Answer: 300 feet
Step-by-step explanation:
Note that:
[tex]120-90 = 30[/tex]
[tex]150-120 = 30[/tex].
Then the balloon rises at a constant rate of 30 meters per minute.
We can represent this situation through an arithmetic sequence as shown below
[tex]a_n =a_1 + d(n-1)[/tex]
Where [tex]a_1=90[/tex] is the first term of the sequence and [tex]a_n[/tex] is the n-th term of the sequence and [tex]d=30[/tex] is the common difference between two consecutive terms.
In this case we look for the height of the balloon after 8 minutes.
Then we look for [tex]a_8[/tex]
[tex]a_8 = 90 + 30(8-1)[/tex]
[tex]a_8 = 90 + 30(7)[/tex]
[tex]a_8 = 300[/tex]
Answer:
[tex]\boxed{\text{300 ft}}[/tex]
Step-by-step explanation:
You have an arithmetic sequence in which
a₁ = 90
a₂ = 120
a₃ = 150
1. Calculate the explicit formula
This is an arithmetic sequence, because there is a constant difference of 30 between consecutive terms.
The explicit formula for the nth term of an arithmetic sequence is
aₙ = a₁ + d(n - 1 )
a₁ is the first term, and d is the difference in value between consecutive terms. Thus,
aₙ = 90 + 30(n - 1) = 90 + 30n - 30
aₙ = 30n + 60
2. Calculate the eighth term
a₈ = 30 × 8 + 60 = 240 + 60 = 300
[tex]\text{In 8 min, the balloon rises }\boxed{\textbf{300 ft}}[/tex]
What is the way to solve this one? Please explain how you got your answer.
Answer:
[tex]\frac{5x-12}{x-1}[/tex]
Step-by-step explanation:
[tex]\frac{8x-5}{x-1}[/tex]-[tex]\frac{3x+7}{x-1}[/tex]
= [tex]\frac{8x-5-3x-7}{x-1}[/tex]
= [tex]\frac{5x-12}{x-1}[/tex]
PLEASE HELP QUICK Graph the line for y+2=32(x+4) on the coordinate plane. does anyone know the cordinates will mark brainliest.
Answer: Graph (-4, -2) and (-2, 1)
Step-by-step explanation:
[tex]\text{The given equation is: }y+2=\dfrac{3}{2}(x+4)\\\\\text{which is of the form: }y-y_1=m(x-x_1)\\\implies(x_1, y_1)=(-4, -2)\quad and \quad m=\dfrac{3}{2}\implies (x+2, y+3)\\\\.\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (-4+2, -2+3)=(-2, 1)[/tex]
So, two possible points are (-4, -2) and (-2, 1).
Plot those two coordinates and draw a line through them.
Answer:
Got it right on the test, here is the answer.
Step-by-step explanation:
choose the correct simplification of the expression (8x^2)^3.
A 24x^6
B 512x^6
C 512x^5
D 24x^5
Answer:
The correct answer option is B. [tex] 5 1 2 x ^ 6 [/tex].
Step-by-step explanation:
We are given the following expression and we are to choose its correct simplification from the given answer options:
[tex] ( 8 x ^ 2 ) ^ 3 [/tex]
Applying the power to the terms inside the bracket to get:
[tex]8^3 \times x^{2.3[/tex]
Solving it further by applying the power property of exponent to get:
[tex] 5 1 2 x ^ 6 [/tex]
Carla is cutting pieces of string that are exactly 24 3/8 in long how many pieces can she cut from a ball of string that is 100 ft
Answer:
4 1/8 pieces
Step-by-step explanation:
Since you are using a string that is 100 ft. long then and you need exactly 24 3/8 ft. sections, you would do these calculations:
3/8 = 0.375
100/24.375 = 4.1026
.1026 = 1/8
4 1/8 ft long pieces
Answer:
The string is cut into 4.1025 pieces.
