Answer:
it would be on 7 since 60-11=49 and the square root of 49 is 7
The cargo of the truck weighs at most 2,800 pounds. Use w to represent the weight (in pounds) of the cargo.To get the 10% discount, a shopper must spend no less than $100. Use d to represent the spending (in dollars) of a shopper who gets the discount
We can write this inequalities as:
If the cargo W has to be 2,800 pounds at most, then:
[tex]W\le2,800[/tex]The shopper has to spend $100 or more to get a discount, so the spending d to get a discount can be written as:
[tex]d\ge100[/tex]Which family spends the largest dollar amount on transportation?Family AFamily BFamily C
SOLUTION:
Step 1:
In this question, we are given the following:
Which family spends the largest dollar amount on transportation?
a) Family A
b) Family B
c) Family C
Step 2:
The details of the solution are as follows:
a) Family A
Total income $ 5, 400
Amount spent on Transportation =
[tex]\begin{gathered} 11\text{ \% of \$ 5,400} \\ \frac{11}{100}\text{ x \$ 5, 400} \\ =\text{ }\frac{59400}{100} \\ =\text{ 594} \\ =\text{ \$ 594} \\ So,\text{ Family A spent \$ 594 on Transportation} \end{gathered}[/tex]b) Family B
Total income $ 4,675
Amount spent on Transportation =
+
[tex]\begin{gathered} 13\text{\% of \$ }4,675 \\ \frac{13}{100}\text{ x \$ }4,675 \\ =\text{ }\frac{60775}{100} \\ =607.75 \\ =\text{ }607.\text{ 75 dollars} \\ So,\text{ Family B spent \$ 607.75 on Transportation} \end{gathered}[/tex]c) Family C:
Total income $ 6,675
Amount spent on Transportation =
+
[tex]\begin{gathered} 9\text{\% of \$ }6,675 \\ \frac{9}{100}\text{ x \$ }6,675 \\ =\text{ }\frac{60,075}{100} \\ =600.75 \\ =\text{ }600.75\text{ dollars} \\ So,\text{ Family C spent \$ 600.75 on Transportation} \end{gathered}[/tex]CONCLUSION:
From the above analysis,
we can see that Family B spent the largest dollar amount on Transportation with the sum of $ 607. 75 ( which is 13% of $ 4,675)
1 pur Una foto de 4 pulgadas por 6 pulgadas se coloca en un marco de imagen con un borde de ancho constante. Si el área del marco, incluida la imagen, es de 80 pulgadas cuadradas, ¿qué ecuación podría usarse para determinar el ancho del borde, x? *
Tenemos una foto de 4 x 6 pulgadas.
Tenemos un marco con borde de ancho constante, lo que significa que alrededor de la foto siempre tenemos un "espesor" constante, que llamaremos "e".
También sabemos que el area total del marco es 80 pulgadas cuadradas.
Podemos dibujar esto así:
El marco tiene un ancho total de 4+2e y un largo de 6+2e.
Entonces, podemos calcular el espesor "e" a partir de calcular el area del marco e igualarlo a 80 pulgadas cuadradas. El area del marco sera igual al ancho por el largo:
[tex]\begin{gathered} A=(4+2e)(6+2e)=80 \\ 4\cdot6+4\cdot2e+2e\cdot6+2e\cdot2e=80 \\ 24+8e+12e+4e^2=80 \\ 4e^2+20e-56=0 \\ 4(e^2+5e-14)=0 \\ e^2+5e-14=0 \end{gathered}[/tex]Debemos aplicar la ecuación cuadrática para calcular e:
[tex]\begin{gathered} e=-\frac{b}{2a}\pm\frac{\sqrt[]{b^2-4ac}}{2a} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{5^2-4\cdot1\cdot(-14)}}{2} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{25+56}}{2} \\ e=-\frac{5}{2}\pm\frac{\sqrt[]{81}}{2} \\ e=-\frac{5}{2}\pm\frac{9}{2} \\ e_1=-\frac{5}{2}-\frac{9}{2}=-\frac{14}{2}=-7 \\ e_2=-\frac{5}{2}+\frac{9}{2}=\frac{4}{2}=2 \end{gathered}[/tex]e=-7 no es una solución válida, ya que el espesor debe ser positivo.
