Answer:
7,400
Step-by-step explanation:
First, we have to see that this is an arithmetic sequence... since to get the next element we add 1 to it. (a geometric sequence would be a multiplication, not an addition)
So, we have a, the first term (a = 53), and we have the difference between each term (d = 1), and we want to find the SUM of the first 80 terms.
To do this without spending hours writing them down, we can use this formula:
[tex]S = \frac{n}{2} * (2a + (n - 1) * d)[/tex]
If we plug in our values, we have:
[tex]S = \frac{80}{2} * (2 * 53 + (80 - 1) * 1) = 40 * (106 + 79 * 1)[/tex]
S = 40 * (106 + 79) = 40 * 185= 7,400
Julian has worked for a beverage company for the last five years. He currently earns $12.00 an hour and $16.00 an hour overtime for any additional hours he works past his eight hour workday. On his busiest day, he earned $128.00. How much overtime did he work? Let h = the number of overtime hours.
For the first 8 hours he makes $12.00 per hour.
$12.00 * 8 = $96.00
Now you have $128.00 = 16.00h + $96.00
Subtract 96 from each side:
32 = 16h
Divide both sides by 16:
h = 2
He worked 2 hours of overtime.
for the polynomial
f(x)=-2x^3-2x^2+7x-25
as
x -> -∞, f(x) -> ∞
True
False
Answer: True
Step-by-step explanation:
By definition for a function of the form:
[tex]ax ^ n + ... + bx + c[/tex]
It is true that if [tex]a <0[/tex] and n is odd then:
[tex]\lim_{n \to -\infty}ax^n + ...+bx+c = \infty[/tex]
In this case
[tex]f(x)=-2x^3-2x^2+7x-25[/tex]
Therefore
[tex]a=-2<0[/tex] and [tex]n =3[/tex] → odd number
Then
[tex]\lim_{n \to -\infty}-2x^3-2x^2+7x-25= \infty[/tex]
This means that when [tex]x \to -\infty,\ f(x) \to \infty[/tex]
The statement x -> -∞, f(x) -> ∞ is True
Answer: Its is True
If set A = {3, 4, 7, 9} and if set D = {9, 4, 3, 7}, A = D.
True
False
True, we have the exactly same values in both domains.
Answer:
this is true!
Step-by-step explanation:
it is true because both have the exactly same values in both domains.
hope this helps :)
Devon's mom ordered 3 pizzas for the girls slumber party to eat. The girls ate 5/2 of the pizza. How is this amount of pizza written as a mixed number?
A. 2 1/2
b. 2 1/5
C. 3
Answer:
2 1/2
Step-by-step explanation:
you have 2 whole pizzas and 1 half (1/2)
Claire purchases a new dress for the prom. The dress is priced $160, but it is on sale for 30% off. Claire's aunt works at the store and can give her an additional 10% off. If the sales tax is 7.5%, how much does Claire pay for the dress? a. $93.24 b. $103.20 c. $108.36 d. $120.40
The dress is originally 160$, but we take 30% off which is that same as .3 .
To find 30% or .3 of 160 we multiply 160 by .3 which gets us 48.
48 is 30% of 160 so to find the new price of the dress we need to subtract
160 - 48 = 112. The new price of the dress is 112$.
Since Claire's aunt works at the store Claire will get an additional 10% off from the "new" price which is 112$. 10% is also .1, so we will multiply 112 by .1 which equals 11.20.
As 10% of 112 is 11.20 so we will subtract 11 dollars and 20 cents from the price. 112 - 11.20 = 100.80$.
For sales tax we will do the same thing, multiply 100.80 by .075 which equals 7.56. This time since we are ADDING sales tax, we will add 100.80 and 7.56 rather than subtract. 100.80 + 7.56 = 108.36.
Claire will be paying 108.36$ for the prom dress.
