Answer:
D. 3x2 + 4x+1
Step-by-step explanation:
This answer is a trinomial because there are 3 terms being used, 3x2, 4x, and 1.
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There are 870 boys and 800 girls in a school.
The probability that a boy chosen at random studies Spanish is 2/3
The probability that a girl chosen at random studies Spanish is 3/5
a) Work out the number of students in the school who study Spanish.
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?
Answer: a) 1060, b) [tex]\dfrac{61}{167}[/tex]
Step-by-step explanation:
Since we have given that
Number of boys = 870
Number of girls = 800
Probability that a boy chosen studies Spanish = [tex]\dfrac{2}{3}[/tex]
Probability that a girl chosen studies Spanish = [tex]\dfrac{3}{5}[/tex]
So, the number of boys in the school who study Spanish would be
[tex]\dfrac{2}{3}\times 870=290\times 2=580[/tex]
So, the number of girls in the school who study Spanish would be
[tex]\dfrac{3}{5}\times 800\\\\=3\times 160\\\\=480[/tex]
So, total number of students who study Spanish would be :
[tex]480+580=1060[/tex]
b) What is the probability, as a fraction in its simplest form, that a student
chosen at random from the whole school does not study Spanish?
Number of students who do not study Spanish would be:
[tex](870+800)-1060\\\\=1670-1060\\\\=610[/tex]
So, the probability of students who does not study Spanish would be :
[tex]\dfrac{610}{1670}=\dfrac{61}{167}[/tex]
Hence, a) 1060, b) [tex]\dfrac{61}{167}[/tex]
There are 1060 students who study Spanish in the school. The probability that a student chosen at random from the whole school does not study Spanish is 610/1670.
Explanation:To work out the number of students in the school who study Spanish, we need to find the number of boys and girls who study Spanish and add them together. The probability that a boy chosen at random studies Spanish is 2/3. So the number of boys who study Spanish is 870 * (2/3) = 580. The probability that a girl chosen at random studies Spanish is 3/5. So the number of girls who study Spanish is 800 * (3/5) = 480. Therefore, the total number of students who study Spanish is 580 + 480 = 1060.
To find the probability that a student chosen at random from the whole school does not study Spanish, we subtract the probability that a student does study Spanish from 1. The probability that a student does study Spanish is 1060 (students who study Spanish) divided by 1670 (total number of students in the school). Therefore, the probability that a student does not study Spanish is 1 - (1060/1670) = 610/1670, which is already in its simplest form.
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John and Sarah are each saving money for a car. The total amount of money John will save is given by the function j(x)= x^2 +2x, where x represents the number of weeks. The total amount of money Sarah will save is given by the function s(x)= -3x+6, where x represents the numbers of weeks.
Explain the point of intersection in context to the problem. Show all work
Answer:
See below.
Step-by-step explanation:
Where the graphs of the functions intersect it represents the number of weeks when they have both saved the same amount of money. So by solving the system we can find the number of weeks and that amount of money.
y = x^2 + 2x
y = -3x + 6 so
x^2 + 2x = -3x + 6
x^2 + 5x - 6 = 0
(x + 6)(x - 1) = 0
So x = 1 ( we ignore the negative)
So after 1 week they have saved the same amount and the amount is -3 + 6 = 3.
Are you sure that -3x + 6 is right - because Sarah does not save anything after year 1 . The equation has a negative slope!!
The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 5 units, then what is the value of k?
Step-by-step explanation:
k is the variable for the translations on the Y-axis so if u move the graph 5 units down then k would be 5
Answer:
k=5
Step-by-step explanation:
It costs $8.50 to park a vehicle at the Wild Rapids Water Park. The admission price to the park is $27.50 per person. If a group in one vehicle spends $228.50 to park and enter the park, how many people attended? Write an equation, and then solve.
Answer:
8 people
Step-by-step explanation:
step1:move 8.50 to the other side
228.50=8.50+27.50x
220=27.50x
step 2:find x by dividing
220=27.50x
x=8
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There are 8 people who attended the park.
To solve the problem, let's define the variables and write an equation. Let x be the number of people who attended. The total cost is the sum of the parking fee plus the admission fees.
The parking fee is $8.50, and the admission fee per person is $27.50. Therefore, the total cost can be expressed as:
Total Cost = Parking Fee + (Admission Fee per Person * Number of People)
This simplifies to:
$228.50 = $8.50 + $27.50 * x
First, subtract the parking fee from the total cost:
$228.50 - $8.50 = $27.50 * x
$220 = $27.50 * x
Now, divide both sides by the admission fee per person to find x:
x = $220 / $27.50
x = 8
Thus, 8 people attended the park.
You roll a 6-sided die two times. What is the
probability of rolling a 6 the first time and 2
the second time?
