal to 18 feet, therefore the circumference is:
[tex]\begin{gathered} C=2\cdot3.14\cdot\frac{18}{2}=2\cdot3.14\cdot9 \\ C=56.52\text{ ft} \end{gathered}[/tex]The circumference of the pool is approximately 57 feet.
Using the following image, solve for CD. 2x - 9 Сс X-9 • E 12 CD |
Answer
CD = 11 units
Explanation
From the image, we can see that
CD = 2x - 9
DE = x - 9
CE = CD + DE
CE = 12
CE = CD + DE
CE = (2x - 9) + (x - 9)
12 = 2x - 9 + x - 9
12 = 3x - 18
We can rewrite this as
3x - 18 = 12
3x = 12 + 18
3x = 30
Divide both sides by 3
(3x/3) = (30/3)
x = 10
CD = 2x - 9 = 2(10) - 9 = 20 - 9 = 11 units
Hope this Helps!!!
The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?(1 Point)a) 84b) 21c) 42d) 32
SOLUTION:
Step 1:
In this question, we are given the following:
The sum of the two numbers is 106. The bigger number is 22 more than the smaller number. Then what is half of the smaller number?
(1 Point)
a) 84
b) 21
c) 42
d) 32
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Le\text{t the two numbers be x and y , such that:} \\ \text{x + y = 106 --- equation 1} \\ x\text{ + \lparen x+ 22 \rparen = 106} \\ 2x\text{ + 22 = 106} \\ \text{2x = 106 - 22} \\ 2x=84 \\ Divide\text{ both sides by 2, we have that:} \\ \text{ x =}\frac{84}{2} \\ \text{x = 42} \\ This\text{ means that the smaller number is 42 and} \\ The\text{ larger number is \lparen 42 + 22 \rparen = 64} \\ Then,\text{ Half of the smaller number = }\frac{42}{2}\text{ = 21 \lparen OPTION B \rparen} \end{gathered}[/tex]CONCLUSION:
The final answer = 21 ( OPTION B )
6200 in standard form
Answer: Six Thousand Two Hundred
Step-by-step explanation:
I need help with my math
Given the equation:
[tex]y=\frac{2}{3}x-3[/tex]We will graph the equation using the intercepts
The X-intercept is the value of x when y = 0
so,
[tex]\begin{gathered} y=0\rightarrow0=\frac{2}{3}x-3 \\ \frac{2}{3}x=3 \\ x=\frac{9}{2}=4.5 \end{gathered}[/tex]The y-intercept is the value of y when x = 0
so,
[tex]x=0\rightarrow y=-3[/tex]So, the graph of the line passes through the points (0, -3) and (4.5, 0)
The graph of the equation is as shown in the following picture:
The correct option is:
Consider the data regarding car costs. The mean is $22,000 and the standard deviation is $2,000.a) Not everyone pays the same price for the same model of car. Use the 68-95-99.7% Rule to find what percentage ofbuyers paid between $18,000 and $26,000.b) The middle 99.7% of car costs are between what values?c) What is the probability a car will cost less than $24,000?d) What is the probability a car will cost more than $26,000?
Answer:
a) 95%
b) $16,000 to $28,000
c) 84%
d) 2.5%
Step-by-step explanation:
Given the mean of car costs is $22,000 with a standard deviation of $2,000, you want to use the empirical rule to find ...
percentage of buyers paying $18–26 thousandrange of values for middle 99.7% of costsprobability of cost less than $24,000probability of cost more than $26,000Empirical ruleThe empirical rule tells you that the center 68% of costs will be between -1 and +1 standard deviations from the mean: $20,000 to $24,000.
95% of costs will lie within 2 standard deviations: $18,000 to $26,000.
The "tails" of the distribution are split equally between the upper values of these ranges and the lower values.
a) 18-26These values are ±2 standard deviations from the mean.
95% of buyers will pay between $18 and 26 thousand.
b) 99.7%The middle 99.7% of the distribution lies between ±3 standard deviations from the mean:
22,000 ± 3(2000) = 22,000 ± 6,000 = {16000, 28000}
The middle 99.7% of costs are between $16,000 and $28,000.
c) < 24We know that 68% of costs are between $20,000 and $24,000, and 50% of costs are below $22,000. The distribution is symmetrical, so 68%/2 = 34% of costs are between $22,000 and $24,000..
The fraction below $24,000 is ...
P(<24) = P(<22) +P(22 to 24) = 0.5 + 0.34 = 0.84
The probability a car will cost less than $24,000 is about 84%.
d) > 26The empirical rule tells us 95% of the distribution is between 18 and 26 thousand. Half the remaining amount is above 26 thousand.
P(> 26) = (1 -0.95)/2 = 2.5%
The probability a car will cost more than $26,000 is about 2.5%.
