Solution
We have the following expression:
[tex]4x-2y+3[/tex]Here we have 3 terms:
[tex]4x,\text{ -2y and 3}[/tex]Variable terms:
[tex]4x,-2y[/tex]Constant term
[tex]3[/tex]Choose the correct translation for the following statement.It must exceed seven.Ox<7Ox57Ox>7Ox27
Solution:
Given that a value or quantity must not exceed ten, let x represent the value or quantity.
Since it must not exceed 10, this implies that
[tex]x\leq10[/tex]The second option is the correct answer.
What is the value of sinθ given that (3, −7) is a point on the terminal side of θ?
Solution
[tex]\begin{gathered} \text{ using pythagoras theorem} \\ \\ OB=\sqrt{OA^2+AB^2}=\sqrt{3^2+7^2}=\sqrt{58} \\ \\ \Rightarrow\sin\theta=\frac{AB}{OB}=-\frac{7}{\sqrt{58}}=-\frac{7\sqrt{58}}{58} \end{gathered}[/tex]One Sunday night, the Celluloid Cinema sold $ 1,585.75 in tickets. If the theater sold a children's ticket for $ 7.7S and an adult ticket for $ 10.25, a) write an equation to represent this situation. b) If the theater sold 75 children's tickets, solve your equation to find the number of adult tickets.
Answer:
98 adult tickets
Explanation:
Part A
Let the number of children's ticket sold = c
Let the number of adult's ticket sold = a
Cost of a children's ticket = $7.75
Cost of an adult's ticket = $10.25
Total income from ticket sales = $1,585.75
An equation to represent this situation is:
[tex]7.75c+10.25a=1585.75[/tex]Part B
If the number of children's ticket sold, c = 75
Then:
[tex]\begin{gathered} 7.75c+10.25a=1585.75 \\ 7.75(75)+10.25a=1585.75 \\ 581.25+10.25a=1585.75 \\ 10.25a=1585.75-581.25 \\ 10.25a=1004.50 \\ \frac{10.25a}{10.25}=\frac{1004.50}{10.25} \\ a=98 \end{gathered}[/tex]The number of adult tickets sold by the cinema is 98.
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes:A graph is titled Distance Vs. Time is shown. The x axis is labeled Time in minutes and shows numbers 0, 1, 2, 3, 4, 5. The y axis is labeled Distance from Ocean Surface in meters. A straight line joins the points C at ordered pair 0,66, B at ordered pair 1, 110, A at ordered pair 2, 154, and the ordered pair 3, 198.Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)Part B: What are the initial value and slope of the graph, and what do they represent? (
We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).
Part A:
Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).
Solve p3 = −512.
p = ±8
p = −8
p = ±23
p = −23
Answer:
B. p = −8
Step-by-step explanation:
Hope this helps you on whatever your doing. :))
if its incorrect, please let me know.
The solution is, the value is, p = −8.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
p^3 = −512.
so, we know, p^3 = p*p*p
and, 512 = 8*8*8
now, we get,
p^3 = - 8*8*8
so, solving we get,
p = -8
Hence, The solution is, the value is, p = −8.
To learn more on multiplication click:
brainly.com/question/5992872
#SPJ2
Skis are listed by a manufacturer for $850, less trade discounts of 35% and 18%. What further rate of discount should be given to bring the net price to $446?
The Solution:
The listing price of the Skis by a manufacturer is $850.
A trade discount of 35% was allowed.
[tex]\begin{gathered} 35\text{ \% of \$850=0.35}\times850=\text{ \$297.50} \\ \text{Price}=850-297.50=\text{ \$552.50} \end{gathered}[/tex]Allowing an extra discount of 18%, we get
[tex]\begin{gathered} 18\text{ \% of \$}552.50=0.18\times552.50=\text{ \$99.45} \\ \text{Price}=552.50-99.45=\text{ \$453.05} \end{gathered}[/tex]We are required to find what further rate of discount should be given to bring the net price to $446.00
[tex]\begin{gathered} 453.05-446.00=7.05 \\ To\text{ find the required percentage of discount, we have} \\ \frac{7.05}{453.05}\times100=0.0155612\times100=1.55612\approx1.56\text{\%} \end{gathered}[/tex]Therefore, the correct answer is 1.56%
The sum of two numbers is 40. If 2 is added to the larger number, theresult is equal to twice the smaller number. What are the two numbers?