*write your answer as a fraction
Answer:
First time : 1/6
Second time : 1/6
Step-by-step explanation:
Answer:
1/6
Step-by-step explanation:
Since it is a six-sided die, you will roll every number at least one time, making the answer 1/6
is the expression 4 - x the same as x – 4? Explain
Answer:
Yes
Step-by-step explanation:
The order of the factors does not alter the product
Yes because of your property’s
Find the inner product for 5,2 multiply -3,7 and state whether the vectors are perpendicular.
Answer:
-1 ; no
Step-by-step explanation:
5 x -3 + 2 x 7 = -1
And since -1 is not zero the vector will not be perpendicular
Answer:
C on edge
Step-by-step explanation:
A toy rocket launched into the air has a height (h feet) at any given time (t seconds) as h=- 16t^2 + 160t until it hits the ground. At what time(s)is it at a height of 9 feet above the ground?
I will comment the other answer choices but help me please
Do I choose A or B?
If so: B
Create a rational function with a non-constant denominator) that has NO vertical
asymptotes.
Answer:
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]
Step-by-step explanation:
A rational function with no vertical asymptotes contains an avoidable discontinuity, an example is presented hereafter:
[tex]y = 3[/tex]
[tex]y = 3\cdot 1[/tex]
[tex]y = 3\cdot \frac{x+1}{x+1}[/tex]
[tex]y = \frac{3\cdot (x+1)}{x+1}[/tex]
If r = 4 and ^a8 = 100, what is the first term of the geometric
sequence?
The first term of the geometric sequence is 0.0061
Step-by-step explanation:
The general form of geometric sequence is a, ar, ar²,ar³,.......
where,
a is the first term of the sequence.r is the common ratio. Here, the common ratio r = 4.The 8th term of the sequence is 100. Hence n = 8.The formula to find the nth term of the geometric sequence is given by :
⇒ [tex]n_{th} term = ar^{n-1}[/tex]
⇒ [tex]8_{th}term = a\times4^{8-1}[/tex]
⇒ [tex]100 = a \times 4^{7}[/tex]
⇒ [tex]100 = a \times 16384[/tex]
⇒ [tex]a = \frac{100}{16384}[/tex]
⇒ a = 0.0061
Therefore, the first term of the geometric sequence is 0.0061
Answer:
The first term of the geometric sequence is 0.0061
can someone help me with this equation plsss i really need it
3(6x–5)–7(3x+10)=0
Answer:
-28 1/3
Step-by-step explanation:
Which of the following are square roots of the number below? Check all that
apply.
64
A. -8
B. 64 1/2
C. 32
D. -(64) 1/2
Answer:
A
Step-by-step explanation:
Just square all of them to find 64
The square roots of 64 are -8 and 8. Neither 32 nor 64 1/2 are square roots of 64.
Explanation:The square root of a number is a value that, when multiplied by itself, gives the original number. When dealing with real numbers, remember that a number can have two square roots: a positive root and a negative root.
For the number 64, we know 8 * 8 equals 64, so 8 is a square root. As a negative number multiplied by a negative number results in a positive number, -8 * -8 also equals 64. Therefore -8 is also a square root of 64.
Option A, -8, and B, '(64) 1/2' or -8, are correct. The square root of 64 is not 32 and 64 1/2.
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a) Write down 375 as the product of prime factors.
Give your answer in index form.
b) Work out the highest common factor of 375 and 150.
Answer:
a) 3x5³
b) 75
Step-by-step explanation:
a) find the Prime factors of 375 by dividing your number by prime numbers (you answers must be whole) use a factor tree to help you
a) do the same to 150
one you have you answers in this case we have
375- 3x5x5x5
150 - 2x3x5x5
you collect all the like terms, this will be 3x5x5 then you just simply multiply it And it gives you 75
375 as a product of prime factors is 3x5^3 and the highest common factor of 375 and 150 is 25.
Explanation:To express 375 as the product of prime factors, you must first determine the prime numbers that when multiplied together will equal 375. The prime factors of 375 are 3 and 5. So, 375 can be written as 3x5^3.
Next, to find the highest common factor of 375 and 150, you need to first find the prime factors of both numbers. As shown above, the prime factors of 375 are 3 and 5. The prime factors of 150 are 2, 3 and 5.
The highest common factor is identified by locating the largest number that can divide both numbers without leaving a remainder. The highest common factor of 375 and 150 is hence, 25 because it's the greatest factor that both numbers have in common.
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0.00005026 as a scientific notation
Answer:
5026*10^-5
Step-by-step explanation:
Answer:
5.026 x 10-5
Step-by-step explanation:
A person invested $690 in an account growing at a rate allowing the money to double
every 7 years. How much money would be in the account after 3 years, to the nearest
dollar?
The amount of money in the account after 3 years would be $828.
