Answer:
n=2.4
Step-by-step explanation:
The value of n is ∛14.
What is Equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).
To solve the equation −8 + n³= 6
Add 8 to both sides of the equation to isolate the term with n:
−8 + n³ + 8 = 6 + 8.
Simplifying the equation gives: n³ = 14.
Take the cube root of both sides to solve for n.
Taking the cube root of n³ = 14
∛(n^3) = ∛14.
Therefore, n = ∛14.
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the depth of water d in a swimming pool increases and decreases by 3% over a one-month period. Match each verbal description of the greatest and least water depths with all equivalent expressions.
The least water depth and greatest depth will be 0.97d and 1.03d.
How to illustrate the expression?An expression is used to show the relationship between the variables.
In this case, the depth of water d in a swimming pool increases and decreases by 3% over a one-month period.
The least water depth will be:
= d - (3% × d)
= d - 0.03d
= 0.97d
The greatest water depth will be:
= d + (3% × d)
= d + 0.03d
= 1.03d
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In 3 billion repetitions of an experiment, a random event occurred in 500 million cases.
The probability of the event is 1.
The probability of the event is 0.
What is the expected probability of this event?
What is the expected probability of the complement of the event?
A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad.
The probability of drawing a bag with bad potatoes is less than 1.
The probability of drawing a bag with good potatoes is greater than 0.
What is the probability of drawing a bag with bad potatoes?
What is the expected probability of the complement of the event?
Answer:
The correct answer is 1/6 for the question, "In 3 billion repetitions of an experiment, a random event occurred in 500 million cases..."
The correct answer is 1/10 for the question, "A shelf has 20 bags of potatoes. Two of the bags have potatoes starting to go bad."
Hope this helps you! May I please get brainliest if I'm correct?
Can someone help i need answers for 1,2,3,5,6,7,8
please help me with my homework
Answer:
a. Using a graphing calculator: 4.486089611
b. To 2 decimal places: 4.49
Which two lines are parallel?
The point (10, y) also lies on line A.
What number does y stand for?
The point (x, 21) also lies on line B.
What number does x stand for?
a. The slopes of lines C and B are the same, therefore, they are parallel.
b. y = 30
c. x = 11
How to Find the Slope of a Line?The slope of a line (m) = change in y/change in x.
Two lines having the same slope (m) value means they are parallel to each other.
a. Slope of line A = change in y/change in x = (9 - 0)/(3 - 0) = 9/3
Slope of line A = 3
Slope of line B = (15 - 1)/(8 - 1) = 14/7
Slope of line B = 2
Slope of line C = (21 - 3)/(12 - 3) = 18/9
Slope of line C = 2
Slope of line D = change in y/change in x = (14 - 2)/(9 - 1) = 12/8
Slope of line D = 3/2
Lines C and B have the same slope, therefore they are parallel.
b. 3 = (9 - y)/(3 - 10)
3 = (9 - y)/-7
-21 = 9 - y
-21 - 9 = -y
-30 = -y
y = 30
c. 2 = (15 - 21)/(8 - x)
2 = -6/(8 - x)
2(8 - x) = -6
16 - 2x = -6
-2x = -6 - 16
-2x = -22
x = 11
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Percent that’s equivalent to 15/50
The percentage that equivalent to 15/50 is 30%
The given term is 15/50
The percentage is defines as a relative value indicating hundredth parts of any number. It is denoted using the percentage symbol "%". We can also say that percentage is a number or ratio expressed as a fraction of 100.
The given term is 15/50
Here the denominator is 50 and numerator is 15
To find the equivalent percentage, first we have to divide 15 by 50, then multiply the result by 100
15/50 = 0.3
Multiply the result by 100
0.3×100 = 30%
Hence, the percent that equivalent to 15/50 is 30%
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A figure is dilated by a factor of 3. Which of following statements about the image of the figure is true?
When a figure is dilated by a factor of 3, the statement about the image of the figure that is true is C Both the area and the perimeter decrease.
What is dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
The x and y coordinates of the original figure are multiplied by the scale factor to discover spots on the dilated image when a dilation in the coordinate plane has the origin as the center of dilation. The algebraic representation of the dilation is (x, y) for scale factor k. (kx, ky).
In this situation, since the figure is dilated by a factor of 3, there will be a reduction. In conclusion, the correct option is C.
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A figure is dilated by a factor of 3. Which of the following statements about the image of the figure is true?
A The perimeter decreases.
B The area decreases.
