Answer:
43
Step-by-step explanation:
The value of y varies directly with x. When y = 21, x = 3. What is the value of y when x is 14.
when y = 21 and x = 3 the ratio of y to x is 21 to 3 or (reduced) 3 y to 1 x
This means y is three times the size of x.
When x = 14 then y = 14 × 3 = 42
Peter's farm has 160 meters of fencing, and he wants to fence a rectangular field thatborders a straight river. He needs no fence along the river side. Find the largest areaof Peter's farm that can be fenced.
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
[tex]P=W+W+L=2W+L[/tex]And this is equal to 160 m. Solving for L,
[tex]160=2W+L\text{ }\Rightarrow\text{ }L=160-2W[/tex]The area of this field is,
[tex]A=WL[/tex]Replace L with the expression we found from the perimeter,
[tex]A=W(160-2W)=160W-2W^2[/tex]The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
[tex]f(x)=ax^2+bx+c\text{ }\Rightarrow\text{ }x_{vertex}=\frac{-b}{2a}[/tex]In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
[tex]W_{vertex}=\frac{-160}{2(-2)}=\frac{160}{4}=40m[/tex]And the length when W = 40 is,
[tex]L=160-2W=160-2\cdot40=160-80=80m[/tex]And the area is,
[tex]A=WL=40m\cdot80m=3200m^2[/tex]Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
hello can you explain to me how I should write this out please
Here, we want to calculate the interquartile range
Mathematically, this is the difference between the lower quartile (1st quartile or 25th percentile) and the upper quartile (3rd quartile or 75th percentile)
We already have the numbers arranged from top to bottom
The count of numbers is 9 numbers
We have the first quartile as;
[tex]\frac{(n+1)}{4}\text{ = }\frac{10}{4}\text{ = 2.5th which is 3rd term}[/tex]The third term here is the weight of baby Selena
The 3rd quartile can be calculated as;
[tex]\frac{3(n+1)}{4}\text{ = }\frac{3(9+1)}{4}\text{ = 7.5 which is 8th term}[/tex]The 8th term is the weight of baby Me
The difference between these weights give the interquartile range as follows;
[tex]\text{Interquartile range =Q}_3-Q_1\text{ = 8 lbs 2 oz - 6 lbs 1 oz = 2 lbs 1 oz}[/tex]El 30 % de que numero es el 30 % del 10 % de 700
Answer:
70
Step-by-step explanation:
[tex]\frac{(700)(0.1)(0.3)}{0.3}=70[/tex]
help me pls I don't understand what I'm supposed to put here
The feedback loops in each situation are classified as follows:
a) Positive.
b) Negative.
What are positive and negative feedback loops?A positive feedback loop is when there is an amplification or growth of the output signal.A negative feedback loop is when there is a damping of the output signal, which is equivalent to a reduction in it's effect.In the context of this problem, in item a, there is a continuous amplification of the output signal, which is the surface temperatures, as they keep increasing, the three effects listed contribute to the increase of temperature, then the system go back to the beginning still with increasing temperatures, hence it is a positive feedback loop.
In item b, we have a loop with changes in the temperature, it increases and then it decreases, and so on, hence it is a negative feedback loop.
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solve for k 8/7=12/k
Answer:
[tex]k=\frac{21}{2}[/tex]Explanation:
Given the equation:
[tex]\frac{8}{7}=\frac{12}{k}[/tex]To solve for k, let us take the reciprocal of both sides, so that k is a numerator.
[tex]\frac{7}{8}=\frac{k}{12}[/tex]Multiply both sides by 12
[tex]\begin{gathered} k=\frac{7}{8}\times12 \\ \\ =\frac{7\times12}{8} \\ \\ =\frac{84}{8} \\ \\ =\frac{21}{2} \end{gathered}[/tex]The mean amount of gasoline charged by Key Refining Co.'s customers is $70 per month. The distribution of amount spent is approximately normal with a standard deviation of $10. Compute the probability (area under the curve) of selecting a customer who spent between $57 and $83 per month.
The probability (area under the curve) of picking a client who spends between $57 and $83 per month is 0.4032.
