Here are the calculations for the given scenarios with distances using the terms "Distance".
A bird starts at 20 meters and changes 16 meters. The total distance traveled by the bird is 36 meters.A butterfly starts at 20 meters and changes -16 meters.
The total distance traveled by the butterfly is 4 meters.A diver starts at 5 meters and changes -16 meters. The total distance traveled by the diver is 11 meters
.A whale starts at -9 meters and changes 11 meters.
The total distance traveled by the whale is 2 meters.A fish starts at -9 meters and changes -11 meters.
The total distance traveled by the fish is 20 meters.
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A chemist wants to make 45 ml of a 17% acid solution by mixing a 13% acid solution and a 19 % acid solution. How many milliliters of each solution should the chemist use?
Answer:
22 millilitres of 13% solution
23 millilitres of 19% solution
Step-by-step explanation:
A + B = 45
13A + 19B = 45 x 17 = 765
-13A - 13B + 13A + 19B = -650 + 765 = 115
5B = 115
B = 23
22 + 23 = 45
A = 22
16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.
Answer:
6.80 x 10⁻⁷ m
Step-by-step explanation:
You can find the value of λ by inserting the given values into the equation and simplifying.
c = vλ <----- Given equation
2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ <----- Insert values
6.80 x 10⁻⁷ m = λ <----- Divide both sides by 4.41 x 10¹⁴
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
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Answer:
D = 67
Step-by-step explanation:
Question 12
From the given graph, use two points to write an equation in point-
slope form and then change to slope-intercept form.
Step 1: Use the two points to find the slope.
Step 2: Use the slope and one point to complete point-slope form.
y-y₁ = m(x-x₁)
Step 3: Change point-slope form into slope intercept form by solving
for y. Show your work!
y=mx+b
Select the equivalent expression. 2^-4 = ?
Answer:
1/16
Step-by-step explanation:
This means 1/2x2x2x2 = 1/16
A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. Her work is shown below. What is Amies error
Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
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For the complete question, refer to the attachment.
check out the pic first
Answer: (0, 16)
Step-by-step explanation:
y = mx + c
c is the y intercept
from the equation, c = 16
(it's not exactly mx but you don't need to solve for x)
Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).
Answer:
a= 100.2
Step-by-step explanation:
You solve it like you ate looking for the hypotenuse
mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.
What addition/subtraction equation should I put?
Answer:
7 - 10
Step-by-step explanation:
Because it is -3 and 7 - 10 = -3
Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Source
StylesFormatFontSize
Answer:
(-2, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]
To solve by substitution, substitute the first equation into the second equation:
[tex]\implies x+4=-2x-2[/tex]
Add 2x to both sides:
[tex]\implies x+4+2x=-2x-2+2x[/tex]
[tex]\implies 3x+4=-2[/tex]
Subtract 4 from both sides:
[tex]\implies 3x+4-4=-2-4[/tex]
[tex]\implies 3x=-6[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=-2+4[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of equations is (-2, 2).
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Substitute y value from first eqn in second equation
y=-2x-2x+4=-2x-23x=-6x=-2Put in first one
y=-2+4=2(-2,2) is the solution
find the value of x from the figure
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
Lets simplify it,
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
Vertex Form:
f(x) = a(bx - c)² + d
f(x) = -1/3(x + 12)² + 9
Standard Form:
f(x) = -1/3(x + 12)² + 9
f(x) = -1/3(x² + 24x + 144) + 9
f(x) = -1/3x² - 8x - 48 + 9
f(x) = -1/3x² - 8x - 39
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Which of the following is an equivalent form of the equation of the graph shown in the xyxyx, y-plane above, from which the coordinates of vertex AAA can be identified as constants in the equation
The equivalent form of the equation y=[tex]x^{2} -2x-15[/tex]given is y=(x+3)(x-5).
Given an equation y=[tex]x^{2}[/tex]-2x-15 and we are required to find the equivalent form of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or any other equation depending on the powers of the variable.
To find the equivalent equations we are required to form factors of the equation. Equivalent equation are those equations which when solved gives the same solution as the equation when solved gives.
y=[tex]x^{2}[/tex]-2x-15
y=[tex]x^{2}[/tex]-5x+3x-15
y=x(x-5)+3(x-5)
y=(x+3)(x-5)
Hence the equivalent form of the equation y= [tex]x^{2}[/tex]-2x-15 given is
y=(x+3)(x-5).