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I will show you the pic .
we have the equation
(2/3)x+5=1
step 1
multiply by 3 both sides
2x+15=3
step 2
subtract 15 both sides
2x=3-15
2x=-12
step 3
divide by 2 both sides
x=-12/2
x=-6If u = 2i - j; v= -5i + 4j and w = j find 4u (v -w).
Answer:
-40
Explanation:
Given
u = 2i - j; v= -5i + 4j and w = j
Required
4u(v-w)
4u = 4(2i) = 8i
v - w = -5i + 4j - j
v - w = -5i + 3j
Substitute
4u(v-w)
= 8i(-5i+3j)
= -40(i*i) [since i*i = 1]
= -40
Hence the required solution is -40
Which number is divisible by both 2, 5, and 10?1. 9002. 8023. 9624. 745
Given:
The numbers are 2,5 &10.
900 is divisible by 2,5 &10.
Therefore, Option 1. 900 is the correct answer.
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
Ayako took a trip to the store 4 1/2mi away. If she rode the bus for 3 5/8mi and walked the rest of the way, how far did she have to walk? Express you answer as a simplified fraction or mixed number
we have that
total distance=4 1/2 miles
Let
x ----> number of miles walked
so
4 1/2=3 5/8+x
solve for x
But first, convert mixed number to an improper fraction
4 1/2=4+1/2=9/2
3 5/8=3+5/8=29/8
substitute
9/2=(29/8)+x
x=(9/2)-29/8
the fractions have different denominators
so
Find out an equivalent fraction
9/2=(9/2)*(4/4)=36/8
so
x=(36/8)-29/8
x=7/8
the answer is 7/8 milesOn a hike, each hiker carries the items shown. Write an expression in simplest form that represents the weight (in pounds) carried by x hikers. sleeping bag: 3.4lb bag: 4.6lb water bottle: 2.2lb
ok
Weight(x) = 3.4x + 4.6x + 2.2x or
W(x) = 3.4x + 4.6x + 2.2x
or
W(x) = 10.2x this is the expression
At a carnival, there is a game where you can draw one of 10 balls from a bucket if you pa $16. The balls are numbered from 1 to 10. If the number on the ball is even, you win $22 If the number on the ball is odd, you win nothing. If you play the game, what is the expected profit?
ANSWER
[tex]\text{\$-5}[/tex]EXPLANATION
To find the expected profit, we have to first find the expected payout.
There is a possibility of drawing up to 10 balls, numbered 1 to 10.
There are 5 even balls and 5 odd balls.
We have to find the probabilty of drawing even or odd balls:
=> The probability of drawing an even ball is:
[tex]P(\text{even)}=\frac{5}{10}=\frac{1}{2}[/tex]=> The probability of drawing an odd ball is:
[tex]P(\text{odd)}=\frac{5}{10}=\frac{1}{2}[/tex]The expected payout is the sum of the product of the probability of drawing each ball and the prize of each ball.
That is:
[tex]\begin{gathered} E(X)=\Sigma\mleft\lbrace X\cdot P(X)\mright\rbrace \\ E(X)=(22\cdot\frac{1}{2})+(0\cdot\frac{1}{2}) \\ E(X)=11+0 \\ E(X)=\text{ \$11} \end{gathered}[/tex]The expected profit can be found by subtracting the cost of playing the game from the expected payout:
[tex]\begin{gathered} Exp.Profit=11-16 \\ Exp.Profit=\text{ \$-5} \end{gathered}[/tex]That is the answer.
i need help i don’t understand the questions are down below
A picture and a frame are given with dimensions. It is required to find the area of the frame.
To find the area of the frame, subtract the area of the picture from the total area (frame + picture).
Recall the area of a rectangle with a length l and a width w:
[tex]A=l\cdot w[/tex]Substitute l=22 and w=20 into the formula to find the area of the picture:
[tex]A=22\cdot20=440[/tex]Notice that the total length of the picture and frame is l=22+x+x=22+2x, while the total width is w=20+x+x=20+2x.
Substitute these dimensions into the area formula:
[tex]\begin{gathered} A=(22+2x)\cdot(20+2x) \\ A=4x^2+40x+44x+440 \\ \Rightarrow A=4x^2+84x+440 \end{gathered}[/tex]Subtract the areas to find the area of the entire frame:
[tex]\text{ Area of frame}=4x^2+84x+440-440=4x^2+84x+0[/tex]The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
To find the area when x=2, substitute x=2 into the expression for the area:
[tex]4(2)^2+84(2)+0=4(4)+168+0=16+168=184[/tex]The area of the frame when x=2 inches is 184 inches squared.