Entonces, la solución es e=2.
Respuesta: el ancho del borde es 2 pulgadas.
How many solutions does the equation 5(m + 3) = 6-7m have? Explain how you found your answer.
Expand the left hand side using distributive property:
[tex]\begin{gathered} 5\cdot m+5\cdot3=6-7m \\ 5m+15=6-7m \\ \text{Add 7m to both sides:} \\ 5m+15+7m=6-7m+7m \\ 12m+15=6 \\ \text{subtract 15 from both sides:} \\ 12m+15-15=6-15 \\ 12m=-9 \\ \text{divide both sides by 12:} \\ \frac{12}{12}m=-\frac{9}{12} \\ m=-\frac{3}{4} \end{gathered}[/tex]Find the coordinates of the stationary points of the curve and use the secondderivative to determine the type of each.
Calculate the derivative of the function, as shown below
[tex]\begin{gathered} y=3x+\frac{108}{x}=3x+108x^{-1} \\ \Rightarrow y^{\prime}=3+108((-1)x^{-1-1})=3-108x^{-2} \\ \Rightarrow y^{\prime}=3-108x^{-2} \end{gathered}[/tex]Set y'=0 and solve for x, as shown below
[tex]\begin{gathered} y^{\prime}=0 \\ \Rightarrow3-108x^{-2}=0,x\ne0 \\ \Rightarrow3=\frac{108}{x^2} \\ \Rightarrow x^2=\frac{108}{3} \\ \Rightarrow x^2=36 \\ \Rightarrow x=\pm\sqrt[]{36} \\ \Rightarrow x=\pm6 \end{gathered}[/tex]Their corresponding y-coordinates are
[tex]\begin{gathered} x=\pm6 \\ \Rightarrow y=3(6)+\frac{108}{6}=18+18=36 \\ \Rightarrow(6,36) \\ \text{and} \\ 3(-6)+\frac{108}{-6}=-18-18=-36 \\ \Rightarrow(-6,36) \end{gathered}[/tex]Therefore, the two stationary points are (6,36) and (-6,-36).
Using the second derivative test,
[tex]\begin{gathered} y^{\prime}=3-108x^{-2} \\ \Rightarrow y^{\doubleprime}=-108(-2x^{-2-1})=216x^{-3} \end{gathered}[/tex]Then,
[tex]\begin{gathered} y^{\doubleprime}(6)=\frac{216}{(6)^3}=1>0\to\text{ local minimum at x=6} \\ \text{and} \\ y^{\doubleprime}(-6)=\frac{216}{(-6)^3}=-1<0\to\text{ local maximum at x=-6} \end{gathered}[/tex](6,36) is a local minimum and (-6,-36) is a local maximum.
What is the unit digit of 8433165483 x 946621539 x 5514381138
The value of the unit digit 8433165483 x 946621539 x 5514381138 will be6.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
For getting a number, we will first multiply each digit by its position and then;
8433165483 x 946621539 x 5514381138
Which is;
3 x 9 x 8
= 27 x 8 = 216
Therefore, the unit digit number will be 6.
Learn more about multiplications;
https://brainly.com/question/14059007
#SPJ1
A number decreased
by the sum of the number and three
Answer:
-3
Step-by-step explanation:
x - (x+3)
x - x -3
-3
Three lakes lost water during a drought. Lake Jensen lost one ninth of its water, Lake Parlow lost 10% of its water, and Lake Stockton lost twenty one two hundredths of its water. Which lake lost the least amount of water?
Lake Jensen
Lake Parlow
Lake Stockton
All three lakes lost the same amount of water.
The lake that lost the least amount of water during the drought is Lake Parlow.
Which lake lost the least amount of water?The amount of water lost by Lake Jensen is written as a fraction. A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 1/8.
The amount of water lost by Lake Parlow is written as a percentage. Percentage is the fraction of an amount that is written as a number out of 100.