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Question is incomplete as question should includes the equation
y= [tex]x^{2}[/tex]-2x-15.
10 points please help me!!!
Step-by-step explanation:
16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)Solve:
2a + 6 = 12
a =
Answer:
8
Step-by-step explanation:
because hhhhhh
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jkkkkk
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vvvvv
dddfff
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kkkkkk
lllll.ssss
2+8+32+128…..,n=9
Evaluate each geometric series described
The value of 2+8+32+128…..,n=9 is 174762
How to evaluate the series?The series is given as:
2+8+32+128…..,n=9
Start by calculating the common ratio (r)
r = 8/2
r = 4
The sum of the series is then calculated as:
[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]
This gives
[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]
Evaluate the difference
[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]
Evaluate the quotient
[tex]S_9 = 174762[/tex]
Hence, the value of 2+8+32+128…..,n=9 is 174762
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Let k be a positive integer. In how many ways can one select three distinct numbers from the set {1,2,..., 3k} such that their sum is divisible by 3
Reduce the numbers in the list modulo 3 to get the set
{1, 2, 0, 1, 2, 0, …, 1, 2, 0}
containing [tex]k[/tex] copies each of 1, 2, and 0.
Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:
3 elements each with the same residue, so0 + 0 + 0 ≡ 0 (mod 3)
1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)
2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)
1 element each with different residues, so0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)
There are
[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]
ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence
[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]
ways of choosing any 3 elements with the same residue, and there are
[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]
ways of choosing any 3 elements with distinct residues.
So, the total number of ways of making the selection is
[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]
Write y=5x-9 in standard form
Will give brainliest!
Answer:
5x - y = 9
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = 5x - 9 ( subtract 5x from both sides )
- 5x + y = - 9 ( multiply through by - 1 )
5x - y = 9 ← in standard form
On purchasing a cell phone, Tia got an offer and got the cell phone for $35\%$ less than the tag price. If she saved $\$140$ on that cell phone. Then price on the tag must be $\$$
On purchasing a cell phone, Tia got an offer and got the cell phone for 35% less than the tag price. If she saved 140 on that cell phone. Then price on the tag is 400.
Since, the cell pone is sold with 35% discount on it.
Tia got that phone at selling price with 35% discount on tag price. Also, she saved around 140 on buying the cell phone.
Therefore, the discount on the cell phone on the tag price is her saving on buying the cell phone.
Hence,
35% discount on tag price=Saved amount
(35/100)×T=140
where T is the tag price.
T=(140×100)35
T=14000/34
T=400
Therefore, on buying the cell phone with 35% discount on tag price costs around 140. Then the tag price is 400.
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A bag contains lettered tiles. the theoretical probability of choosing a vowel is 40%. the bag contains 78 consonants. how many tiles are in the bag?
The total number of ties present in the bag are 130.
What is probability?Calculating or estimating how likely something is to occur is what probability is all about. The likelihood of an event occurring can be expressed using words like "certain," "impossible," or "probable."
Formula for probability is -
Probability(Event) = Favourable Outcomes/Total Outcomes
It P(E) is the probability for occurring any event.
'x' be the favourable outcome.
'n' be the total outcome.
Then,
P(E) = x/n.
Calculation for the total tiles present the bag.
The probability of choosing a vowel is 40% = 0.4.
Then, the probability of choosing a consonants will be 1 - 0.4 = 0.6 or 60%.
Let P(E) be the probability of the occurrence of the consonants.
Then,
P(E) = total number of consonants/total tiles in the bag.
Let 'T' be the total tiles in the bag.
0.6 = 78/T
T = 78/0.6
T = 130
Therefore, the total tiles present in the bag are 130.
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A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?
Answer:
8:35 PM
Step-by-step explanation:
First, subtract 15 from 50.
50-15=35
Add that 15 taken from 50 to 7:45.
7:45 + 0:15 = 8:00
Add 35 to 8:00
8:00 + 0:35 = 8:35
The next movie will start at 8:35 PM.
Hope this helps!
How would you describe the graph for the equation |x| <4?