Given,
Mean, μ = $70
Standard Deviation, σ = $10
z = (x-μ) ÷ σ
P(The consumer was charged from around $70 and $83),
P(70 ≤ x ≤ 83) = P((70 - 70) ÷ 10)) ≤ z ≤ ((83-70) ÷ 10)) = P(0 ≤ z ≤ 1.3)
=P(z ≤ 1.3) - P(z ≤ 0)
=0.9032 - 0.500 = 0.4032 = 40.32%
P(70 ≤ x ≤ 83) = 40.32%
Customers with Key Refining Company loans typically spend an average of $70 monthly on gasoline and servicing. With either a standard deviation of $10, the expenditure distribution is about normal. For z = 1.3, the area under the curve is 0.4032.
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solve for x: 3/2+1/2x=2x
Here we will try to solve an equation involving a variable ( x ) given as follows:
[tex]\frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ = 2x}[/tex]We use the following basic mathematical operations when solving any equation:
[tex]\text{Multiplication, Division, Addition, Subtraction}[/tex]We will first try to isolate our vairable ( x ) on either side of the " = " sign. We will try to isolate ( x ) on the right hand side of " = " sign. To do this we will employ the mathematical operation of " Subtraction ".
We will subtract ( 1 / 2 x ) from both sides of " = " sign:
[tex]\begin{gathered} \frac{3}{2}\text{ + }\frac{1}{2}\cdot x\text{ - }\frac{1}{2}\cdot x\text{ = 2x - }\frac{1}{2}\cdot x \\ \\ \frac{3}{2}\text{ = x}\cdot\text{ (}\frac{4\text{ - 1}}{2}) \\ \\ \frac{3}{2}\text{ = }\frac{3}{2}\cdot x \end{gathered}[/tex]The next mathematical operation we will apply is " Division ". We will divide the left hand side of the equation with right hand side constant as follows:
[tex]\begin{gathered} x\text{ = }\frac{\frac{3}{2}}{\frac{3}{2}} \\ \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1}} \end{gathered}[/tex]The solution to the given equation is as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 1 }}[/tex]Janna is measuring the dimensions of her bedroom to determine how much paint she should buy for the walls. If her measuring tape has increments of 0.01 meter, which of the following could be the length of one wall with the correct number of significant digits?A)2.51 meters B)2.5 metersC)2.513 metersD)3 meters
The option that can be the length of one wall with the correct number of the significant digit is A)2.51 meters.
How to illustrate the information?From the information given, Janna is measuring the dimensions of her bedroom to determine how much paint she should buy for the walls was stated that the measurements have increments of 0.01 meter.
It's important to note that there are 2 decimal places.
In this case, the appropriate option is 2.51 meters.
In conclusion, the correct option is A.
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Julia sells subs for $6 each. How many subs will she need to sell to break even each month based on the costs listed below?
Labor costs (management & workers) = $11,000
Insurance = $400
Rent = $1300
Utilities = $300
Average cost of ingredients/packaging for each sub = $1.32
Answer:
2777.7777... subs
Step-by-step explanation:
11000+400+1300+300=13000
6-1.32=4.68
13,000/4.68
=2777.777777...
The student council raises money for the school dance every year through an auction. Each auction ticket costs $125. If the student council needs to raise greater than or equal to $2,000, which inequality represents the number of auction tickets,t, the student council must sell?
The inequality that represents the number of auction tickets,t, the student council must sell is given as 125t ≥ 2000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤
Let the total number of tickets be represented by t.
The auction ticket costs $125 and the student council needs to raise greater than or equal t $2,000. This will be 125t ≥ 2000.
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Find the average rate of change of k(x) = 4x + 11 over the interval [-19, -17].
Step 1:
Concept:
Use the rate of change formula below.
[tex]\begin{gathered} \text{Rate of change = }\frac{k(b)\text{ - k(a)}}{b\text{ - a}} \\ k(x)\text{ = 4x + 11} \\ a\text{ = -19} \\ b\text{ = -17} \end{gathered}[/tex]Step 2
Find k(a) and k(b)
[tex]\begin{gathered} k(-19)\text{ = 4(-19) + 11 = -76 + 11 = -65} \\ k(-17)\text{ = 4(-17) + 11 = -68 + 11= - 57} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \text{Rate of change = }\frac{-57\text{ - (-65)}}{-17\text{ - (-19)}} \\ =\text{ }\frac{-57\text{ + 65}}{-17\text{ + 19}} \\ =\text{ }\frac{8}{2} \\ =\text{ 4} \end{gathered}[/tex]You are the manager of a rental car company. A customer, Sandy Furrow, has asked you for an estimate of charges for a nine day rental of an SUV. She expects to drive 670 miles. If the company charges $55.50 per day plus 15 1/2 cents
per mile for this category of vehicle, what would be the total rental charge (in $) for Sandy's trip?