Answer:
c
Step-by-step explanation:
what are the coordinates of the focus of the parabola? (X+1)^2=-8(y-2)
A. (-1,1)
B. (-1,2)
C. (-1,0)
D. (1,-2)
Answer:
C. (-1, 0)
Step-by-step explanation:
(You don't need a picture to figure this out...it's simple algebraic manipulation.)
We could start off by rewriting the equation for the parabola with the negative on the other side, which tells us then that the parabola opens downward:
[tex]-(x+1)^2=8(y-2)[/tex]
Dividing both sides by -1 doesn't change anything. Because this parabola opens downward, the focus is p units below the vertex at the same x-coordinate. The vertex can be found from the equation to be (-1, 2). The standard form of a parabola of this type is
[tex]-(x-h)^2=4p(y-k)[/tex]
where is the number of units between the vertex and the focus. Our equation to find p is:
4p = 8 so p = 2.
That means that the focus is 2 units below the vertex at the x coordinate of -1. Moving 2 units down from the y coordinate of 2 leaves us at a y coordinate of 0. Therefore, the coordinates of the focus have to be (-1, 0)
Evaluate the expression −11−(−7−9) by rewriting the subtraction as addition
Answer:
5
Step-by-step explanation:
Let's rewrite this a bit.
[tex]-11-(-7-9)=-11+7+9[/tex]
This is because there is a -1 before the expression inside the parentheses, so every sign is reversed.
Now we can add.
[tex]-11+7+9=5[/tex]
Kevin ate 2 slices of cake. Ben ate 1 slice. If Kevin ate 2/6 of the cake and all the slices are the same size, what fraction of the cake was eaten in total
1/2 of the cake was eaten
1+2=3. 3/6=1/2
All the slices are the same size
How many liters of pure water should be mixed with 18 liters of a 12% saline solution to make a saline solution that is 3% salt?
Four litres of pure water should be mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
To find the litres of pure water mixed:
Given:
Pure water is mixed with 18 litres of a 12% saline solution to make a saline solution that is 3% salt.
Amount of pure water mixed =?
Now,
As given in the question, we have
18 litres of 12% saline solution
= 18 × (12/100)
= 2.16 litres
To make a saline solution containing 3% salt
Hence, four litres should be mixed to obtain a saline solution having 3% salt.
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The box plots below show student grades on the most recent exam compared to overall grades in the class:
Which of the following best describes the information about the medians?
a. The exam outlier at 60 makes the IQR narrower and the median higher.
b. The class data is more evenly spread, which pulls its median down.
c. The class median is lower than the exam median.
d. The class Q3 is higher than the exam Q3.
i dunno man, B looks about right.
Answer: c. The class median is lower than the exam median.
Step-by-step explanation:
the median is at a lower point on the number line, its to the left of the exam, so that means its lower
What is the domain of a sine function?
Answer:
The domain is all real values
Step-by-step explanation:
The domain is the set of all possible x-values which will make the function "work", and will output real y-values.
In this case, we can observe from the graph that the function is defined for all x-values. So the domain is all real values.
A spherical storage tank has a diameter of 14 ft. How many cubic feet of water will it hold? (Use pi=22/7 .)
V = (π/6)d^3
Using π = 22/7 and d = 14 ft, the volume is
V = (22/7)/6*(14 ft)^3 = 4,312/3 ft^3
?ABC has the points A(1, 7), B(-2, 2), and C(4, 2) as its vertices. The measure of the longest side of ?ABC is units. ?ABC is triangle. If ?ABD is formed with the point D(1, 2) as its third vertex, then ?ABD is triangle. The length of side AD is units.
The solution involves using the distance formula to calculate the lengths of the sides of triangles ABC and ABD, and the Pythagorean theorem to identify the type of triangles they are by their side lengths.
To determine the characteristics of triangle ABC with vertices A(1, 7), B(-2, 2), and C(4, 2), we use the distance formula which is relevant because the length of the side of the triangle labeled a is the difference in the x-coordinates of points A and B. The same applies for side b, being the difference in the y-coordinates of points B and C. The length of side c is derived from the Pythagorean theorem, understanding that c represents the longest side of a right triangle, which is the hypotenuse.