Step-by-step explanation:
We are given the following information:
Length of the string = 100 feet
Length of one piece = [tex]24\displaystyle\frac{3}{8} = \displaystyle\frac{195}{8} ~feet[/tex]
Number of pieces =
Formula:
[tex]\text{Number of pieces} = \displaystyle\frac{\text{Length of string}}{\text{Length of one piece}}[/tex]
Number of pieces =
[tex]\displaystyle\frac{100}{\frac{195}{8} } = \displaystyle\frac{100\times 8}{195}\\\\=\displaystyle\frac{800}{195} = 4\displaystyle\frac{4}{39} = 4.1025[/tex]
Thus, the string is cut into 4.1025 pieces.
Suppose an investment of $1700 doubles in value every 10 years how much is investment worth after 20 years
Answer:
doubles every 10 years
20 years, so it has doubled 2 times
1700 times 4=6800
it is worth $6800
Assume that a population of newly discovered small creatures called “porgs” in a remote island lays eggs with three distinct appearances: patterned with dots, white, or dark grey. Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs. You randomly selected 25 eggs, 10 of which were dotted, 13 were grey and 2 were white. Based on this information, what is the probability that you would only collect 2 white eggs?
you have a 1/12.5 chance of getting a white egg. so the theoretical possibility of getting only two white eggs is 1/156.25. so it is very unlikely to get two white eggs
Answer:
0.029
Step-by-step explanation:
Last year, the porgs laid 30 dotted eggs, 40 grey eggs, and 15 white eggs.
Total eggs = 30+40+15 = 85 eggs
White eggs = 15
So, probability of getting 1 white egg = [tex]\frac{\text{No. of white eggs}}{\text{Total no. of eggs}}[/tex]
= [tex]\frac{15}{85}[/tex]
Remaining white eggs = 14
Total eggs remaining = 84
Probability of getting 1 white egg on second draw = [tex]\frac{14}{84}[/tex]
So, the probability that you would only collect 2 white eggs =[tex]\frac{15}{85} \times \frac{14}{84}[/tex]
=0.029
Hence the probability that you would only collect 2 white eggs is 0.029.
Two rigid transformations are used to map JKL To MNQ-
The first is a translation of vertex L to vertex Q. What is the
second transformation?
a reflection across the line containing LK
a reflection across the line containing jk
a rotation about point l
a rotation about point k
Answer:
Step-by-step explanation: it’s c
Answer:
C. a rotation about point L
Step-by-step explanation:
the ratio of chicken to pigs to horses in a farm is 10:2:3.if there is 120 chickens in the farm then the number of the horses in the farm is
Answer:
36
Step-by-step explanation:
The 10 part of the ratio represents 120 chickens. Divide 120 by 10 to find the value of one part of the ratio.
120 ÷ 10 = 12 ← value of 1 part of the ratio, hence
3 parts = 3 × 12 = 36 ← number of horses
The number of horses on the farm is 36.
Given that, the ratio of chicken to pigs to horses on a farm is 10:2:3 and the number of chickens on the farm is 120.
What is the ratio?Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.
We can write the given ratio 10:2:3 as 10x: 2x: 3x.
So, 10x=120
⇒x=12
Then, the number of horses=3x=36
Therefore, the number of horses on the farm is 36.
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When 60% of a number is added to the number, the result is 192
Answer:
the number (x) is 120.
Explanation:
100% + 60% = 160% = 1.6
(just multiply it by 1.6 because it is equal to 60%)
The equation for the problem can be expressed as x + 0.6x = 192. To solve for x, you simplify the equation and isolate x, resulting in the answer of 120.
Explanation:This problem is a simple algebraic problem in which we're trying to find a number that satisfies a given condition. To solve this, we need to express the problem as an equation. Let's assume the number we're looking for is denoted as x. So, according to the problem, we have the following equation:
x + 0.60x = 192
The steps to solve this equation are as follows:
Combine like terms: 1x + 0.60x = 1.60xTo isolate x, divide both sides of the equation by 1.60: x = 192 / 1.60Doing the division on the right side, we find x = 120, which is our number.