Explanation:To determine the amount of money in the account after 3 years, we need to find the number of times the money doubles in a period of 3 years, given that it doubles every 7 years. To find this, we divide 3 by 7 to get the number of doubling periods which is approximately 0.4286. Since the money doubles every 7 years, we multiply the initial investment of $690 by 2 raised to the power of 0.4286 to find the final amount.
Using the formula A = P(1+r)^n, where A is the final amount, P is the initial investment, r is the interest rate per period, and n is the number of periods, we have P = $690, r = 100% (as the money doubles), and n = 0.4286. Substituting these values into the formula, we get A ≈ $827.84. Hence, the amount of money in the account after 3 years, to the nearest dollar, would be $828.
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Final answer:
To calculate the future value of an investment that doubles every 7 years after 3 years, we use the exponential growth formula with an annual interest rate determined by the Rule of 70, resulting in approximately $918.
Explanation:
To determine how much money will be in the account after 3 years given that the amount doubles every 7 years, we can use the formula for exponential growth. The formula is A = P(1 + r/n)nt, where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (as a decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
Since the money doubles every 7 years, the effective annual interest rate 'r' that would cause this can be found using the Rule of 70. The Rule of 70 states that to find the number of years required to double the money at a given interest rate, you divide 70 by the annual interest rate. Here, we have that number already (7 years), so we can rearrange to find the interest rate: rate = 70 / time to double. Therefore, the interest rate is 70 / 7, which equals 10% or 0.10 as a decimal.
However, we are looking for the amount after 3 years, not 7. Thus, we need to adjust our formula to account for this shorter time period:
A = P(1 + r)^t
A = 690(1 + 0.10)^3
A = 690(1.331)
A ≈ $918
So, after 3 years, the investment would grow to approximately $918, to the nearest dollar.
Find the area of the polygon.
_12 cm
| 19 cm
12 cm
The area of the polygon is |
square centimeters.
Answer:
[tex]A = 1172.965\,cm^{2}[/tex]
Step-by-step explanation:
Let be a side of 12 cm (l) and an apothem of 19 cm (p). First, the number of sides has to be determined:
[tex]n =\frac{360^{\textdegree}}{2\cdot \tan^{-1}\left(\frac{6\,cm}{19\,cm} \right)}[/tex]
[tex]n = 10.271[/tex]
The polygon has ten sides and the side length shall be re-adjusted:
[tex]\theta = \frac{360^{\textdegree}}{10}[/tex]
[tex]\theta = 36^{\textdegree}[/tex]
The side length is:
[tex]l = 2\cdot (19\,cm)\cdot \tan 18^{\textdegree}[/tex]
[tex]l = 12.347\,cm[/tex]
The area of the polygon is:
[tex]A = \frac{n\cdot l \cdot p}{2}[/tex]
[tex]A = \frac{(10)\cdot (12.347\,cm)\cdot (19\,cm)}{2}[/tex]
[tex]A = 1172.965\,cm^{2}[/tex]
In a survey, 15 high school students said they could drive
and 15 said they could not. Out of 60 college students
surveyed, 30 said they could drive. Micah concluded that
knowing that a person is in college means they are more
likely to drive. Is Micah's conclusion correct?
Answer:
No
Step-by-step explanation:
this is because only 50% of the college students said they could drive there fore it doesn't make sense.
Answer:No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.
Step-by-step explanation: its on e2020
What do the three red tiles in the model of the equation below represent?
2 long x tiles and 3 square 1 tiles = 3 negative x tiles
–3
3
–3x
3x
Answer:
the answer is c
Step-by-step explanation:
Answer:
The answer is -3x because the red tiles represent -x so since there are 3 -x tiles the answer would be -3x
Taylor is thinking of a three-dimensional object.
All interior angles are right angles.
The object has 8 vertices.
Only 4 of the object's 6 faces are congruent.
Which figure best describes the object that Taylor is thinking of?
A.
cube
B.
rectangular prism
C.
triangular prism
D.
square pyramid
NEED HELPP
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Bree made 48 cookies. She used 1,104 chocolate chips for all of the cookies. How many chocolate chips were in each cookie?
Answer:
23
Step-by-step explanation:
its 23 beacuase 1104 divided by 48 is 23 so its 23 chips
Answer: 23
Step-by-step explanation: 1,104 divided by 48 = 23
A touch tank has a height of 3 feet. Its length is three
times the width. The volume of the tank is 270 cubic feet.
Find the length and width of the tank,
3 ft
Answer:
5.5 cu ft vol = L*w*h* w=x L= 3x h=3
270= 3[3x*x]
Final answer:
To find the length and width of the touch tank, we need to use the formula for the volume of a rectangular tank. By substituting the given values and solving the equation, we can find the width and length.
Explanation:
Let's assume that the width of the touch tank is x feet. So, the length of the tank would be 3x feet.
