1) Gathering the data
10.3 mg of impurity per gallon of water
? μg of impurity per liter?
2) Since this is a matter of units conversion, then let's work remembering
the Metrical and Customary equivalences:
1 μg = 0.001 mg
1 gallon = 3.78 liters
3) As we have a ratio, let's write it as a ratio:
[tex]undefined[/tex]Identify the explicit formula for the sequence given by the following recursive formula: A) f(n) = –2 + 4(n – 1)B) f(n) = –4 + 2(n – 1)C) f(n) = 4 – 2(n – 1)D) f(n) = 2 – 4(n – 1)
Given the recurssive formula;
[tex]f(n)=\begin{cases}f(1)=-2 \\ f(n)=f(n-1)+4\text{ if n>1}\end{cases}[/tex]Let's find the sequence using the recurssive formula, we have;
[tex]\begin{gathered} f(2)=f(2-1)+4 \\ f(2)=f(1)+4 \\ f(2)=-2+4 \\ f(2)=2 \\ f(3)=f(3-1)+4 \\ f(3)=f(2)+4 \\ f(3)=2+4 \\ f(3)=6 \\ f(4)=f(4-1)+4 \\ f(4)=f(3)+4 \\ f(4)=6+4 \\ f(4)=10 \end{gathered}[/tex]Thus, we have the sequence as;
[tex]-2,2,6,10,\ldots[/tex]We observed that the sequence is an arithmetic sequence with a common difference of 4 and first term of -2.
So, the recursive formula is;
[tex]\begin{gathered} f(n)=f(1)+d(n-1)_{} \\ f(n)=-2+4(n-1) \\ f(n)=-2+4n-4_{} \\ f(n)=4n-6 \end{gathered}[/tex]CORRECT OPTION: A
Sonia opened a savings account and then added the same amount to the savings account every week. After 5 weeks, her savings account had a total of $45. After 10 weeks, her savings account had a total of $70. Which equation represents the amount of money (y), in dollars, in Sonia's savings account after x weeks?
First let's find the amount Sonia puts in her account each week.
To do so, let's find the amount increased between weeks 5 and 10:
[tex]70-45=25[/tex]The account increased $25 in 5 weeks, so for each week, we have:
[tex]\frac{25}{5}=5[/tex]So Sonia puts $5 in her account each week. Now, we need to find the initial value in the account. If after 5 weeks the account has $45, we can subtract $45 by 5 times the amount per week:
[tex]45-5\cdot5=45-25=20[/tex]So the initial amount is $20.
Now that we have the initial amount and the amount she puts per week, we have the following equation for the amount of money y after x weeks:
[tex]y=5x+20_{}[/tex]So the correct option is the third one.
prove the formula sin 3 A + sin A = 4 sin A cos2A
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
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Please help me with this question! Will give brainliest !!! I need it ASAP
Answer:
The number is not a square number because the exponent is an odd number.
Step-by-step explanation:
Square numbers or perfect squares are any numbers that once put to the square root equals a whole number. Such as 4 is a square number because the square root of 4 is 2 or 2 to the second power. Numbers that are raised to even powers also fall under this rule. For example, 16 is a square number as it is equal to 2 to the fourth power, or 16 to the fourth root is 2. Since 1953125 can also be written by 5 to the ninth power it does not go under this rule due to the power being 9. 9 is an odd number. For it to be a perfect square the exponent would have to be an even number.
Suppose a person who jumps on Earth returns to the ground in 0.4 second. On Phobos, the same jumper will take 6.4 minutes to return to the ground. How many times longer would it be on Phobos than on Earth for the jumper to return to the ground? Explain.
The times longer would it be on Phobos than on Earth for the jumper to return to the ground is 16 times.
How to calculate the value?From the information, it was given that the person who jumps on Earth returns to the ground in 0.4 second and that on Phobos, the same jumper will take 6.4 minutes to return to the ground.
The number of times longer will be calculated by dividing the values that are given. This will be:.= Time on Phobos / Time on Earth
= 6.4 minutes / 0.4 minutes
= 16
This shows the concept of division of numbers.
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Patrice found airpods on sale for $84. The sale sales tax is 5%. What is the total Patrice will pay for the airpods?