The total cost of her trip will be of $159.7.
What is equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation.
given:
Cost of 16 cents per mile= 16/100 = 0.16
Cost of $52.50 per day =52.50
linear function for the charge y in function of the number of miles x is:
y(x) = 0.16x + 52.50
The cost of driving 670 miles
So, y(670) = 0.16 x 670 + 52.50
y(670) = 107.2 + 52.50
y(670) = 159.7
Hence, The total cost of her trip will be of $159.7.
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Function Notation - Transformationsill send a picture of the question
Let's see how two points on the left are mapped to their corresponding points on the right:
Point A has a corresponding point at A'. We have:
f(A) = A'
f(-6, -3) = (2, 4)
Point B has a corresponding point at B'. We have:
f(B) = B'
f(-4, -1) = (4, 6)
Now, notice that:
2 = -6 + 8
4 = -3 + 7
So, for (x, y) = (-6, -3), we have:
f(x, y) = (2, 4) = (x + 8, y + 7)
Notice that the same happens to the mapping of the other point:
4 = -4 + 8
6 = -1 + 7
So, for (x, y) = (-4, -1), we have:
f(x, y) = (4, 6) = (x + 8, y + 7)
Therefore, the rule for the transformation is
f(x, y) = (x + 8, y + 7)
HURRY!!!
What is the value of |243| + |−23| − |−16|?
Answer:
250
Step-by-step explanation:
everything u need is in the picture
The circumference of a circle is 16 M what is the diameter of the circle
Given
Circumference, C = 16m
Find
diameter
Explanation
We know Circumference of a circle
[tex]\begin{gathered} C=2\pi r \\ 16=2\times\frac{22}{7}\times r \\ \frac{16\times7}{2\times22}=r \\ \frac{4\times7}{11}=r \\ \frac{28}{11}=r \end{gathered}[/tex]diameter = 2r
[tex]undefined[/tex]
Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50dollar per T-shirt ordered.
As Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.
To ascertain the maximum or lowest values of a scenario with many restrictions, a system of linear inequalities is frequently utilized. Inequalities reflect a limit of what is permitted or achievable rather than a precise quantity.
It is given that Ekua designs and sells T-shirts for $1 13 each. Ekua has to spend $280 per month, $9.50 dollar per T-shirt ordered.
We have to find the maximum number of T-shirts she can buy,
⇒ $280 / $9.50
⇒ 29.47 ≅29
Thus, Ekua has to spend $280 per month and the cost of each sheet is $9.50 / dollar. The inequality followed is T≤29.
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Karma has 110 pounds of rice to sell. A vendor offers her $0.01 per 5 grams for her rice. How much money will karma make if she sells her rice to this vendor
Karma will make $99.78 if she sells 110 pounds of rice to the vendor
Quantity of rice available with Karma = 110 pounds
A pound is a unit of weight that is mostly used in the United States, Great Britain, and other English-speaking nations. A pound is approximately 0.454 kilos. A quantity of something is said to weigh one pound if it weighs that much.
The conversion rate of pounds to grams:
1 pound = 453.59 grams
So, 110 pounds will be equal to:
110*453.59
=49894.9 grams
Selling price for 5 grams = $0.01
Selling price for 1 gram:
The selling price of 5 grams/ Price for 5 grams
0.01/5
=$0.002
Selling price for 49894.9 grams = 49894.9*0.002
= $99.78
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The lengths of the sides of a triangle are 5,6, and 7. If the perimeter of a similar triangle is 36, what is the length of the shortest side of the similar friangle? A) 5 B) 10 C) 4 D) 6
The length of the sides of a triangle are 5, 6 and 7.