C Both the area and the perimeter
decrease.
D Both the area and the perimeter
increase.
If DZ = 6, ZR = 2, and EZ= 8, what is IR?
Answer:
8/6*(8)=32/3 or 10.66666.... or 10.7 rounded
Step-by-step explanation:
They are similar triangles
so we cam compare the size of the big triangle DIR to the smaller triangle DEZ
More specifically
EZ:DZ=IR:DR
8:6=IR:(6+2)
4:3=IR:8
the to solve for IR
we multiply by 8 each side
4/3*8=32/3
Antonio enjoys mountain biking. He has found that the maximum gradient which he can
cycle up is 0.3 and the maximum gradient he can safely descend is 0.5. Antonio's map has
a scale of 2 cm to 1 km with contours every 25 m. What is the minimum distance between
the contours (lines on a map showing the height of land) on his map that allows him to go
a up-hill
b down-hill?
0.166 meters is the minimum distance between the contours on the map that allow Antonio to go uphill. For downhill, it is 0.1 meters.
Given,
The maximum gradient uphill is 0.3 meters.
The maximum gradient downhill is 0.5 meters.
distance according to the scale,
1000m ÷ 2m = 500 meters
a) distance for uphill,
= 25 ÷ (500 × 0.3)
= (25 × 10) ÷ (500 × 3)
= 250 ÷ 1500
= 1 ÷ 6
= 0.166 meters
b) distance for downhill,
= 25 ÷ (500 × 0.5)
= 250 ÷ (500 × 5)
= 250 ÷ 2500
= 1 ÷ 10
= 0.1 meters
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Please help me with this problem
[tex]x^{2} +5x-3=-4x-3\\x^{2} +5x+4x-3+3=0\\x^{2} +9x=0\\\\x(x+9)=0\\x=0 or x+9=0\\x= -9[/tex]
I hope this helps.
Answer:
x = 0
or
x = (-9)
Step-by-step explanation:
[tex] {x}^{2} + 5x - 3 = - 4x - 3[/tex]
transfer like terms to the same side of the equation
[tex] {x}^{2} + 5x + 4x = - 3 + 3[/tex]
Add/subtract like terms
[tex] {x}^{2} + 9x = 0[/tex]
Now we can factor terms
[tex] {x}^{2} = x \times x \: and \: 9x = 9 \times x[/tex]
we can write them with their common divisor
x*(9+x) = 0 for this equation to be correct either x = 0 or (9+x) = 0
if x = 0 well then that's the first value of x
if (9+x) = 0 then x = -9 and this is the second value of x
What is the explicit formula for this geometric sequence?
8, 4, 2, 1,...
The explicit formula of the given geometric sequence is a(n) = 8(1/2)ⁿ⁻¹.
What is a geometric sequence ?Every term in a geometric series is obtained by multiplying the term before it by the same number aₙ= aₙ₋₁ + d is the general phrase for it. The common ratio is denoted by the number r. Any term in the sequence can be used to find it by dividing it by the word before it.
Any number series in which the ratio of succeeding terms is constant is referred to as a geometric sequence. where r is the proportion shared by all following terms. For instance, "2,6,18,54,162,486,1458,...
We have a sequence: 8, 4, 2, 1
The above sequence represents the geometric sequence with common ratio:
r = 4/8 = 1/2
First term a = 8
nth term:
a(n) = 8(1/2)ⁿ⁻¹
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Find the perimeter of the figure to the right.
The perimeter is
(Simplify your answer.)
4y
meters.
2y meters
7y meters
6 meters
18 meters
6y meters
Answer:
72 m
Step-by-step explanation:
We observe that 7y+6=18, and thus y=12/7.
So, the perimeter is:
[tex]2(18+7y+6) \\ \\ =14y+48 \\ \\ =14(12/7)+48 \\ \\ =72[/tex]
Mrs. Kwan is packaging apples in paper
bags. She needs to package 30 red apples
and 24 green apples so that there is the same
number of apples in each bag. But she
cannot mix the different apples, and there
can be no apples left over. What is the
greatest number of apples she can package
In each bag?
If 1/4 of the box is green apples, then 3/4 of the box is red apples. Thus, 3 times the number of green apples is equal to the number of red apples, which would give 3 * 5 = 15 red apples.
Suppose a jar contains 8 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
Step-by-step explanation:
Drawing two marbles at once is the same as drawing one and then drawing the second without replacing the first.