The amount of water lost by Lake Stockton is written as a decimal. A decimal is the standard form used to write non-integers.
twenty one two hundredths = 21 / 200 = 0.105.
In order to compare the water lost by the three lakes, convert the fraction and the decimal to percentage.
1/9 x 100 = 11.11%
0.105 x 100 = 10.5%
To learn more about percentages, please check: https://brainly.com/question/25764815
#SPJ1
a relationship between decimal, fraction, or 3 Three students wrote percentage. Maggie wrote 75% = Bieber wrote 0.05 = 50% Lee Yung wrote == 0.375 Whích students wrote a correct equation? A. All the above B. None of the above C. Beiber and Lee Yung only D. Lee Yung only 8
To change decimal or fraction to percent multiply them by 100
Example: 1/4 x 100% = 25%, 0.2 x 100% = 20%
Let us check the answer of the 3 students
Maggie wrote 75% = 3/5
Since
[tex]\frac{3}{5}\times100=\frac{300}{5}=60[/tex]Then 3/5 = 60%, not 75%
Maggie is wrong
Bieber wrote 0.05 = 50%
Let us check
0.05 x 100% = 5%, not 50%
Bieber is wrong
Yung wrote 3/8 = 0.375
Let us check
[tex]\begin{gathered} \frac{3}{8}\times100=\frac{300}{8}=\frac{\frac{300}{2}}{\frac{8}{2}}=\frac{150}{4} \\ \frac{150}{4}=\frac{\frac{150}{2}}{\frac{4}{2}}=\frac{75}{2}=37.5 \end{gathered}[/tex]Since 0.375 x 100% = 37.5%
Yung is right
The answer is Lee Yung only
The answer is D
Mr. and Mrs. Hill hope to send their son to college in fourteen years. How much money should they invest now at an interest rate of 9.5% per year, compounded continuously, in order to be able to contribute $8500 to his education?Round your answer to the nearest cent.
continuouslyUsing the formula for a compounded continously
[tex]P=P_0\cdot e^{r\cdot t}[/tex]where P is the amount on the account after t years compounded at an interest rate r when Po is invested in an account.
then,
[tex]\begin{gathered} 8500=P_0\cdot e^{0.095\cdot14} \\ 8500=P_{0^{}}\cdot e^{1.33} \\ P_0=\frac{8500}{e^{1.33}} \\ P_0=2248.056\approx2248.06 \end{gathered}[/tex]Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
The total company's net operating income (NOI) is $103,500.
What is a Net operating income?In accounting, a Net operating income refers to the figure that equals to all revenue from the property minus all reasonably necessary operating expenses.
The computation of the Net operating income is as follows:
= Gross Income - Operating Expenses
= (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200]
= (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]
= 950,000 - (5,01,900 + 2,07,400 + 137,200)
= 950,000 - 8,46,500
= $1,03,500
In conclusion, the total company's net operating income (NOI) is $103,500.
Know more about net operating income
brainly.com/question/15834358
#SPJ1
Round 0.145 to the nearest hundredth
The hundredths are two places from the right of the decimal point, in this case, in the hundredth place we have a 4 (0.145). if the digit on the right of the hundredths is 5 or more, and the second digit (in the hundredth place) is less than 9, then we have to add 1 to it and remove the third digit. In this case, the third digit is 5 and the second digit is 4, then we have to remove the 5 and add 1 to the 4, then we get:
0.145 rounded to the nearest hundredth is 0.15
Brett colors 25% of the total shapes on his paper. He colors 14 shapes. How many total shapes are there on Brett’s paper?
Answer:
56 i think because if 25% = 1/4 and 14 is 25% you would need to multiply 14 by 4 to get 100% or 4/4
Determine the probability of the given opposite event.What is the probability of rolling a fair die and not getting an outcome less than 3?
The Opposite Event rule is the probability that event A happens is equal to one minus the probability that A does not happen.