If the perimeter of a similar triangle is 36
Perimeter of a triangle = a + b+ c
The perimeter of the first triangle is
P = 5 + 6 + 7
P = 11 + 7
P = 18
To find the smallest lengths
18 / 36 = 5 / x
Introduce cross multiplication
36 x 5 = 18 * x
180 = 18x
Divide both sides by 18
180/18 = 18x/18
x = 180/18
x = 10
The answer is 10
Jack borrows $2,700 at a rate of 8.2% per year. How much total will he pay if it takes 3 months to repay the loan?
well, a year has a total of 12 months, so 3 months is really 3/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$2700\\ r=rate\to 8.2\%\to \frac{8.2}{100}\dotfill &0.082\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ A=2700[1+(0.082)(\frac{1}{4})] \implies A = 2700(1.0205)\implies A=2755.35[/tex]
A florist has 60 tulips and 72 daffodils. The florist will make bouquets with the same number of tulips and the same number of daffodils in each, using all the flowers.
What is the greatest number of bouquets the florist can make?
Enter the correct answer in the box.
The greatest number of bouquets that the florist can make is 12.
What is the greatest number of bouquets that the florist can make?The greatest number of bouquets that the florist can make can be determined by calculating the highest common factor of 60 and 72. The factor of a number is the number that divides another number without any remainder. The highest common factor of two or more numbers is the highest factor that is common to two or more numbers.
Factors of 60 =1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72.
Highest common factor = 12
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please answer asap im begging
Answer:
y = 3x + 3 :D
Step-by-step explanation:
Equation of line: y = mx + b :)
b: Y intercept
m: Slope
Now lets solve :)
Lets find M first :)
We need 2 points so lets use (0,3) and (1,6) :)
We fist need to subtract :)
6 - 3 = 3
1 - 0 = 1
Now we divide :)
3/1 = 3
Lets put that into our equation :)
y = 3x + b
Now lets find B :)
To find b, we need to see where the line intercepts the y axis! This will be at point (0,3)!
The y intercept will be 3 :)
The final equation will be y = 3x + 3 :)
Have an amazing day!!
Please rate!
1. Solve the Systemy = 2x - 6y = -6x - 14
x = -1
Explanation:The given equations:
y = 2x - 6
y = -6x - 14
Since both equations are equal to y, we will equate the right hand side of both equations.
y = y
2x - 6 = -6x - 14
collect like terms:
2x + 6x = -14 + 6
8x = -8
divide both sides by 8:
8x/8 = -8/8
x = -1
I need help with this homework assignment it’s due by mid night
step 1
see the attached figure to better understand the problem'
step 2
Hypotenuse is AB
Opposite side is BC
Adjacent side is AC
because, the opposite side is the side opposite to the given angle (35 degrees)
adjacent side is the side adjacent to the given angle (35 degrees) and the hypotenuse is the greater side of a right triangle (is the opposite side to the angle of 90 degrees)
step 3
To find out the value of L
we use
cos(35)=40/L -----> adjacent side divided by the hypotenuse
step 4
solve for L
L=40/cos(35)
step 5
L=48.83 ft
step 6
the length of the ladder must be greater than 48.83 ft
step 7
A 50 ft ladder long is enought
because 50 > 48.83
help plwsty Graph the equation: y-1 = 2/3(x-3)?
The given expression : y-1=2/3(x-3)
Simplify the equation :
[tex]\begin{gathered} y-1=\frac{2}{3}(x-3) \\ y=\frac{2}{3}x-\frac{2}{3}(3)+1 \\ y=\frac{2}{3}x-2+1 \\ y=\frac{2}{3}x-1 \end{gathered}[/tex]for the graph we need atleast two coordinates
Let at x=0 then
y=2/3(0)-1
y=-1
Cooridnate = (0,-1)
Now, let x=9 then
y=2/3(9)-1
y=2(3)-1
y=5
Coordinate =(9,5)
Plot these point (0,-1) & (9,5)on the graph and join them by staright line
The graph will be ;
If a bug can flap its wings at a rate of 69 times in 4 seconds, how manytimes do they flap their wings in 1.476 minutes? Round to 1 decimal.w
First, we need to change 1.476 minute to seconds
1.476 minutes = 1.476 x 60= 88.56 seconds
Let the number of times they flap there wings in 1.476 minute be X
69 times = 4 seconds
X = 88.56 seconds
cross-multiply
4X = 69(88.56)
4X= 6110.64
Divide both-side of the equation by 4
X = 1 527.66 ≈ 1 528 times
PLEASEEEEEEEE HELPPP
If Greg has 1 1/2 servings of cereal for breakfast each day, he can consume 8 breakfasts from a box of cereal.