Starting with 8 red balls and 14 blue balls, the probability of drawing a red ball is 8/22 = 4/11.
Assuming red was drawn in the first draw, the probability of getting a red ball in the second draw means that you are drawing from a collection containing 7 red balls and 14 blue balls, so the probability is: 7/21 = 1/3.
So when calculating the odds of the second draw, we took into account the change in the number of hits and the number of chances, so these two events are independent and the total probability is the product of the two individual probabilities.
P(2 reds) = (4/11) (1/3) = 4/33
The probability that both marbles are red is 4/33.
What will the probability be?It should be noted that from the information given, the jar contains 8 red marbles and 14 blue marbles.
The total marbles will be:
= 8 + 14 = 22
The probability of selecting the first red marble will be:
= 8/22 = 4/11
The probability of selecting the second red marble will be:
= 7/21 = 1/3
Therefore, the probability that both marbles are red will be:
= 4/11 × 1/3
= 4/33
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Find all x-intercepts of the function. Express your answer as a list of x-values.
f(x) = 5x¹ - 80
The x-intercept of the function is found to be x = (y + 80)/5 and the values of x calculated are 17,18,19 and so on.
What is an illustration of intercept?Given, the x-axis and y-axis are intersected by two intercepts, P(2,0) and Q(0,3). => 3x + 2y – 6 = 0, Consequently, the line's equation is 3x + 2y - 6 = 0. Figure.
How do x and y intercept work?A line's x-intercept and y-intercept are the points at which the x- and y-axes, respectively, are crossed.
The given function is:
f(x) = 5x¹ - 80
Let,
y = f(x)
∴ y = 5x – 80
y + 80 = 5x
(y + 80)/5 = x
∴ x = (y + 80)/5
If y = 5,
x = (5 + 80)/5 = 17
If y = 10,
x = (10 + 80)/5 = 18
If y = 15,
x = (15 + 80)/5 = 19
Thus, by substituting y values in multiples of 5, we can get x values as 17, 18, 19 and so on.
Thus, the x-intercept of the function is found to be x = (y + 80)/5 and the x values calculated are 17,18,19 and so on.
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at what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.
Part A) The tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Part B) The tank will finish draining in 7.5 minutes.
Part C) Jada arrived 4.5 minutes before the water tank was empty.
What is rate of change?The rate of change (ROC) measures how quickly a variable alters over a predetermined amount of time.
Given Data
Up to 10 gallons can be stored in a water tank.
A drain continuously drains water from the tank when it is operational.
When Jade first noticed the tank, there were 7 liters of water inside.
3 minutes later, there were 5 gallons of water remaining.
Part A: How quickly is the tank's water level changing?
In three minutes, the gallons were reduced from seven to five. It indicates that 2 gallons were lost in three minutes.
Thus, gallons Change in gallons per minute would be -[tex]\frac{2}{3}[/tex]. As a result, the tank's water level is changing at a rate of -[tex]\frac{2}{3}[/tex] gallons per minute.
Note that a negative sign means there are less gallons of water available.
Part B) How long will it take for the tank to entirely drain?
The amount of time it will take the tank to entirely empty is denoted by the letter "m."
As,
2.3 gallons per second (5 gallons) in (m minutes).
So,
m = 5 ([tex]\frac{3}{2}[/tex])
= [tex]\frac{15}{2}[/tex]
= 7.5 min.
As a result, the tank will finish draining in 7.5 minutes.
Part C: How long did it take the water tank to fill up entirely before Jada arrived?
When there are 10 gallons of water, r is complete. This means that there are now 7 gallons more of water than there were when Jada arrived, an increase of 3 gallons.
Let 'm' be the time in minutes when the water tank was full and before Jada arrived.
So,
([tex]\frac{2}{3}[/tex]) (m) = 3
m = 3([tex]\frac{3}{2}[/tex]) = [tex]\frac{9}{2}[/tex]
= 4.5 min.
The water tank was thus full before to Jada's arrival by 4.5 minutes.
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When solving an equation, why do you think there may be no solutions? How can you tell if an equation will have no solutions as the answer?
A linear equation has no solutions if both sides of the equation have distinct constant values but the same variable term.
An equation will have no solutions if the variables are the same on either side.
What is an equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. An equation is a formula that uses the equals sign to connect two expressions to show that they are equal.
For example, an equation can be illustrated as:
x + 5 = x - 5
Collect like terms
x - x = 5 - 5
0
This illustrates that the equation gas no solution.