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Which expression is not equivalent to the other three?
A: 2x + 2+ 2x + 3x – 8
B:4 + 7x – 2
C:–2 + 5x + 2x – 4
D:8x – x – 6
Answer:
b. 4+7x-2
Explanation:
when you add like terms for the first equation it becomes 7x-6
the second one becomes 7x+2
the third one becomes 7x-6
and the last one is also 7x-6
which means the second one is not equivalent
Answer:
B. 4 + 7x – 2
Step-by-step explanation:
HEEEELLLLLLLLLLPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP ME
Answer:
41.79%
Step-by-step explanation:
To be on the swim team, we look at the right most (total) number int he table of "on the swim team" row. That is 28.
The grand total is the bottom-rightmost. That is 67.
Hence, probability of being on swim team is 28/67 = 41.79%
What is the domain for the function f(x) = 2^x-5.
Answer:
X= All real Numbers
Step-by-step explanation:
Answer:
All real numbers
Step-by-step explanation:
The domain is the set of x values that we can plug into the function and it will have a y value.
The domain is the "allowed" x values of a function.
Exponential functions of the form [tex]y=a^x[/tex], where a is a constant have domain of "all real numbers".
The function in this problem is of this form with a "-5" at the end, which shifts the function vertically 5 units down. This doesn't affect x values (or domain)
Hence, the domain is the set of all real numbers.
how many 3/4 pound bags of peanuts can be from 5 pound bag
Final answer:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, divide the weight of the 5 pound bag by the weight of each 3/4 pound bag.Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.
Explanation:
To determine how many 3/4 pound bags of peanuts can be made from a 5 pound bag, we need to divide the weight of the 5 pound bag by the weight of each 3/4 pound bag. We can use the division operation to solve this.
5 pounds ÷ 3/4 pounds = 5 ÷ 3/4
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3.
5 ÷ 3/4 = 5 × 4/3 = 20/3
Therefore, 20/3 or 6 and 2/3 3/4 pound bags of peanuts can be made from a 5 pound bag.
Someone please help me
Answer:
1 mi/1.61 km
Step-by-step explanation:
we know that
1 mile= 1.61 kilometers
To convert 1 kilometer to miles
use proportion
so
1/1.61 mi/km=x/1 mi/km
x=1 mi/1.61 km
Answer:
[tex]\frac{1 mi}{1.61km}[/tex]
Step-by-step explanation:
We are given the unit values of inch, foot and mile to convert into centimeters.
Using these conversion units, we are to determine whether which expression in the answer options can be used as the conversion factor to convert kilometers to miles.
So using the given conversion units, we can see that the following is the conversion factor to convert kilometers to miles.
[tex]\frac{1 mi}{1.61km}[/tex]
Find the coordinates of the point where y-4x=1 crosses the y axis
Answer:
(0, 1)
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
y - 4x = 1 ( add 4x to both sides )
y = 4x + 1 ← in slope- intercept form
with y- intercept c = 1 ⇒ (0, 1) ← coordinates of y- intercept
The coordinates of the point where y-4x=1 crosses the y axis is (0, 1)
The following information should be considered:
The equation of a line in slope - intercept form is y = mx + c Here m is the slope and c the y- intercept.Now y - 4x = 1.So here we have to add 4x to the both sides. So, y = 4x + 1.Now the coordinates is (0,1)
Therefore we can conclude that The coordinates of the point where y-4x=1 crosses the y axis is (0, 1)
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Which equation represents a line that passes through (5, 1) and has a slope of 1/2?
y – 5 = 1/2(x –1)
y – 1/2 = 5(x –1)
y – 1 = 1/2(x –5)
y – 1 = 5(x-1/2)
Answer:
The correct answer is C
Step-by-step explanation:
If a straight line passes through [tex](x_1,y_1)[/tex] and has a slope of [tex]m[/tex] , its equation is;
[tex]y-y_1=m(x-x_1)[/tex]
In this case, we have [tex](x_1,y_1)=(5,1)[/tex] and [tex]m=\frac{1}{2}[/tex].