We have 2 numbers. We can call them x and y, being x the smaller one.
The sum of this two numbers is 40, so we can write:
[tex]x+y=40[/tex]We know that if 2 is added to the larger number (that we name as y), the result is twice the smaller number, that would be 2x. Then, we can express this as:
[tex]y+2=2x[/tex]We can express y in function of x from the second equation and then replace it in the first equation to solve for x:
[tex]y+2=2x\Rightarrow y=2x-2[/tex][tex]\begin{gathered} x+y=40 \\ x+(2x-2)=40 \\ 3x-2=40 \\ 3x=40+2 \\ 3x=42 \\ x=\frac{42}{3} \\ x=14 \end{gathered}[/tex]Now, we can calculate y as:
[tex]\begin{gathered} y=2x-2 \\ y=2(14)-2 \\ y=28-2 \\ y=26 \end{gathered}[/tex]Answer: the two numbers are 14 and 26.
John recently purchased $4,106.00 worth of a stock that is expected to grow in value by 8% each year for the next ten years.Assuming this growth forecast holds, which function will show the value of John's stock in tyears?A(t) = 1.08(54,106)A(O) = 54,106(1.1)A(0) = 54,106(1.08)A(t) = $4,106(1.08)
The exponential growth formula:
[tex]A(t)=A_0(1+r)^t[/tex]Given:
[tex]\begin{gathered} A_0=\text{ \$4106} \\ t=10yrs \\ r=8\%=\frac{8}{100}=0.08 \end{gathered}[/tex]Therefore,
[tex]A(t)=4106(1+0.08)^t=4106(1.08)^t[/tex]Hence, the answer is
[tex]A(t)=\text{ \$}4106(1.08)^t[/tex]Find the sum of the first nine terms of the geometric series 1 – 3 + 9 - 27+....
Hello there. To solve this question, we'll have to remember some properties about geometric series.
Given that we want the sum of
[tex]1-3+9-27...[/tex]First, we find the general term of this series:
Notice they are all powers of 3, namely
[tex]\begin{gathered} 1=3^0 \\ 3=3^1 \\ 9=3^2 \\ 27=3^3 \\ \vdots \end{gathered}[/tex]But this is an alternating series, hence the general term is given by:
[tex]a_n=\left(-3\right)^{n-1}[/tex]Since we just want the sum of the first 9 terms of this geometric series, we apply the formula:
[tex]S_n=\frac{a_1\cdot\left(1-q^n\right?}{1-q}[/tex]Where q is the ratio between two consecutive terms of the series.
We find q as follows:
[tex]q=\frac{a_2}{a_1}=\frac{\left(-3\right)^{2-1}}{\left(-3\right)^{1-1}}=\frac{-3}{1}=-3[/tex]Then we plug n = 9 in the formula, such that:
[tex]S_9=\frac{1\cdot\left(1-\left(-3\right)^9\right?}{1-\left(-3\right)}=\frac{1-\left(-19683\right)}{1+3}=\frac{19684}{4}[/tex]Simplify the fraction by a factor of 4
[tex]S_9=4921[/tex]This is the sum of the nine first terms of this geometric series and it is the answer contained in the second option.
A box of a granola contains 16.8 ounces . It cost $5.19 . What is the cost , to the nearest cent , of the granola per ounce ? A . $0.12 B . $0.31 C . $3.24
The cost per unit ounce is obtained by computing the quotient:
[tex]c=\frac{C}{N}.[/tex]Where:
• c is the cost per unit ounce,
,• C is the cost,
,• N is the number of ounces that you get for C.
In this problem we have:
• C = $5.19,
,• N = 16.8 ounces.
Computing the quotient, we get:
[tex]c=\frac{5.19}{16.8}\cong0.31[/tex]dollars per ounce.
Answer: B. $0.31
Zales sells diamonds for $1,100 that cost $800. What is Zales’s percent markup on selling price? Check the selling price.
Zales's percent markup on the selling price as required in the task content is; 37.5%.
Percentages and markup priceIt follows from the task content that the percent markup on the selling price be determined according to the given data.