To find the final cost with tax. You find the 5% of $84 and add that result to the initial cost:
[tex]84\cdot\frac{5}{100}=4.2[/tex][tex]84+4.2=88.2[/tex]Then, Patrice will pay $88.2 for the airpods
40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.
To earn a profit of more than $2000, then s must be greater than 42
This makes the answer to be s > 42
The correct answer is the second option
I'll send you the pic a
Let's complete the four equations, as follows:
1. 5 * x = 15
Solving for x:
5x = 15
Dividing by 5 at both sides:
5x/5 = 15/5
x = 3
3 is the value to fill in the box
2. 4 * x = 32
Solving for x:
4x = 32
Dividing by 4 at both sides:
4x/4 = 32/4
x = 8
8 is the value to fill in the box
3. 6 * x = 9
Solving for x:
6x = 9
Dividing by 6 at both sides:
6x/6 = 9/6
x = 1.5
1.5 is the value to fill in the box
4. 12 * x = 3
Solving for x:
12x = 3
Dividing by 12 at both sides:
12x/12 = 3/12
x = 3/12
Simplifying:
x = 1/4
1/4 or 0.25 is the value to fill in the box
hi i'm stuck on diameter and radius and chord and the arc measure explanations. And i'm also stuck on this question
• Chord: ,a line segment connecting ,any two points, in a curve (circle).
,• Diameter: ,a chord passing ,through the center ,of the figure.
,• Radius: ,a line segment going ,from the center, to any point in the circumference.
The difference between them is that the chord is any two points touching the circumference, the diameter has to go through the center to any two points, and the radius goes from the center to just one point in the circumference.
Then, the line segment that meets the requirements of being the diameter in circle F is segment CD as it passes through the center.
The radius could be CF, DF, and EF. While a chord could be AB.
Answer: CD
Grandma’s Guide to Cooking MeasurementsDried Seasonings 1 pinch = 2 smidgens1 dash = 2 pinches1 sprinkle = 3 pinches1 teaspoon = 8 dashesBased on Grandma's guide to cooking, how many smidgens are in one teaspoon?Do not include units with your answer.
32
Explanation:1 pinch = 2 smidgens
1 dash = 2 pinches
Therefore, 1 dash = 2 x 2 smidgens
1 dash = 4 smidgens
1 teaspoon = 8 dashes
1 teaspoon = 8 x 4 smidgens
1 teaspoon = 32 smidgens
There are 32 smidgens in 1 teaspoon
the net of a rectangular prism is shown below. the surface area of each face is labeled. which vakues represent the dimensions, in meters, of the rectangular prism.
The answer is 5, 9, 10
Alisa walks 3.5 miles in 30 minutes. At this rate, how many miles can she walk in 45 minutes?385.7 miles5 miles386 miles5.25 miles
Given:
Alisa walks 3.5 miles in 30 minutes.
To find:
The number of miles if she walks 45 mins.
Explanation:
The unit rate for speed is,
[tex]\begin{gathered} Speed=\frac{Distance}{Time} \\ =\frac{3.5}{30} \end{gathered}[/tex]The distance covered when she walks 45mins,
[tex]\begin{gathered} Distance=Speed\times Time \\ =\frac{3.5}{30}\times45 \\ =5.25miles \end{gathered}[/tex]Final answer:
The number of miles she walks in 45mins is 5.25miles.
Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.
step 1
the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder
Find out the volume of the cylinder
we have
r=2.8/2=1.4 cm
h=10.7 cm
[tex]V=\pi\cdot r^2\cdot h[/tex]substitute given values
[tex]\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}[/tex]Find out the volume of the frustum
the formula to calculate the volume is
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack[/tex]we have
R=5.6/2=2.8 cm
r=2.8/2=1.4 cm
h=1.9 cm
substitute given values
[tex]V=\frac{1}{3}\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack[/tex][tex]V=8.689\pi\text{ cm3}[/tex]Adds the volumes
V=20.972pi+8.689pi
V=29.661pi cm3
Multiply by the density
29.661pi*0.0173=1.6 lb
therefore
the answer is 1.6 lbwhat is 6!3! over 2!5!
Answer:
16
Step-by-step explanation:
6!3!
-------
2!5!