The volume of a rectangular tank is given by the formula volume = length × width × height. We can substitute the given values into this formula.
270 = (3x) * x * 3
Simplifying the equation, we get:
270 = 9x^2
Dividing both sides of the equation by 9:
x^2 = 30
Taking the square root of both sides of the equation:
x = √30 ≈ 5.48
Therefore, the width of the touch tank is approximately 5.48 feet. Since the length is three times the width, the length would be approximately 3 × 5.48 = 16.44 feet.
Which sphere has a volume of approximately 113.1 cubic inches?
A.Glass ball: r = 3 inches
B.Soccer ball: r = 4 inches
C.Lamp: d = 10 inches
Answer:
it's a glass ball r = 3 inches
Step-by-step explanation:
edgenutiy
Answer:
glass ball 3 inches ( ; ( :
Step-by-step explanation:
Which sphere has a volume of approximately 113.1 cubic inches?
Glass ball: r = 3 inches
A glass ball.
Soccer ball: r = 4 inches
A soccer ball.
Lamp: d = 10 inches
A round lamp.
The Lumberjack Hardware store found that 5 out of every 10 paint sprayers they recently received were not properly assembled. If they received 385 paint sprayers, about how many paint sprayers can they expect to be faulty?
Answer: 193 faulty paint sprayers
Step-by-step explanation: 5/10 is = to 1/2 so half of them are faulty
next divide 365 by 2 to get 192.5 remember if the decimal is 5 or greater you can round up since you cannot have half a paint sprayer you have to round up to 193 paint sprayers
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Find the rule of f(2)
Answer:
f(2) = 25
Step-by-step explanation:
Given
f(x) = [tex](5)^{x}[/tex]
To evaluate f(2) substitute x = 2 into f(x)
f(2) = [tex](5)^{2}[/tex] = 25
Peter ran 4 ⅔ miles on Tuesday. On Wednesday, he ran ⅘ of this distance. How far did he run?
Answer:
3.73333
Step-by-step explanation:
Answer:
Step-by-step explanation:
Distance = 4/5 of 4 2/3
[tex]=\frac{4}{5}*\frac{14}{3}\\\\=\frac{4*14}{5*3}[/tex]
= 56/15
= 3 11/15 miles
40.40
What is the area of the base of the cone below? Round the answer to the nearest tenth if necessary.
V = 52 in 3
14.7 in2
Please hurry 29 points
17.3 in2
18 5 in 2
19.5in 2
Answer:
D) 19.5 in^2
Step-by-step explanation:
Volume is 1/3base * height
52in^3 = 1/3x*8
multiply by 3
156in^3 = x*8
divide by 8
19.5 = x
x = 19.5
Answer:
D
Step-by-step explanation:
what is -2(x-5)-4=-22 ??
Answer:
x = 14
Step-by-step explanation:
-2(x-5)-4=-22
Distribute
-2x +10 -4 = -22
Combine like terms
-2x+6 =-22
Subtract 6 from each side
-2x+6-6 = -22-6
-2x = -28
Divide each side by -2
-2x/-2 = -28/-2
x = 14
The cost to enter a waterpark increases from $56 per person to $73 per person. What percent of the entry fee increase
Final answer:
The percent increase of the waterpark's entry fee is approximately 30.36%, which is calculated by finding the difference between the new and original cost, dividing by the original cost, and then converting that number to a percentage.
Explanation:
To calculate the percent increase of the entry fee to the waterpark, we need to follow these steps:
Find the amount of the increase by subtracting the original cost from the new cost.Divide the amount of the increase by the original cost.Multiply the result by 100 to convert it to a percentage.Step 1: The increase in cost is $73 - $56 = $17 per person.
Step 2: The increase divided by the original cost is $17 ÷ $56 ≈ 0.30357.
Step 3: To find the percent increase, we multiply the result from step 2 by 100: 0.30357 × 100 ≈ 30.36%.
Therefore, the percent increase of the entry fee is approximately 30.36%.
To find the percent increase in the entry fee, subtract the old fee from the new fee, divide by the old fee, and multiply by 100. The entry fee increase is approximately 30.36%.
Explanation:To find the percent increase in the entry fee, you need to calculate the difference between the new fee and the old fee, and then divide that difference by the old fee. Finally, multiply the result by 100 to get the percentage.
Find the difference in the fees: $73 - $56 = $17Divide the difference by the old fee: $17 ÷ $56 ≈ 0.3036Multiply the result by 100 to get the percentage: 0.3036 × 100 ≈ 30.36%The entry fee increase is approximately 30.36%.
A carpenter finds that the measure of an angle formed between a vaulted ceiling and one wall is 67°. How many degrees is the supplement of this angle?
Answer:
113 degrees
Step-by-step explanation:
To find the supplement angle, subtract 67 degrees from 180 degrees
180 - 67 = 113 degrees
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