If P(A) is the probability of A happening, and N(A) is the probability of A don't happen, we can write:
[tex]P(A)=1-N(A)[/tex]Now we can see:
[tex]N(A)=1-P(A)[/tex]This, we if we calculate the probability of getting less than 3, ve can calculate the probability of not getting less than 3.
Then, what are the results that are less than 3? Those are 1 and 2. Thus are the favorable outcomes, and since is a fair dice, there are 6 total possible outcomes.
The probability of A = getting less than 3, is:
[tex]\begin{gathered} P(A)=\frac{2}{6} \\ P(A)=\frac{1}{3} \end{gathered}[/tex]
Now we can calculate the probability of not getting less than 3:
[tex]\begin{gathered} N(A)=1-\frac{1}{3} \\ \end{gathered}[/tex][tex]N(A)=\frac{2}{3}[/tex]
The probability of not getting less than 3 is:
[tex]Probability=\frac{2}{3}\approx0.666[/tex]Or in percentage:
[tex]Probability=66.67\%[/tex]Select the correct answer. Angela is driving across the state to her friend's house. She just filled her fuel tank to its maximum capacity of 26 gallons. If the amount of gas in her car decreases by 2 gallons every 48 miles, which of the following graphs best represents the number of gallons of fuel remaining?
Let L be the amount of gas Angela has at distance d. At d=0 she has 26, and we know that every 48 miles the gas decreases 2 gallons, so the rate of decrease of gas per mile is
[tex]\frac{2\text{ }}{48}=\frac{1}{24}[/tex]Then, the linear equation that models this problem is
[tex]L=-\frac{1}{24}d+26[/tex](I used the minus sign since the amount decreases).
The gas will run out of gas whe she has driven
[tex]\begin{gathered} 0=-\frac{1}{24}d+26 \\ \frac{1}{24}d=26 \\ d=624\text{ miles} \end{gathered}[/tex]Then the graph that best fits the model is number Z. And the answer is D.
Kaitlin got a prepaid debit card with $15 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 21
cents per yard. If after that purchase there was $4.92 left on the card, how many yards of ribbon did Kaitlin buy?
yards
Answer:
Kaitlin bought 48 yards of ribbon.
Step-by-step explanation:
Hey! Let's help you with your question here!
So, let's start by figuring out what we know and what we need to figure out. First of all, we started with $15 and ended with $4.92. We also know that the price of the ribbon is $0.21 per yard and we need to figure out how many yards of ribbon she purchased.
In order to figure this out, we first want to know the difference in the price between what we started and what we ended up with. So, we can subtract! It would look like this:
[tex]15-4.92=10.08[/tex]
So, we figured out that the difference in the price is $10.08, but how do we find out how many yards of ribbon Kaitlin bought? Well, since we know that it is $0.21 cents for a yard of ribbon, we can just take the difference in price and divide it by how much a ribbon cost for a yard of it. So it would look like this:
[tex]10.08/0.21=48[/tex]
We have a nice whole number and that's our answer! Therefore, Kaitlin bought 48 yards of ribbon.
Mathematical Way:
To do it in a more mathematical way, we can put it in the form of a formula. We know that the end total is $4.92 and the initial is $15. We also know that it's $0.21 cents per yard of ribbon but we don't know how many yards she bought. We can let the number of yards she bought represent x in the formula, so we have:
[tex]15=0.21x + 4.92[/tex]
This formula makes sense because we start with $15 at the beginning, so we want to add $4.92 from 0.21x because the end total is the remainder of how many yards Kaitlin bought. The process is essentially the same as the method above. If we were to solve the formula, it would give us the same answer:
[tex]15=0.21x+4.92[/tex]
[tex]15-4.92=0.21x[/tex] - Moving the 4.92 over to the left side, beginning to isolate x.
[tex]10.08=0.21x[/tex] - Subtracting $4.92 from $15.
[tex]\frac{10.08}{0.21} =\frac{0.21x}{0.21}[/tex] - We divide by $0.21 to solve for x.
[tex]48=x[/tex]
And here, we get the exact same answer, 48 yards of ribbon.
Can you please help me out with a question
Given data:
The given radius is r=16 ft.