Since the cost of diamonds is; $800 while the diamonds sell for $1,100. It follows that the markup on the selling price of the diamonds is;
Markup = Selling price - Cost price.
Hence, we have;
Markup = 1,100 - 800.
Therefore, the markup is; $300.
On this note, the percent markup can be determined as follows;
= (300/800) × 100%.
= 37.5%.
Ultimately, the percent markup on the diamonds is: 37.5%.
Read more on percentages;
https://brainly.com/question/19247356
#SPJ1
the output is 9 less than 5 times the input"
Let the output is y and the input is x, then
output is means y =
9 less than 5 times input means 9 less than 5x
Then
y = 5x - 9
Debra will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $50 and costs anadditional $0.15 per mile driven. The second plan has an initial fee of $59 and costs an additional $0.11 per mile driven.for what amount of driving do the two plans cost the same? i need the answer for miles and cost
First plan cost is modeled as:
50 + 0.15x
where x are the miles driven
Second plan cost is modeled as:
59 + 0.11x
If the two plans cost the same, then:
50 + 0.15x = 59 + 0.11x
0.15x - 0.11x = 59 - 50
0.04x = 9
x = 9/0.04
x = 225 miles
which corresponds to a cost of:
50 + 0.15*225 = $83.75
LE Answer two questions about Systems A and B: System A System B 3.7 +12y = 15 x+4y=5 10y = -2 73 - 10y = -2 1) How can we get System B from System A? Choose 1 answer: A Replace one equation with the sum/difference of both equations B Replace only the left-hand side of one equation with the sum/difference of the left-hand sides of both equations C Replace one equation with a multiple of itself D Replace one equation with a multiple of the other equation 2) Based on the previous answer, are the systems equivalent? In other words, do they have the same solution? Choose 1 answer: А Yes B No
The first equation from System A is what is called a linear combination of the first equation of System B: the equation are equivalent.
System A equation is equal to the System B equation multiplied by a factor of 3 on both sides, so they contain the same information.
Answer: Yes. The systems are equivalent as their equations are equivalent.
Suppose the purr of a cat has a sound intensity that is 320 times greater than the threshold level. Find the decibel value for this cats purr. Round to the nearest decibel.
The decibel value for this cats purr round to the nearest decibel is; 25
How to calculate the decibel level?Decibel (dB) is a unit for expressing the ratio between two physical quantities, such as measuring the relative loudness of sounds. One decibel (0.1 bel) is equal to 10 times the common logarithm of the power ratio.
Decibels are a unit of measure used to describe how loud a sound is. Now, I₀ is the intensity of threshold sound, which is sound that can barely be perceived by the human ear.
The loudness of a sound, in decibels, with intensity I is given by;
dB = 10 log₁₀(I/I₀)
We are given the intensity of a cat’s purr as I = 320I₀
Thus;
dB = 10 log₁₀(320I₀/I₀)
dB = 10 log₁₀(320)
dB = 25.05 ≈ 25
Read more about Decibel Level at; https://brainly.com/question/26209360
#SPJ1
The side-by-side boxplots show consumer ratings of name brand and store brands of peanut butter.
name brands
al The median of name brands peanut butter is
grester thas the median of store
brands. (Hint* greater than or less than)
b) Approximately
% of name brands peanut butter data values are
greater than the median of the store brands peanut butter data values.
a. Median for name brands is greater than the median for store brands data values in the boxplots given.
b. Approximately 75% of the data values of name brands is greater than the median of the data values of store brands.
How to Find the Median of a Data in a Boxplot?A boxplot displays the distribution of a data such that the median is represented by the vertical line that divides the rectangular box.
25% of a data distribution is represented by the beginning of the edge of the box, while 50% is represented by the median, and 75% is represented by the point at the end of the edge of the box in the boxplot.
Therefore:
a. The median of name brands peanut butter is approximately 82-83.
The median of store brands is approximately less than 80.
Thus, we can conclude that, the median for name brands is greater than the median for store brands.
b. The median for store brands is approximately below 25% of the data values for name brands. Therefore, we would conclude that, approximately 75% of name brands data value are greater, compared to the median of the store brands data value.