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
b.) A closed circle on 4 with a solid line drawn to a closed circle on -4.
c.) A closed circle on 4 with a solid line drawn to an open circle on -4.
d.) An open circle on 4 with a solid line drawn to a closed circle on -4.
Answer:
a.) An open circle on 4 with a solid line drawn to an open circle on -4.
Explanation:
Open circles are used for signs: < and >
Closed circles are used for signs: ≤ and ≥
Here in the given expression: |x| < 4
[<] sign is used so open circle is used
If |y| < a then -a < y < a
so here, -4 < x < 4
Both circles should be opened, drawn with a solid line from -4 to 4.
At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand
Answer: 30 degrees
Step-by-step explanation:
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30
The value of the Mean & Standard deviation is 1.30 and 1.18.
According to the statement
we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.
And we have to find the mean and standard deviation from the given data which is related to the probabilities values
So, according to the given data
The formula to compute the mean is:
Mean = summation [x*p(x)]
Compute the mean as follows:
Mean = summation [x*p(x)]
Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]
Mean = 0 +0.05 + 0.64 + 0.21 + 0.28
Mean = 1.18
The mean of the random variable x is 1.18.
And after calculating the variance from the formula get
The value of standard deviation is 1.30
So, The value of the Mean & Standard deviation is 1.30 and 1.18.
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solve for x -
[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]
ty! :)
Hello,
x² + 5x + 6 = 0
a = 1 ; b = 5 ; c = 6
∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0
2 solutions :
[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]
[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]
S = { -3 ; -2}
Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w
The equation that represents the relationship between n and w is w = 10n + 8.
How to illustrate the expression?From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8
ounces and each letter weighs 10 ounces.
Let represent the number of letters
Let w represent the weight of the banner.
In this case, when n = 6, w = 68 and when n = 7, w = 78.
Therefore, the relationship will be:
w = 10n + 8
To confirm let's use n = 6
10n + 8
10(6) + 8
= 68
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Answer:
Step-by-step explanation:
w=10n+8
A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?
The length of the square pool is 8. 49cm
How to determine the areaNote that the formula for finding the area of a square is given as;
Area = length^2
We have
Area = 72 m²
Substitute into the formula
I^2 = 72
Find the square root of both sides
I= √72
I = 8. 49cm
The length of the square pool given as I is 8. 49cm
Thus, the length of the square pool is 8. 49cm
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3\sqrt(6)*6\sqrt(6)
Please quick reply!
Answer: 3
Step-by-step explanation:
Multiply the numerator to get 3 x 6 is 18
Multiply the denominator to get √6 x √6 = 6
Divide 18 by 6 to get the answer is 3
The weights of certain machine components are normally distributed with a mean of 7.75 ounces and a standard deviation of 0.07 ounces. Find the two weights that separate the top 4% and the bottom 4%. These weights could serve as limits used to identify which components should be rejected. Round your answer to the nearest hundredth, if necessary.
The weight that separates the top 4% is x = 7.87 (round nearest hundredth) .
The weight that separates the bottom 4% is x = 7.63 (round nearest hundredth).
What is normal distribution?The majority of the observations are centred around the middle peak of the normal distribution, which is a continuous distribution of probability that really is symmetrical around in its mean.
The probability for values that are farther from of the mean tapered down equally both in directions.
Now, use z-chart to find the z-value for that separates the top 4% and the bottom 4%.
The values of z = +1.75 and z = -1.75
Let the weight of the machines be 'x'.
Use the formula for z- value
z = (x - μ)/ σ
Where,
σ is standard deviation = 0.07 ounces.
μ is mean = 7.75 ounces.
Substitute all the values and calculate the weight.
case 1: when z = +1.75
1.75 = (x - 7.75)/0.07
x = (1.75×0.07) + 7.75
x = 7.872
x = 7.87 (round nearest hundredth)
case 2: when z = -1.75
-1.75 = (x - 7.75)/0.07
x = (-1.75×0.07) + 7.75
x = 7.6275
x = 7.63 (round nearest hundredth)
Therefore,
x = 7.87 (round nearest hundredth) is weight which separates top 4%.
x = 7.63 (round nearest hundredth) is weight which separates bottom 4%.
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