(1 × 2 × 3 × 4 × 5 × 6)(1 × 2 × 3)
--------------------------------------------
(1 × 2)(1 × 2 × 3 × 4 × 5)
(720)(6)
-------------------
(2)(120)
4320
------------ = 18
240
I hope this helps!
I have a bag, with some balls in it. All but four are blue, all but four are green, and all but four are red.
In total, how many balls are there in the bag?
===============================================
Explanation:
x = total number of balls
x-4 = number of blue
x-4 = number of green
x-4 = number of red
3(x-4) = 3x-12 = total number of blue, green, or red
x - (3x-12) = x-3x+12 = -2x+12 = number of other colors
If there are other colors, then we want this quantity to be larger than 0, so,
-2x+12 > 0
-2x > -12
x < -12/(-2)
x < 6
There are less than 6 balls in the bag.
At the same time, we want each x-4 to be greater than zero
x-4 > 0
x > 4
------------------
We found that x > 4 and x < 6
This combines to 4 < x < 6 which has us land on x = 5
This computes x-4 = 5-4 = 1, showing there's one of each blue, green and red. There are 5-1-1-1 = 2 balls of some other color not mentioned.
------------------
If x = 6, then,
x-4 = 2 each of blue, green and red
There wouldn't be any other color since 6-2-2-2 = 0
A store manager records a positive number to show when a deposit is made to the store's bank account and a negative number to show withdrawals.
Which equation could represent how the store manager records making 3 withdrawals of $36 each?
O 3 x 36 108
O 3x-36= -108
-3 x 36 108
O-3 x-36= -108
Answer:
03*36 108 the positive number
I need help on this question
Answer:
Real zeros are: x = 0, x = 1 and x =2
***Your graph is incorrect. See mine for the correct graph***
Step-by-step explanation:
We have the polynomial
[tex]$\displaystyle \:x^{4}-3x^{3}+2x^{2}\:=\:0$[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}x^2:\\\\[/tex]
[tex]=x^2\left(x^2-3x+2\right)[/tex]
[tex]\mathrm{Factor}\:x^2-3x+2:[/tex]
For an expression of the form ax² + bx + c we can find factors if we find two values u and v such uv = c and u + v =b and factor into (ax +ux)+ (vx+c)
We have here a = 1, b = -3 c = 2
==> u = -1, v = -2
[tex]\:x^2-3x+2 = (x-1)(x-2)[/tex]
So the original expression becomes
[tex]\:x^2-3x+2 = x^2\left(x-1\right)\left(x-2\right)[/tex]
To find the zeros, set this equal to 0 and solve for x
[tex]x^2\left(x-1\right)\left(x-2\right)=0[/tex]
We end up with 3 roots corresponding to the 0 values for each of the three terms
[tex]x^2 = 0 == > x = \pm 0 = 0\\\\[/tex]
[tex](x - 1) = 0 == > x = 1\\\\(x - 2) = 0 == > x = 2\\\[/tex]
Answer real zeros are: x = 0, x = 1 and x =2
**** Your graph is incorrect. Check mine. The zeros happen where the curve intersects the x axis and these are at x = 0, x = 1, x =2
The point S is plotted on the coordinate grid below. Plot the point S', the reflection
of S over the x-axis.
Click on the graph to plot a point. Click a point to delete it.
Answer:
(1, -2)
Step-by-step explanation:
Reflecting a point over the x-axis means [tex](x,y) \longrightarrow (x, -y)[/tex].
5 In nahiangle Bcm. Ireos B = / 13 which function also cauals
Given data:
The given measurement of angle C is 90 degrees.
The given value of cos(B) =5/13.
The sum of all angles of triangle is,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^{\circ} \\ \angle A+\angle B+90^{\circ}=180^{\circ} \\ \angle A+\angle B=90^{\circ} \\ \angle B=90^{\circ}-\angle A \end{gathered}[/tex]Substitute the above value in the given expression.
[tex]\begin{gathered} \cos (90^{\circ}-A)=\frac{5}{13} \\ \sin A=\frac{5}{13} \end{gathered}[/tex]Thus, the correct answer is sin(A), so the third option is correct.
Simplify the expression (3^1/4)^2 to demonstrate the power of a power property. Show any intermittentstepsthat demonstratehow you arrived at the simplified answer.