The expression for the surface area is,
[tex]\begin{gathered} SA=4\pi(r)^2 \\ =4\pi(16ft)^2 \\ =1024\pi ft^2 \end{gathered}[/tex]The expression for the volume of the sphere is,
[tex]\begin{gathered} V=\frac{4}{3}\pi(r)^3 \\ =\frac{4}{3}\pi(16ft)^3 \\ =\frac{16384\pi}{3}ft^3 \end{gathered}[/tex]Thus, the surface area is 1024π sq-ft, and volume is (16384π)/3 cube-ft.
help meeeeeeeeee pleaseee !!!!!
The composition of the function (g o f)(5) is evaluated as: (g o f)(5) = g(f(5)) = 6.
How to Determine the Composition of a Function?To find the composition of a function, we have to first evaluate the inner function for the given value of x that is given as its input. After that, the output of the inner function would then be used as the input for the outer function, which would now be evaluated for the composition of the function.
Given the functions:
f(x) = x² - 6x + 2
g(x) = -2x
We need to find the composition of the function, (g o f)(5), where the inner function is f(x), and the outer function is g(x).
Therefore:
(g o f)(5) = g(f(5))
Find f(5):
f(5) = (5)² - 6(5) + 2
f(5) = -3
Substitute x = -3 into g(x) = -2x:
(g o f)(5) = -2(-3)
(g o f)(5) = 6
Learn more about composition of function on:
https://brainly.com/question/10687170
#SPJ1
Write an absolute value inequality that represents all real numbers more than 4 units away from x
We have to write as inequality the following
"All real numbers more than 4 units away from x""4 units away from x" means four units plus x. So, the expression would be
[tex]|x|>4[/tex]Where x represents real numbers.
This expression is referring to all real numbers more than 4 units and less than -4 units because according to the property of absolute values for inequalities, we have
[tex]|x|>x-4\rightarrow x>x-4,or,x<-(x-4)[/tex]This is represented in the following graph to see it better
For x=1
[tex]\begin{gathered} |1|>x-4\rightarrow1>1-4,or,1<-(1-4) \\ 1>-3 \\ 1<3 \end{gathered}[/tex]Both results are true.
To find this absolute value inequality we used the following property
[tex]|x|>a\rightarrow a>b,or,a<-b[/tex]Where the absolute value inequality has "more than" we rewrite the expression in two inequalities.
Which type of statically graphic uses bars to describe the data ?Dot plot Box plot Histogram
HISTOGRAM
Explanations:
Data are reported using visuals to make reporting easier and ease the understanding of the audience.
Some of the graphic used in statistics to report data and make inference include:
• Bar charts
,• line charts
,• Dot plot
,• Box plot
,• Histogram etc.
Bar charts and histograms make use of bars to report data. This charts are important to detect outliers that may be present in our data.
We can therefore conclude that the type of statically graphic that uses bars to describe data is the HISTOGRAM
2) What is the sum of all the angles in the rectangle
the sum of all the angles in a rectangle is 360°
6) Write the equation of the line, in point-slope form, that passes through the point (-2,5) and has a slopeof 3.
Write the equation of the line, in point-slope form, that passes through the point (-2,5) and has a slope
of 3
___________________________________________________
The point-slope form
y-y1 = m (x-x1)
The slope (m)= 3
The point (x1, y1) = (-2,5)
____________
Replacing
y-5 =3 (x- (-2))
_______________
Answer
(y-5) =3 (x +2)
Do you have any questions regarding the solution?
During the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week. During a rainy stretch in the summer, his grass grew a total of 8 inches in 4 weeks.
Based on the growth rate of Mr. Salina's grass per week in the summer, and in spring, the relationship is not proportional.
How are relationships proportional?When relationships are said to be proportional, it means that they increase or decrease by the same rate.
In the spring, Mr. Salina's grass grows at a rate of 1.5 inches per week.
In the rainy stretch of summer, this rate goes to:
= Total number of inches / Number of weeks
= 8 / 4
= 2 inches per week
This means that the relationship is not proportional and one rate is higher than the other.