The price of one breakfast from a regular-sized box of cereal is $0.54 if the box costs $4.29.
Greg could consume 4 additional breakfast portions from a single family-sized box.
How to find unit rate of Greg's breakfast?A regular-sized box of cereal = 12 servings
If Greg eats 1 1/2 servings for breakfast every day
Number of breakfast Greg can eat in a regular-sized box = A regular-sized box of cereal / servings of breakfast eaten everyday
= [tex]\frac{12}{\frac{11}{2} }[/tex]
=[tex]\frac{12}{\frac{3}{2} }[/tex]
multiply by the reciprocal of [tex]\frac{3}{2}[/tex]
= 12 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{24}{3}[/tex]
= 8 breakfast
Cost of regular-sized box of cereal = $4.29.
Cost of one breakfast from a regular-sized box of cereal = Cost of regular-sized box of cereal ÷ Number of breakfast Greg can eat in a box
= [tex]\frac{4.29}{8}[/tex]
= 0.53625
Approximately,
$0.54 per breakfast
If Greg purchased the family-sized box of cereal that contains 18 servings
Family-sized box of cereal divided by the daily serves of breakfast is the number of breakfasts Greg can consume.
= 18 servings / [tex]\frac{11}{2}[/tex]
= 18 ÷[tex]\frac{3}{2}[/tex]
= 18 × [tex]\frac{2}{3}[/tex]
= [tex]\frac{36}{3}[/tex]
= 12 servings
Consequently, the number of additional breakfasts Greg may consume from a single family-sized package
= Number of breakfast Greg can eat in a family-sized box - Number of breakfast Greg can eat in a regular-sized box
= 12 servings - 8 servings
= 4 servings
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What is the next fraction in the sequence 19/20,4/5,13/20,1/2
Find the first 5 terms of the following sequence. For the first term let a_1=1. Round your answer to the nearest hundredth.a_n= \frac{2^n}{n^2} 1st term = Answer2nd term = Answer3rd term = Answer4th term = Answer5th term = Answer
1st term
Given:
[tex]a_1=1[/tex]With the formula of the sequence:
[tex]\begin{gathered} a_1=\frac{2^1}{1^2}=\frac{2}{1}=2 \\ \\ a_1=2 \end{gathered}[/tex]________
Second term:
[tex]\begin{gathered} a_2=\frac{2^2}{2^2}=\frac{4}{4}=1 \\ \\ a_2=1 \end{gathered}[/tex]____________
Third term:
[tex]\begin{gathered} a_3=\frac{2^3}{3^2}=\frac{8}{9}\approx0.89 \\ \\ a_3=0.89 \end{gathered}[/tex]_________
Fourth term:
[tex]\begin{gathered} a_4=\frac{2^4}{4^2}=\frac{16}{16}=1 \\ \\ a_4=1 \end{gathered}[/tex]-________________
Fifth term:
[tex]a_5=\frac{2^5}{5^2}=\frac{32}{25}=1.28[/tex]The area of a trapezoid is given by the formula A = (a + b). Solve the formula for b.
Starting from the given formula:
[tex]A=\frac{h}{2}(a+b)[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \Rightarrow2\times A=2\times\frac{h}{2}(a+b) \\ \Rightarrow2A=h(a+b) \end{gathered}[/tex]Divide both sides by h:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}=\frac{h(a+b)}{h} \\ \Rightarrow\frac{2A}{h}=a+b \end{gathered}[/tex]Substract a from both sides of the equation:
[tex]\begin{gathered} \Rightarrow\frac{2A}{h}-a=a+b-a \\ \Rightarrow\frac{2A}{h}-a=b \end{gathered}[/tex]Therefore:
[tex]b=\frac{2A}{h}-a[/tex]QUESTION ATTACHED
PLEASE HELp
Answer:
yh no question....thanks for the points tho :)