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Graph the quadratic equation ^^2m² + m +3 = 0
Given -
2m² + m +3 = 0
To Find -
2m² + m +3 = 0
Step-by-Step Explanation -
2m² + m +3 = 0
We will first calculate the roots of the equation:
[tex]\begin{gathered} m\text{ = }\frac{-b\text{ }\pm\sqrt{b^2\text{ - 4ac}}}{2a} \\ \\ Here,\text{ } \\ \\ a\text{ = 2, b = 1, c = 3} \\ \\ On\text{ Putting the values in the equation,} \\ \\ m\text{ = }\frac{-1\pm\sqrt{1^2\text{ - 4}\times2\times3}}{2\times2} \\ \\ m\text{ = }\frac{-1\pm\sqrt{-23}}{4} \end{gathered}[/tex]So, Both the roots are imaginary.
having d = -23
Final Answer:
Graph :
Ax+By=C2y=3x+6 in standard format
The given equation written in standard format is 3x - 2y = -6
Standard form of linear equations with two variablesFrom the question, we are to write the given equation in standard format.
The given equation is
2y = 3x + 6
The standard form of a linear equation with two variables is
Ax + By = C
Where x and y are the variables
A is the coefficient of x
B is the coefficient of y
and C is the constant
Now, we will write the given equation in the format
2y = 3x + 6
Subtract 3x from both sides of the equation
2y - 3x = 3x - 3x + 6
-3x + 2y = 6
Multiply through by -1
3x - 2y = -6
The standard format of the equation is 3x - 2y = -6
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find the median of the numbers 34, 48, 52, 61, 76, 76, 61, 84, 61, 39, 83, 61, 79, 81, 56, and 88.
Answer:
61
Step-by-step explanation:
the graph shows then number of possible passengers for a given number of roller coasters cars that leave the platform
oluition
or this case we have the folllowing:
Part a
e select (0,0) and (3,24)
the slope would be:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{24-0}{3-0}=8[/tex]then the equation for this case would be:
y= 8x +b
Using (0,0) we can find b:
0 ) 8*0 +b
b= 0
Then the equation is:
y= 8x
Part b
or this case we can conclude that for each n8 passengers is required a new car for the rooller coaster
A solar panel has an area of x2 + 13x + 42. Find the possible dimensions of the solar panel.
Answer: x+6 and x+7
Step-by-step explanation:
[tex]x^{2} +13x + 42 = 0\\D = b^{2} - 4ac = 169 - 4*42 = 169 - 168 = 1\\x_{1} = (-13 + 1)/2 = -6\\x_{2} = (-13 -1)/2 = -7\\\\So, x^{2} + 13x + 42 = (x+6)(x+7) \\\\\\[/tex]
Hence, the possible dimensions are x+6 and x+7.
Answer: (x + 6) and (x + 7)
Step-by-step explanation: Determine if the polynomial terms contain a common factor. In this case, there's no common factor. Next, find two numbers whose product is 42 and whose sum is 13. The only pair of numbers that satisfies these conditions is 6 and 7. Finally, write the polynomial in factored form as (x + 6)(x + 7). Therefore, the possible dimensions of the rectangle are (x + 6) by (x + 7).
19. Ciara is saving for a video game. The first week, she puts $2 dollars in an
envelope. Each week after that, she puts twice as much in the envelope as
she did the previous week. How many dollars does she save on the 6th
week? How many dollars does she save in all?
Answer:
On sixth week , she collects 2⁶ = $64.
She saves 2(1+2+4+8+16+32) = $126 in all.
Given the following preimage and image coordinates, what is the line of reflection?
The given coordinate's line of reflection is the x-axis, Option D.
After intersecting the co-ordinates A(-3,5), B(2,8) and C(-4,-5) of line 1 and co-ordinates A'(-3,-5), B'(2,-8) and C'(-4,5) of line 2. It is deduced that both lines are similar.
The point of intersection of lines 1 and 2 is on the X-axis as the reflection of the coordinate,
A(-3,5) on the negative x-axis and positive y-axis is A'(-3,-5) on the negative y-axis and the negative x-axis.
B(2,8) on the positive x-axis and positive y-axis is B'(2,-8) on the negative y-axis and the positive x-axis.
C(-4,-5) on the negative x-axis and negative y-axis is C'(-4,5) on the positive y-axis and the negative x-axis.