To find the required equation: you have to substitute [tex]x_1=5,y_1=1[/tex] and [tex]m=\frac{1}{2}[/tex] into the equation to obtain:
[tex]y-1=\frac{1}{2}(x-5)[/tex]
The correct answer is C
If A • B*2 = 1.8 x 10*-7, and C•B/D = 7.2 x 10*-4, find the value of A•D*2/C*2
Answer:
-7.2
Step-by-step explanation:
The value of expression A•D²/C² is 1.8 x 10⁻⁷ / D².
To find the value of A•D²/C², we can first rearrange the given equations and then manipulate them to get the desired expression.
Given equations:
A • B² = 1.8 x 10⁻⁷
C • B/D = 7.2 x 10⁻⁴
Let's manipulate the second equation to get C by itself:
C • B/D = 7.2 x 10⁻⁴
C = (7.2 x 10⁻⁴) • (D/B)
Now, substitute the expression for C from the second equation into the first equation:
A • B² = 1.8 x 10⁻⁷
A = (1.8 x 10⁻⁷) / B²
Now, we have expressions for both A and C:
A = (1.8 x 10⁻⁷) / B²
C = (7.2 x 10⁻⁴) • (D/B)
Now, let's find the value of A•D²/C²:
A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B/D)²
Since (B/D)² = B²/D²:
A•D²/C² = ((1.8 x 10⁻⁷) / B²) • (B²/D²)
Now, B² in the numerator and denominator cancel out:
A•D²/C² = 1.8 x 10⁻⁷ / D²
Thus, the value of A•D²/C² is 1.8 x 10⁻⁷ / D².
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4x-2y-x+5y-8
What is the coefficient of the x-term of the fully simplified expression ?
The snack bar at the school purchases water bottles at wholesale and then marks them up to make a profit. It marks up the water bottles by 33 percent, an amount of $0.28. Percents Total 33% 33% 33% 100% $0.28 $0.28 $0.28 What was the wholesale price of each water bottle? $0.56 $0.84 $0.93 $1.12
PLS HELP QUICK IM TIMED!!!!
Answer:
Say that the price at the whole for a bottle is some x
We know that the Snack Bar sold them at 33% profit which is in dollars $0.28
i.e 33% x=0.28
so now its a matter of finding what x is
writing this in algebraic form
0.33x=0.28
divide both sides of the equation by 0.33
0.33x/0.33=0.28/0.33
Therefore x=0.85 roughly
so the price per bottle at the whole sell is 85 cent
the snack bar is selling it for 1.13 dollars
assuming no tax applied
Step-by-step explanation:
Answer:
0.84 (B)
Step-by-step explanation:
What is the equation of the line in point-slope form?
Answer:
A
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 4, - 4) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = [tex]\frac{0+4}{4+4}[/tex] = [tex]\frac{4}{8}[/tex] = [tex]\frac{1}{2}[/tex]
Using (a, b) = (- 4, - 4), then
y - (- 4) = [tex]\frac{1}{2}[/tex] (x - (- 4)), that is
y + 4 = [tex]\frac{1}{2}[/tex] (x + 4) → A
a boat is 60% full with 48. What is the maximum carrying capacity?
Answer:
80
Step-by-step explanation:
60%=48
10%=8
8*10=80
Answer:80
Step-by-step explanation:
60/100*x=48
60/100=3/5 so,
3/5*x=48
3x=48*5
x=240/3
x=80
therefore the maximum capacity is 80 people
Which fraction is between 0 and 1/2
The Fraction that is between 0 and 1/2 is 2/10
The fraction 1/2 can also be written as 5/10. If you were to make a number line, you would be able to see that 2/10 is between. Here, let me order them from least to greatest:
< - 0 - - 2/10- - - 1/2- - 7/10- 3/4 - 8/10 - >
As you can see, 2/10 is between 0 and 1/2 (5/10).
Four students found the mean of the data set 26, 31, 39, 30, 16, 16, 18, 38. Which student found the correct mean?