The perimeter is the sum of the side lengths of the frame given as:
[tex]P=2(l+w)[/tex]Substitute l=22+2x and w=20+2x into the formula:
[tex]P=2(22+2x+20+2x)=2(4x+42)=8x+84[/tex]Substitute x=10 to find the perimeter when x=10:
[tex]P=8(10)+84=80+84=164[/tex]The perimeter is 164 inches.
Answers:
The area of the entire frame is 4x²+84x+0.
First-term is 4x², the second term is 84x, and the third term is 0.
The area of the frame when x=2 inches is 184 inches squared.
The perimeter when x=10 is 164 inches.
AREA AND VOLUMEInvestigating the effects on the area for non-proportiona
(a)
Let:
w1 = Original width
l1 = Original length
w2 = New width
l2 = New length
A1 = Original area
A2 = New Area
so:
[tex]\begin{gathered} w2=3w1=3\cdot10=30ft \\ l2=2l1=2\cdot50=100ft \\ A2=w2\cdot l2=3000ft^2 \end{gathered}[/tex]Answer:
New length: 100ft
New width: 30 ft
New Area: 3000ft²
-------------------------------------------
(b)
[tex]\frac{A2}{A1}=\frac{3000}{500}=6[/tex]Answer:
The area of the new walkway will be 6 times the area of the current walkway
---------------------------------------
(c)
[tex]\begin{gathered} 8\cdot500=x\cdot50\cdot4\cdot10 \\ 4000=2000x \end{gathered}[/tex]Solve for x:
[tex]\begin{gathered} x=\frac{4000}{2000} \\ x=2 \end{gathered}[/tex]Answer:
Make the new length 2 times the current length.
can you help I dont know how to do it
four segments
[tex]MS,MT,MN,MY[/tex]A ray
[tex]\bar{MY}[/tex]Collinear points
[tex]Y,M,N[/tex]Use logarithmic differentiation to find the derivative of y with respect to xy = (10x + 2)^x
Given: An equation-
[tex]y=(10x+2)^x[/tex]Required: To determine the differentiation of y with respect to x.
Explanation: The differentiation of a logarithmic function is-
[tex]\begin{gathered} y=a^x \\ \frac{dy}{dx}=a^x\ln(a) \end{gathered}[/tex]Taking log both sides on the given equation as-
[tex]\begin{gathered} \ln y=\ln(10x+2)^x \\ =x\ln(10x+2) \end{gathered}[/tex]Now, differentiating with respect to x using product rule as-
[tex]\frac{1}{y}\frac{dy}{dx}=\ln(10x+2)\frac{d}{dx}(x)+x\frac{d}{dx}\ln(10x+2)[/tex]Further simplifying as-
[tex]\frac{dy}{dx}=y[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Substituting the value of y as-
[tex]\frac{dy}{dx}=(10x+2)^x[\ln(10x+2)+\frac{10x}{10x+2}][/tex]Final Answer: Option D is correct.
The temperature, in degrees Fahrenheit, of a cup of water placed in a freezer can be modeled by the function f(m)=210(0.94)^m , where m represents the number of minutes after the water was placed in the freezer.
What is the average rate of change from Minute 4 to Minute 11 and how can that rate of change be interpreted?
1. The average rate of change from Minute 4 to Minute 11 is of -8.23 º/min.
2. This means that the temperature decreased from Minute 4 to Minute 11 by an average of 8.23 º/min.
How to obtain the average rate of change of a function?The average rate of change of a function is obtained by the change in the output of the function divided by the change in the input of the function. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
The function in this problem is defined as follows:
f(m) = 210(0.94)^m.
The numeric value of the temperature at Minute 11 is of:
f(11) = 210(0.94)^11 = 106.32º.
The numeric value of the temperature at minute 4 is of:
f(4) = 210(0.94)^4 = 163.96º.
The change in the input is of:
11 - 4 = 7.
Hence the average rate of change is of:
(106.32 - 163.96)/67 = -8.23º min -> decrease of 8.23º each min.
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how much it is -6 1/2 + 12?
In the given fraction, the value of -6 1/2 + 12 is 11/2
Fraction:
The fraction represents the part of a whole. And the fraction is the number is expressed as a quotient, in which the numerator is divided by the denominator.
Given,
Here we have the fraction -6 1/2 + 12.
Now, we need to find the value of this fraction.
To solve this one, first we have to convert the mixed fraction into normal one, then we get,
To convert the mixed fraction fist we have to multiply the denominator by the whole number, then we get
6 x 2 = 12
Then add these value into the numerator, then we get
12 + 1 = 13
So, the fraction is -13/2.
Now, we have to add these two,
=> -13/2 + 12
The fractions have unlike denominators.
First, we have to find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(-13/2, 12/1) = 2
Then we have to multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. Then we get,
=> -13/2 + 24/2
=> 11/2
Therefore, the resulting fraction is 11/2.
To know more about Fraction here.
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