Learn more about median of boxplot on:
https://brainly.com/question/14277132
#SPJ1
Determine if the proportion is true 1/6= 3/18 Proportion is not true Proportion is true
Question: Determine if the proportion is true 1/6= 3/18
Solution:
we have the following equation that it may be true or false:
[tex]\frac{1}{6}\text{ = }\frac{3}{18}[/tex]But, the above equation is equivalent to:
[tex]1\text{ x 18 = 3 x 6}[/tex]But 1x 18 = 18, and 3x 6 = 18 so the above equation is equivalent to
[tex]18\text{ = 18}[/tex]The above equality always is true, so we can conclude that the proportion is true.
write the equation of the line in slope-intercept form given the follow[tex]slope = - \frac{5}{4} \: y - intercept \: (0 \: - 8)[/tex]
Let's begin by identifying key information given to us:
[tex]\begin{gathered} slope=-\frac{5}{4}\: \\ y-intercept\: (0\: -8) \end{gathered}[/tex]The point-slope equation is given by:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-intercept\: (0\: -8)\Rightarrow(x_1,y_1)=(0,-8) \\ (x_1,y_1)=(0,-8) \\ m=-\frac{5}{4} \\ y-\mleft(-8\mright)=-\frac{5}{4}(x-0) \\ y+8=-\frac{5}{4}x-0 \\ y=-\frac{5}{4}x-8 \\ \\ \therefore\text{The slope-intercept form is }y=-\frac{5}{4}x-8 \end{gathered}[/tex]What is the average rate of change of the function f(x) = 2x^2 + 4 over the interval (-4,-1] ?
The average rate of change is:
[tex]\frac{f(-1)-f(-4)}{-1+4}=\frac{f(-1)-f(-4)}{3}[/tex][tex]f(-1)=2(-1^2)+4=6[/tex][tex]f(-4)=2(-4^2)+4=2(16)+4=36[/tex]then computing the first formula, the average rate of change of f(x) is
[tex]\frac{6-36}{3}=-10[/tex]Find the domain of the rational function.f(x)=x−1/x+4
Given:
[tex]f(x)=\frac{x-1}{x+4}[/tex][tex]\begin{gathered} \text{Let, x+4=0} \\ x=-4 \end{gathered}[/tex]Domain:
[tex]-\infty<-4<\infty[/tex][tex](-\infty,-4)\cup(-4,\infty)[/tex]determine the -domain- and -range- of the graphanswer in interval notation
Explanation: Let's consider two things
- Domain = represented by the minimum and maximum x-values
- Range = represented by the minimum and maximum y-values
Step 1: Let's take a look at the picture below
As we can see above
max x-value = + ∞
min x-value = - ∞
max y-value = 4
min y-value = - ∞
Final answer: So the final answer is
[tex]\begin{gathered} \text{domain}\Rightarrow(-\infty,+\infty) \\ \text{range}\Rightarrow(-\infty,4) \end{gathered}[/tex].
Charlie buys a new car with a sticker price of $9,684. For the down payment,he trades in his old car for $1,400. He finances the balance and makes36 monthly car payments of $253. What is the total amount paid for thecar, including interest?
The total amount = 36 x 253 + 1400 = 9108 + 1400 = $10508
Therefore,
the total amount paid with interest $10508
x + 4y = 4 2x + 4y = 8x=4y=-2
x + 4y = 4
2x + 4y = 8
x=4
y=-2
we know that
If a ordered pair is a solution of a equation, then the ordered pair must satisfy the equation
we have the ordered pair (4,-2)
Verify if the ordered pair is a solution of the given equations
Equation 1
x+4y=4
substitute the value of x and the value of y in the given equation
(4)+4(-2)=4
4-8=4
-4=4 ------> is not true
the ordered pair is not a solution of the equation
Equation 2
2x + 4y = 8
substitute the value of x and the value of y in the given equation
2(4)+4(-2)=8
8-8=8
0=8 -----> is not true
the ordered pair is not a solution of the equation
Where can I find L1 and L4 for a missing vertical angles?
The vertical angle theorem states that the opposite angles formed by two lines that intersect each other are always equal to each other.