Find out more on proportional relationships at https://brainly.com/question/10424180
#SPJ1
Find the value of x so that f(x) = 7.YA6f4200246XX =
The blue line in the graph indicates the function f(x).
The values in the y-axis are the value of the function, that is, the value of f(x) for a given value of x. The x-axis indicates what value of x generates the value in the y-axis.
So, if we want to find the value of x that gives us f(x) = 7, we need to find where is the value '7' in the y-axis, then we draw an horizontal line from this value toward the line of the function (blue line).
This horizontal line will intersect the function in a certain point. This point is where the function has the value 7.
Now, to find the value of x of this point, we draw a vertical line from this point downwards, until it intersects the x-axis.
This way, looking at the image, we can see that the value of x that gives us f(x) = 7 is the value x = 5.
I need help in math can you please help me
We have the following:
[tex]\begin{gathered} \sin \theta=-\frac{8}{17} \\ \theta=\sin ^{-1}(-\frac{8}{17}) \\ \theta=-28.07 \end{gathered}[/tex]now, in Quadrant III (180° to 270°):
[tex]\theta=180+28.07=208.7[/tex]now, for cosine:
[tex]\cos 2\theta=\cos (2\cdot208.7)=0.538=\frac{539}{1000}[/tex]The answer is 539/1000
If y varies directly with x and y = 90 when 3 = 15, then what is y when = 4?y =+
Recall than a direct variation implies the following type of relationship between y and x:
y = k * x
where k is a constant value
Then you have (by dividing by x, the following:
y / x = k (the constant)
then, we are told that when y = 90 , x = 15, so we have:
90 / 15 = k
6 = k
so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?
so we write:
y = k * x
y = 6 * 4
y = 24
This is the value of y when x is 4 since the constant k is 6 as we found above.
Another example:
We need to find the variation relationship for a case that when y = 6, x = 12
We think the same way we did before, starting with the fact that a direct variation is of the form:
y = k * x
given the info that when x = 12, y = 6, we can find the constant k:
6 = k * 12
divide by 12 both sides:
6/12 = k
1/2 = k
So k is 1/2 (one half)
Then we can write the variation as:
y = (1/2) x
(the product of 1/2 times x)
Identify each pair of angles as corresponding, alternate interior, alternate exterior, consecutiveinterior, vertical, or adjacent.
SOLUTION
Given the image on the answer tab;
Explanation;
The two angles are said to be adjacent angles when they share the common vertex and side.
Considering our question;
Susan is putting 11 colored lightbulbs into the string of lights that are three blue light bulbs to yellow light bulbs and six orange light bulb how many distinct orders of lightbulbs are there is two lightbulbs of the same color are considered identical(not distinct)
Using combinations, the number of ways is 36,036.
How to find a number of ways?Combinations are a method of calculating the total outcomes of an event where the order of the outcomes is irrelevant. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations, where n represents the total number of items and r represents the number of items chosen at a time.How many distinct orders of light bulbs are there?
Since we have given thatNumber of white light bulbs = 5Number of orange light bulbs = 6Number of blue light bulbs = 2Total number of light bulbs = 13So, the number of distinct orders of light bulbs if two bulbs of the same color are considered identical.
Therefore, using combinations, the number of ways is 36,036.
To learn more about a number of ways refer to:
brainly.com/question/25966410
#SPJ13
400 meters to 350 meters increase or decrease
In this case we have a negative change, therefore decrease
answer: decrease
Given the following piecewise function, determine the value of g(4) - 3g(3).
Piecewise Function
We are given the piecewise function shown in the figure.
We are required to calculate g(4) - 3g(3).
First, we calculate g(4). Since 4 is greater than 3, we use the second function:
[tex]g(4)=4^4+4^2+4-3=273[/tex]Now we need to calculate g(3). We use the same function because 3 is greater or equal to 3:
[tex]g(3)=3^4+3^2+3-3=90[/tex]Now we calculate:
g(4) - 3g(3) = 273 - 3*90 = 273 - 270 = 3
Answer: 3