(3^1/4)²
= (3^1/4) x (3^1/4)
=(3)^1/4 + 1/4
=(3)^1/2
Which can also be expressed as
= √3
²
Determine the X intercepts of the para bola whose graph is given below write your answer as ordered pairs separated by a comma if necessary
The x-intercepts are (-1, 0) and (4, 0)
Explanation:Given:
A graph of a parabola
To find:
the x-intercepts of the parabola in ordered pairs
The x-intercept is the value of x when y = 0
On a graph, it is the value of x when the line crosses the x-axis
The line crosses the x axis at x = -1 and x = 4
The x intercept in ordered pairs will be in the form (x, y)
when x = -1, y = 0
when x = 4, y = 0
The x-intercepts are (-1, 0) and (4, 0)
The sum of two numbers is 83. The difference of the 2 numbers is 13. What is the product of the two numbers?A.1632B.1650C.1666D.1680
Answer:
Let the first number be
[tex]=x[/tex]Let the second number be
[tex]=y[/tex]The sum of two numbers is 83 can be represented below as
[tex]x+y=83\ldots\ldots(1)[/tex]The difference of the 2 numbers is 13 can be represented below as
[tex]x-y=13\ldots\ldots\text{.}(2)[/tex]Step 1:
From equation (1) make x the subject of the formula to to give equation (3)
[tex]\begin{gathered} x+y=83\ldots\ldots(1) \\ x=83-y\ldots\text{.}(3) \end{gathered}[/tex]Step 2:
Substitute equation (3) in equation (2)
[tex]\begin{gathered} x-y=13\ldots\ldots\text{.}(2) \\ x=83-y\ldots\text{.}(3) \\ 83-y-y=13 \\ 83-2y=13 \\ \text{collect similar terms,} \\ -2y=13-83 \\ -2y=-70 \\ \text{divide both sides by -2} \\ \frac{-2y}{-2}=\frac{-70}{-2} \\ y=35 \end{gathered}[/tex]Step 3:
Substitute y= 35 in equation (3)
[tex]\begin{gathered} x=83-y\ldots\text{.}(3) \\ x=83-35 \\ x=48 \end{gathered}[/tex]Hence,
The product of the two numbers will be calculated as
[tex]\begin{gathered} =x\times y \\ =35\times48 \\ =1680 \end{gathered}[/tex]Hence,
The final answer is = 1680
OPTION D is the final answer
please give a VERY SHORT EXPLANATION NOT LONG! i inserted a picture of the question
If the amount of time spent is lesser than or equal to 250, so the price is $29, so we have the first part of the piecewise equation:
[tex]f(x)=29,\text{ x <= 250}[/tex]Then, for an amount of time greater than 250, the extra minutes are charged by 0.35 per minute, and this extra cost will add the fixed cost of $29, so the second part of the equation is:
[tex]f(x)=29+(x-250)0.35,\text{ x>250}[/tex]The option that shows the correct piecewise equation is option A.
Which of the following size measures will form a right triangle
From the given side lengths, let's find the measures that will form a right triangle.
Apply Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]Where:
• a ,and ,b, are lengths of the legs
,• c is the length of the hypotenuse.
Now, let's start from the first measures in option a.
• 48m, 64m, and 85m
[tex]\begin{gathered} 48^2+64^2=85^2 \\ \\ 2304+4096=7225 \\ \\ 6400\ne7225 \end{gathered}[/tex]The measures in option a will NOT form a right triangle since the left side of the equation does not equal the right side.
• 27 yd, 36 yd, 45 yd
[tex]\begin{gathered} 27^2+36^2=45^2 \\ \\ 729+1296=2025 \\ \\ 2025=2025 \end{gathered}[/tex]The measures in option B will form a right triangle because the Equation is true.
ANSWE
HELP PLEASEEEEE!!!!!!
A horizontal line with evenly spaced numerical increments is referred to as a number line. How the number on the line can be answered depends on the numbers present. The use of the number is determined by the question that it corresponds to, such as when graphing a point.
The visual depiction of numbers, such as fractions, integers, and whole numbers, spread out uniformly along a single horizontal line is known as a number line. A number line can be used as a tool for operations like addition and subtraction as well as comparison and sorting of numbers.