Then, if we apply this to the figure shown we can say that by the vertical angle theorem
[tex]\begin{gathered} L1=L3 \\ L2=L4 \\ Meaning\colon \\ L1=45.5 \\ L4=134.5 \end{gathered}[/tex]If A and B are two random events with probabilities of P(A) = 4/9, P(B) = 2/9, P(A ∩ B) = 1/9, calculate P(B|A).a.1/4b.3/4c. 1/2d.1
Answer:
A. 1/4.
Explanation:
Given two random events A and B:
[tex]\begin{gathered} P(B|A)=\frac{P(B\cap A)}{P(A)} \\ P(B\cap A)=P(A\cap B) \end{gathered}[/tex]Substitute the given values:
[tex]P(B|A)=\frac{\frac{1}{9}}{\frac{4}{9}}=\frac{1}{9}\div\frac{4}{9}=\frac{1}{9}\times\frac{9}{4}=\frac{1}{4}[/tex]The value of P(B|A) is 1/4.
Convert: 1200 liters =kiloliters
We have from the question 1200 liters, and we need to convert it into kiloliters.
To find the equivalent in kiloliters to 1200 liters, we can proceed as follows:
1. Find the equivalent between these two measures:
[tex]1\text{ kiloliter=}1000\text{ liters}[/tex]2. Then we have:
[tex]\begin{gathered} 1200liters*\frac{1kiloliter}{1000liters}=\frac{1200}{1000}\frac{liters}{liters}kiloliters=1.2kiloliters \\ \\ \end{gathered}[/tex]Therefore, in summary, we can conclude that 1200 liters are equivalent to 1.2kiloliters.
Help me please I paid for the tutor Version of this app and it can’t fine me a tutor like I just paid 100 dollars for nothing
The Solution.
The function is increasing on the interval below:
[tex](-2.5,1)[/tex]The function is decreasing on the intervals below:
[tex](-\infty,-2.5)\cup(1,\infty)[/tex]The Caldwell family placed a large back-to-school order online. The total cost of the clothing was $823,59 and the shipping weight was 32 lb. 10 oz. They live in the LocalZone (shipping = $5.87, plus $. 11 per lb. for each lb. or fraction of a lb. above 15 lbs.) and the sales tax rate is 7.5%. Find the total cost of the order.$864.43$876.77$893.21o $901.22None of these choices are correct.
The breakdown of fees paid by the Caldwell family are calculated and shown below;
[tex]\begin{gathered} \text{Total cost of clothing = \$823.59} \\ \text{Sales tax = 7.5\% of \$823.59} \\ =\frac{7.5}{100}\times823.59=61.769 \\ \text{Sales tax = \$61.77} \\ \\ \text{Shipping fe}e \\ \text{Total weight of item = 32lb 10oz }\approx\text{ 33lb} \\ \text{The excess weight above 15lbs = 33 - 15=18lbs} \\ \text{Shipping cost on the extra 18lbs = \$0.11}\times18=1.98 \\ \text{Total cost on shipping = \$5.87+\$1.98=\$7.85} \end{gathered}[/tex]The total cost of the order will now be
Total cost of clothing = $823.59
Shipping cost = $7.85
Sales tax = $61.77
TOTAL = $823.59 + $7.85 + $61.77 = $893.21
Therefore, the total cost of the order is $893.21
cuales son los dos numeros enteros cuyo producto es 294 y cuyo cociente es 6?
1.- You need two equations
- x*y = 294
- x/y = 6
2.- Solve for x
x = 6y
(6y)y = 294
3.- Simplifying
6y^2 = 294
-Solve for y
y^2 = 294/6
Given the conversion factor which cube has the larger surface area?
Given the surface area of a cube as
[tex]\begin{gathered} SA=6l^2 \\ \text{where l is the length} \end{gathered}[/tex]Given Cubes A and B
[tex]\begin{gathered} \text{Cube A} \\ l=19.5ft \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B } \\ l=6m\text{ } \\ \text{ in ft}\Rightarrow\text{ 1m =3.28ft} \\ l=6\times3.28ft=19.68ft \end{gathered}[/tex]Find the surface area of the cubes and compare them to know which one is larger
[tex]\begin{gathered} \text{Cube A} \\ SA=6\times19.5^2=6\times380.25=2281.5ft^2 \end{gathered}[/tex][tex]\begin{gathered} \text{Cube B} \\ SA=6\times19.68^2=6\times387.3024=2323.8144ft^2 \end{gathered}[/tex]Hence, from the surface area gotten above, Cube B has a larger surface area than Cube A