Considering triangle ABD with an additional point D(1, 2), we first need to determine the lengths of the sides by using the formula for distance between two points in a coordinate plane for sides AB, BD, and AD. This will help to ascertain the type of triangle ABD is, based on the lengths of its sides. The length of side AD can be directly obtained since points A and D have the same x-coordinate.
The longest side of triangle ABC, which we determine by comparing the calculated lengths of AB, BC, and AC, will help us state whether the triangle is isosceles, scalene, or equilateral. For triangle ABD, once we have the lengths of AB, BD, and AD, we can determine its type similarly. This understanding stems from the standard geometric principles and the properties of triangles in a Euclidean space.
Need help,
plezz
What is the length of the major axis of the conic section shown below?
(x-3)^2/49 + (y+6)^2/100=1
A. 20
B. 10
C. 14
D. 7
Answer:
A. 20.
Step-by-step explanation:
The denominators 49 and 100 are the squares of 1/2 of the lengths of the minor and major axis. The standard form is x^2/a^2 + y^2/b^2 = 1 so
a = 2 * √49 and b = 2 * √100.
The length of the major axis is therefore 2* √100
= 2 * 10
= 20 (answer).
Answer: A. 20
Step-by-step explanation:
For the general equation of ellipse :-
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
If a > b , then the length of major axis = 2a
If b> a , then the length of major axis = 2b
The given equation : [tex]\dfrac{(x-3)^2}{49}+\dfrac{(y+6)^2}{100}=1[/tex]
Which can be written as :
[tex]\dfrac{(x-3)^2}{7^2}+\dfrac{(y+6)^2}{10^2}=1[/tex]
Here 10 >7 , then the length of major axis =2(10)=20 units
Monica brought some postage stamps.She uses 10 stamps on letters and 5 stamps on postcards.Then her grandmother gives her 20 more stamps. She now has 35 stamps left. How many stamps did Monica originally have?
to find out how many stamps monica originally had, you’d have to do the equation given, “reversed”
equation given: 35 + 20 - 5 - 10
but because we are trying to find how many she originally had left, you’d have to do opposite operations (reverse) in the equation given.
35 - 20 + 5 + 10 = 30
so, this means that monica had 30 stamps originally
What is the value of X on this triangle?
[tex]\bf (x-4)+(3x)+100=180\implies x-4+3x+100=180 \\\\\\ 4x+96=180\implies 4x=84\implies x=\cfrac{84}{4}\implies x=21[/tex]
Express the length of the kite string in terms of trigonometric ratios. A) 70cos40° B) 70sin40° C) 40 sin70° D) 70 sin40°
Answer:
D
Step-by-step explanation:
just took it
70 over sin40 degrees
Answer:
The length of the kite string in terms of trigonometric ratios, if we call it L, is [tex]L=\frac{70}{sin(40\°)}ft[/tex]
Step-by-step explanation:
As we have to use the trigonometric ratios, and knowing that in a right triangle the relation
[tex]hypotenuse*sin(angle)=opposite leg[/tex]
is valid. We call the hypotenuse as L, and we know the other two data (angle and opposite leg), so we have that
[tex]L*sin(40\°)=70ft\Leftrightarrow L=\frac{70}{sin(40\°)}ft[/tex]
Then,
[tex]L=\frac{70}{sin(40\°)}ft[/tex]
is the answer that we are looking for to solve the problem.
The half-life of a certain substance is 20 years. How much of a 100 gram sample will be left after 20 years?
[tex]\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ t=\textit{elapsed time}\dotfill &20\\ h=\textit{half-life}\dotfill &20 \end{cases} \\\\\\ A=100\left( \frac{1}{2} \right)^{\frac{20}{20}}\implies A=100\left( \frac{1}{2} \right)^1\implies A=50[/tex]
50 grams of that sample will be left after 20 years since it’s only gone through one half-life exactly.