Given:
As from the Figure we have
-1 3/4 = -7/4 = -1.75, which is represented by point 1 on the number line.
and, 14/8 = 1.75, which is represented by point 7 on the number line.
and, 1.125, which is represented by point 6 on the number line.
and, -0.875, which is represented by point 4 on the number line.
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Solve for x
4x = -5
Put the answer in its simplest form.
Answer:
[tex] \sf x=-1.25 [/tex]
[tex]\sf--------------------------------------------------------------------- [/tex]
Step-by-step explanation:
4x = -5
Divide both sides by 4 to single out the variable
4x/4 = -5/4
x = -1.25
f(x) = -5x -4 and g(x) = x^2 + 3 find (g+f)(x)
f(x) = -5x -4
g(x) = x^2+3
To find (g+f)(x) , simply add both equations:
(g+f)(x)= x^2+3 + (-5x -4 )
(g+f)(x)= x^2+3 -5x -4
Combine like terms
(g+f)(x)= x^2-5x+3-4
(g+f)(x)= x^2-5x-1
Cassie’s latest financial goal is to eliminate her credit card debt
Based on Cassie's financial goal to eliminate her credit card debt, the graph that would best model her situation in terms of scale and label is B. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)
How to model a graph?When modeling a graph, the time period is often the independent variable. This means that the time period which are in months (months that Cassie makes monthly payments) need to be on the x-axis and will be labelled from 0 to 12 months for the months of the year.
The amount of credit card debt would then be on the y-axis. It is best to have a scale that is larger than the maximum debt Cassie has to that the data can be included properly. So a limit of 0 - 8,000 is best and would properly incorporate the $5,000 she already owes.
Full question is:
Cassie's latest financial goal is to eliminate her credit card debt. She has about $5,000 in credit card debt. She determines that she can afford to make
monthly payments of about $500. To track her progress, she plans to create a graph to model her situation. How should Cassie label and scale her
graph?
A.X-axis scale, 0-8; label, Total Debt ($) y-axis scale, 0-5,000; label, MonthsB. X-axis scale, 0-12; label, Months y-axis scale, 0-8,000; label, Total Debt ($)C. X-axis scale, 0-8; label, Years y-axis scale, 0-5,000; label, Total Debt ($)D. x-axis scale, 0-12; label, Total Debt ($) y-axis scale, 0-8,000; label, YearsFind out more on models at https://brainly.com/question/22049822
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9.) What type of relationship is indicated by the following set of ordered pairs (linear or quadratic)? Explain/Show
how you know by finding successive differences
X
-2
-1
0
1
2
3
Y=-4x-3
Y
14
-1
-6
-1
14
39
10.) Write the equation for question 9 showing all your work for full credit.
11.) Calculate fl-7) for the equation you wrote in Q10. Pls answer all 3 question will mark Brainliest
Step-by-step explanation:
9)
it is not linear, because while x is increasing with every data point by 1, y is decreasing and increasing again, and the differences from one point to the other vary.
for a linear relationship also y has to change in a constant way, and the difference from one point to the next would be the same for all points.
10)
so, since it is not linear, it is quadratic then (since that was our only given alternative).
y = ax² + bx + c
we know c from point (0, -6). c = -6.
for a and b we need to use 2 data points with their x and y coordinates.
let's start with the first (-2, 14)
14 = a×(-2)² + b×-2 - 6 = 4a - 2b - 6
we can simplify that
7 = 2a - b - 3
and then
10 = 2a - b
the next point is (-1, -1)
-1 = a×(-1)² + b×-1 - 6 = a - b - 6
5 = a - b
so, we have the 2 equations
10 = 2a - b
5 = a - b
from the second we get
a = 5 + b
and that we can use in the first equation
10 = 2×(5 + b) - b = 10 + 2b - b
0 = b
therefore
5 = a - b = a - 0 = a
a = 5
and the equation is
y = 5x² - 6
11)
f(-7) = 5×(-7)² - 6 = 5×49 - 6 = 245 - 6 = 239
what is the area of the Shaded region used 3.14
In this problem, the area of the shaded region is equal to the area of the complete square, minus the area of the four circles
so
REmember that
The length side of the complete square is equal to two times the diameter of one circle
A=(2*12)^2-4*pi*(12/2)^2
assume pi=3.14
A=576-4(3.14)(36)
the area of the Shaded region is A=123.84 ft^2