Ashrita's work
26 +31 +39+30+ 16 + 16+ 18+ 38
26.75
Collette's work
26 +3864 - 32
Daniel's work
26+31+39 + 30+ 16+ 18+ 38
198 - 28.29
Lora's work
30+ 16 - 46 - 23
Answer:
Ashrita
Step-by-step explanation:
The mean of any set of data is found by finding the summation of all the values in the set of data then dividing it by the number of entries in the data.
Mean=Σfx/Σf
Σf=26+31+39+30+16+16+18+38= 214
Σf= 8= the number of entries.
Mean=214/8=26.75
Ashrita's work was correct.
Answer:
Ashrita
Step-by-step explanation:
When you are finding the mean of some numbers you are meant to add all the numbers then divide by the amount of numbers
The parent function f(x)=x3 and a translation, g(x), are shown on the graph. Which represents g(x), then the translated function?
ANSWER
The correct answer is A
EXPLANATION
The parent function is
[tex]f(x) = {x}^{3} [/tex]
The function g(x) is obtained by shifting the graph of the parent function, 4 units left and 6 units up.
Therefore the transformation is of the form:
[tex]g(x) = f(x + 4) + 6[/tex]
Hence the transformed function has equation:
[tex]g(x) = {(x + 4)}^{3} + 6[/tex]
The correct answer is A
The resulting function g(x) after the translation will be g(x) = (x+4)³ + 6
Translation of functionsTranslation is a way of changing the position of an object on an xy plane. According to the graph shown, the parent function of the graph is f(x) = x^3.
The translates function shows an upward translation by 4 units and horizontal translation to the left by 6 units. The resulting function g(x) after the translation will be g(x) = (x+4)³ + 6
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What is the slope of the line passing through (5, -6) and (4, 3)
Answer:
-9
Step-by-step explanation:
Answer:
slope = - 9
Step-by-step explanation:
Calculate the slope m using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (5, - 6) and (x₂, y₂ ) = (4, 3)
m = [tex]\frac{3+6}{4-5}[/tex] = [tex]\frac{9}{-1}[/tex] = - 9
Geometry please help
Check the picture below.
Answer:
x=6.9 inches
Step-by-step explanation:
If a tangent and a secant are draw to a circle from the same exterior point, the square of the length of the tangent is equal to the product of the total length of the secant and the length of the external segment of the secant.
From the given diagram,
(8+4)×4=x²
12×4=x²
x²=48
x=6.9 inches
In the expression 6^8 what does the exponent show
Answer:
6^8=6*6*6*6*6*6*6*6
=1679616
Step-by-step explanation:
In this expression the exponent shows that how many times 6 will be multiplied.
6^8=6*6*6*6*6*6*6*6
=1679616
Line CD passes through points C(1, 3) and D(4, –3). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b?
–5
–2
1
5
Answer:
5
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/ (x2-x1)
= (-3-3)/(4-1)
=-6/3
= -2
Then we can use point slope form to make the equation
y-y1 = m(x-x1)
y-3 = -2(x-1)
Distribute
y-3 = -2x+2
Add 3 to each side
y-3+3 = -2x+2+3
y = -2x+5
Since this is in slope intercept form, y = mx +b, the y intercept is 5
Answer: D. 5
Step-by-step explanation: First we need to find the slope
m = (y2-y1)/ (x2-x1)
= (-3-3)/(4-1)
=-6/3
= -2
Then we can use point slope form to make the equation
y-y1 = m(x-x1)
y-3 = -2(x-1)
Distribute
y-3 = -2x+2
Add 3 to each side
y-3+3 = -2x+2+3
y = -2x+5
Since this is in slope intercept form, y = mx +b, the y intercept is 5
Round 140.430 to the nearest whole number
Answer:
140
Step-by-step explanation:
if you are rounding you round if 5 or over go up and if 4 or lower go down
Which expression is equivalent to 6x+8?
okay l gonna give you stright answer it B okay