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[tex]x^{2} -7x=12[/tex]
Can you help me with this question
The component form of vector is (-6,8)
What is vector ?Geometrical objects with magnitude and direction are called vectors. A line with an arrow pointing in its direction can be used to represent a vector, and the length of the line corresponds to the vector's magnitude. As a result, vectors are depicted as arrows and have starting and ending points. It took 200 years for the idea of vectors to develop. Physical quantities like displacement, velocity, acceleration, etc. are represented by vectors.Additionally, the development of the field of electromagnetic induction in the late 19th century marked the beginning of the usage of vectors. Here, we'll examine the definition of vectors as well as their characteristics, mathematical formulas, and uses.
The component form of vector is (-6,8)
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Using the measurements shown, which of these parallelograms is it
possible to work out the area of?
Answer:
B, D, E
Step-by-step explanation:
We can find the area of B since the height and lengths is known, so the area is just 2*4 = 8 cm^2
D also has the height and length given, it is 4*3 = 12 cm^2
E gives 3 values, but only focus on the height and length, which are 2 and 5 respectively. 3 is also a side length, but there is no height to match that length. The area of E is 2*5 = 10 cm^2
The reasons A, C, and F don't work:
A seems like it would work, until you realize that 5 is a height, not a length, and so is 2. They are both heights, and multiplying heights together won't usually get you an accurate area unless the shape is a rectangle.
C has a length, but no height. the 3 cm is pretty much an arbitrary measurement.
F has two lengths, which would only give the area if the shape was a rectangle, which it is not.
I need help ASAP, thanks
ANSWER
x = 4 or x = -9
STEP-BY-STEP EXPLANATION:
As you can see from the question provided, you were given the following logarithms equation
[tex]\log _6x+log_6(x\text{ + 5) = 2}[/tex]Recall that,
[tex]\text{Log}_xA+log_xB=Log_x(A\text{ x B)}[/tex][tex]\begin{gathered} \text{Let} \\ \log _xA=log_6x \\ \log _xB=log_6(x\text{ + 5)} \end{gathered}[/tex]The next thing is to replace the values and simplify
[tex]\begin{gathered} \log _6x(x\text{ + 5) = 2} \\ x(x+5)=6^2 \\ \text{Open the parenthesis} \\ x^2\text{ + 5x = 36} \\ x^2\text{ + 5x - 36 = 0} \end{gathered}[/tex]As you can see from the last process, the logarithms function resulted in a quadratic equation.
The next thing is to solve the equation using the factorization method.
Note that, the general quadratic function is given below as
[tex]ax^2\text{ + bx + c = 0}[/tex]Relating the two equations, you will have the following data
• a = 1
,• b = 5
,• c = -36
The next thing is to find the value of ac
[tex]\begin{gathered} ac\text{ = 1 }\cdot\text{(-36)} \\ ac\text{ = -36} \end{gathered}[/tex][tex]\begin{gathered} x^2\text{ -4x + 9x - 36 = 0} \\ x(x\text{ - 4) + 9(x - 4) = 0} \\ (x\text{ - 4) (x + 9) = 0} \\ (x\text{ - 4) = 0 or (x + 9) = 0} \\ x\text{ - 4 = 0 or x + 9 = 0} \\ x\text{ = 0 + 4 or x - 9 = 0} \\ x\text{ = 4 or x =-9} \end{gathered}[/tex]Hence, the values of x are 4 and -9
Which equation is in the point slope-form and is depicted by this graph
Explanation
iven the points (-1,-4) and t(3,2). The points slope form of the equation can be found using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ where\text{ x}_1,y_1=-1,-4 \\ x_2,y_2=3,2 \end{gathered}[/tex]We would then substitute the value into the formula;
[tex]\begin{gathered} y-(-4)=\frac{2-(-4)}{3-(-1)}(x-(-1)) \\ y+4=\frac{6}{4}(x+1) \\ y+4=\frac{3}{2}(x+1) \end{gathered}[/tex]Answer: Option 3
Find the x intercepts of the graph of the function.
g(x)=-1(x-4)(x+2). Hint x intercepts happen when g(x)=0.
(Show Work)
The X- intercept of the graph of the function at x =>-4 and x = 2.
The provided function is g(x)=-1(x-4)(x+2).
The x intercept of the function means, that point at which the graph of function will have the y coordinate as zero.
So, the x intercept of the function will be at the point where the function g(x) will be equal to zero.
g(x) = 0
-1(x-4)(x+2) = 0
(4-x)(x+2) = 0
Here,
We will get two values of x at which g(x) will be zero,
X = 4 and -2.
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