Salim bought 31/4kg oranges,151/2kg pineapples and 103/4kg bananas. Find the total weight of fruits. If he used 23/4oranges ,121/4kg pineapples and 61/2kg bananas to make juice in a day then find the weight of fruits left?
Answer:
109 kg total
57 3/4 after
Step-by-step explanation:
31/4 orange
302/4 pineapples
103/4 bananas
436/4 total=109
436/4-205/4=231/4=57 3/4
Justin packed two suitcases for his trip and compared the weights of the items he packed in each of the suitcases. Which statement is true about the box plots? The data for suitcase 1 have an outlier. The data for suitcase 2 have an outlier. Suitcase 1 contains the lightest and heaviest item. Suitcase 2 contains the lightest and heaviest item.
Answer:
A
Step-by-step explanation:
What is the answer to the following problem:
1+1
Answer: 2
Step-by-step explanation:
add the 1 to the other 1 and it equals 2
Answer:
2
Step-by-step explanation:
1 and 1 is 2
Find the length of the hypotenuse.
18
9√2
√18
18√2
Answer:
18
Step-by-step explanation:
The hypotenuse is BC.
According to the Pythagorean Theorem;
[tex]BC^2=AC^2+AB^2[/tex]
Since the base angles are equal:
[tex]AC=BC=9\sqrt{2}[/tex]
We substitute the given values into the formula to obtain:
[tex]BC^2=AC^2+AB^2[/tex]
[tex]BC^2=(9\sqrt{2})^2+(9\sqrt{2})^2[/tex]
[tex]BC^2=81(2)+81(2)[/tex]
[tex]BC^2=162+162[/tex]
[tex]BC^2=324[/tex]
Take positive square root.
[tex]BC=\sqrt{324}[/tex]
[tex]BC=18[/tex]
Hence the hypotenuse is 18 units
Using the parallelogram pictured, find the length of the shorter diagonal. Round your answer to the nearest inch.
Answer:
21 in
Step-by-step explanation:
The law of cosines is helpful for this. The angle opposite the shorter diagonal is the supplement of the angle shown, so is 60°.
If we designate the known sides as "a" and "b", the short diagonal as "c" and the smaller angle as C, then the law of cosines tells us ...
c^2 = a^2 + b^2 -2ab·cos(C)
For the given dimensions, we have ...
c = √(15^2 +24^2 -2·15·24·cos(60°)) = √441 = 21 . . . inches
y varies inversely as x. y = 12 when x = 7. Find y when x = 6.
hope it helps you!!!!!!!!!!!!!
Answer: Y=2 !! ;) XD ;P
How much carpet do I need for the Master Bedroom?
Answer:
The carpet needed is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The area of the master bedroom is the area of a rectangle
so
The area is equal to
[tex]A=bh[/tex]
we have
[tex]b=16\ units[/tex]
[tex]h=18\ units[/tex]
substitute
[tex]A=(16)(18)=288\ units^{2}[/tex]
therefore
The carpet needed is [tex]288\ units^{2}[/tex]
A fair coin is tossed 6 times. Compute the probability of tossing 6 tails in a row.
-----------------------------
Enter your response as a reduced fraction.
Answer:
1/6
Step-by-step explanation:
The probability of tossing 6 tails in a row with a fair coin is 1/64, as each toss's outcome is independent and the probability of tail on a single toss is 1/2.
Explanation:To compute the probability of tossing 6 tails in a row with a fair coin, you recognize that for each individual toss, the probability of getting a tail is ½. Since each toss is independent, you simply multiply the probabilities of each event occurring consecutively. Therefore, the probability of tossing 6 tails in a row is:
(½) × (½) × (½) × (½) × (½) × (½) = ½6
½6 = 1/64
So, the probability of tossing 6 tails in a row is 1/64.
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Can I get an explanation please.
Answer:
The correct option is letter D.
Step-by-step explanation:
We have the following expression:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
We now that sqrt(a*b) = sqrt(a)sqrt(b)
Applying this rule, we have:
sqrt(y^3) + sqrt(9y^3) - 3y*sqrt(y)
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y)
Also we know that a*sqrt(b) = sqrt(b*a^2)
Applying this we have:
sqrt(y^3) + 3sqrt(y^3) - 3y*sqrt(y) = sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3)
Then the result is:
sqrt(y^3) + 3sqrt(y^3) - 3sqrt(y^3) = sqrt(y^3) = y*sqrt(y)
The correct option is letter D.
Which statement is true?
The answer is:
The second option,
[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]
Why?Discarding each given option in order to find the correct one, we have:
First option,[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[2m]{xy}[/tex]
The statement is false, the correct form of the statement (according to the property of roots) is:
[tex]\sqrt[m]{x}\sqrt[m]{y}=\sqrt[m]{xy}[/tex]
Second option,[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]
The statement is true, we can prove it by using the following properties of exponents:
[tex](a^{b})^{c}=a^{bc}[/tex]
[tex]\sqrt[n]{x^{m} }=x^{\frac{m}{n} }[/tex]
We are given the expression:
[tex](\sqrt[m]{x^{a} } )^{b}[/tex]
So, applying the properties, we have:
[tex](\sqrt[m]{x^{a} } )^{b}=(x^{\frac{a}{m}})^{b}=x^{\frac{ab}{m}}\\\\x^{\frac{ab}{m}}=\sqrt[m]{x^{ab} }[/tex]
Hence,
[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]
Third option,[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=ab\sqrt[n]{x}[/tex]
The statement is false, the correct form of the statement (according to the property of roots) is:
[tex]a\sqrt[n]{x}+b\sqrt[n]{x}=(a+b)\sqrt[n]{x}[/tex]
Fourth option,[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=m\sqrt{xy}[/tex]
The statement is false, the correct form of the statement (according to the property of roots) is:
[tex]\frac{\sqrt[m]{x} }{\sqrt[m]{y}}=\sqrt[m]{\frac{x}{y} }[/tex]
Hence, the answer is, the statement that is true is the second statement:
[tex](\sqrt[m]{x^{a} } )^{b}=\sqrt[m]{x^{ab} }[/tex]
Have a nice day!
In an experiment, the temperature fell 48° in 8 minutes. If the temperature fell at the same rate every minute, how many degrees did it change each minute?
Answer:
6 per minute
Because you divide by 8 minutes
(08.06 MC) The distances (y), in miles, of two cars from their starting points at certain times (x), in hours, are shown by the equations below: Car A y = 55x + 32 Car B y = 42x + 58 After how many hours will the two cars be at the same distance from their starting point and what will that distance be? (5 points) 2 hours, 142 miles 2 hours, 145 miles 3 hours, 142 miles 3 hours, 145 miles
Answer:
2 hours, 142 miles
Step-by-step explanation:
Write a distance formula for both cars and then equate these formulas:
Car A: y = 55x + 32 = y = 42x + 58: Car B
Then 55x + 32 = y = 42x + 58 → 13x = 26, and so x = 2
That distance will be 55(2) + 32, or 142 miles.
The cars will reach the same point after 2 hours (first possible answer)
An equation is formed when two equal expressions. The correct option is A, 2hours, and 142 miles.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given the equation for the distance covered by car A in x hours is y = 55x + 32, similarly, the equation for the distance covered by Car B in x hours is y=42x+58.
Now, to know at what time and at what distance the two cars will meet we need to solve the two equations. Since the car will cover the same distance we can write,
y = y
55x + 32 = 42x + 58
55x - 42x = 58 - 32
13x = 26
x = 2
Substitute the value of x in any one of the equations,
y = 55x + 32
y = 55(2) + 32
y = 110 + 32
y = 142
Thus, the car will meet after 2 hours, and the distance will be 142 miles.
Hence, the correct option is A, 2hours, and 142 miles.
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