The monthly salary for Job B after x months, which includes a 4% monthly raise, can be represented by the exponential function S(x) = 2000 * (1 + 0.04)^x, where S(x) is the salary and x is the number of months.
Explanation:To represent the monthly salary for Job B after x months, we need to account for the 4% raise each month. Since the starting salary is $2000, and the raise is 4% (or 0.04 in decimal form) of the previous month's salary, the function to represent the monthly salary can be written using a geometric sequence formula.
Let S(x) be the salary at month x. The function will be an exponential function in the form:
S(x) = 2000 * (1 + 0.04)^x
Here, 2000 is the initial salary, 0.04 represents the 4% raise, and x is the number of months that have passed.
how do you solve
-4/7 + 2/7x - 14x + 4/7
Answer:
-96/7x
Step-by-step explanation:
-4/7+2/7x-14x+4/7
-4/7+4/7+2/7x-14x
2/7x-14x
2/7x-98/7x
-96/7x
Answer:
-96/7
Step-by-step explanation:
A steel ball is traveling through water with a speed of x meters per second, where x is positive the drag force, F
At what speed in meters per second does the ball have a force of 0.5 N on it
the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
To find the speed at which the drag force F on the steel ball is 0.5 N, we need to solve the equation:
[tex]\[ F = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Given that [tex]\( F = 0.5 \)[/tex], we can substitute this value into the equation and solve for x:
[tex]\[ 0.5 = 0.5 + 0.004(x + 50)(x - 2.5) \][/tex]
Subtracting \( 0.5 \) from both sides, we get:
[tex]\[ 0 = 0.004(x + 50)(x - 2.5) \][/tex]
Now, since the product of two factors is equal to zero, at least one of the factors must be zero. So we have:
[tex]\[ x + 50 = 0 \][/tex] or [tex]\[ x - 2.5 = 0 \][/tex]
Solving these equations:
1. [tex]\( x + 50 = 0 \)[/tex]
[tex]\[ x = -50 \][/tex]
2. [tex]\( x - 2.5 = 0 \)[/tex]
[tex]\[ x = 2.5 \][/tex]
Since the speed cannot be negative, the only valid solution is [tex]\( x = 2.5 \)[/tex] meters per second.
Therefore, the speed at which the ball has a force of 0.5 N on it is [tex]\( 2.5 \)[/tex] meters per second.
The complete Question is given below:
A steel ball is traveling through water with a speed of x meters per second, where x is positive. The drag force, F , in newtons (N) is: F=0.5+0.004(x+50)(x-2.5) At what speed in meters per second does the ball have a force of 0.5N on it?
What is 83.9 rounded two decimal places
Find the value of the expression below. Express your answer in scientific notation.
The value of the expression is [tex]8.8 \times 10^{-2}[/tex].
Solution:
Given expression:
[tex]$\frac{\left(4.8 \times 10^{8}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \times 10^{-6}\right)[/tex]
To find the value of the given expression:
Using exponent rule: [tex]a^m\times a^n=a^{m+n}[/tex]
[tex]$\Rightarrow\frac{\left(4.8 \times 10^{8-6}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \right)[/tex]
[tex]$\Rightarrow\frac{\left(4.8 \times 10^{2}\right)}{\left(1.2 \times 10^{4}\right)} \times\left(2.2 \right)[/tex]
Using exponent rule: [tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]$\Rightarrow\frac{\left(4.8 \times 10^{2-4}\right)}{1.2} \times 2.2[/tex]
[tex]$\Rightarrow\frac{\left(4.8 \times 10^{-2}\right)}{1.2} \times 2.2[/tex]
Since [tex]\frac{4.8}{1.2}=4[/tex]
[tex]$\Rightarrow(4 \times 10^{-2})\times 2.2[/tex]
[tex]$\Rightarrow 8.8 \times 10^{-2}[/tex]
Hence the value of the expression is [tex]8.8 \times 10^{-2}[/tex].
I have a question! Well duhh thats why you see this
A baseball is moving at a speed of 2.2m/s when it strikes the catchers glove. The paddding of the glove is compressed by 24mm before the ball comes to a stop. We want to find the average acceleration of the baseball while its compressing the glove
jp i dont need help ppl keep wanting to see what i look like so sorry!
42 : 36 : 54 in simplest form
Step-by-step explanation:
42:36:54 divide this by 6
= 7 : 6 : 9 simplest form
570 times what gets 690
Answer:
1.21052631579 is the exact answer or 1.2 is if you round it
Step-by-step explanation:
This is the answer I got from dividing 690 by 570. Hope this helped
Answer:
1.21 to the nearest hundredth.
Step-by-step explanation:
570 * x = 690
x = 690/570
x = 1.210526316.
What is the missing number from 81,-,9,-,1
Answer:
-27 and -3
Step-by-step explanation:
81, -27, 9, -3, 1
The missing numbers in the sequence are -27 and -3. The sequence is 81, -27, 9, -3, 1
What is Sequence?Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
The given sequence is 81,-,9,-,1
we have to find the missing number.
As we observe when 81 is divided by -3 we get -27.
Now when -27 divided by -3 we get 9
When 9 is divided by -3
we get -3
When -3 is divided by -3
the value will be 1.
81, -27, 9, -3, 1
Hence, the missing numbers in the sequence are -27 and -3. The sequence is 81, -27, 9, -3, 1
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On a certain hot summer's day, 391 people used the public swimming pool. The daily prices are $1.25 for children and $2.25 for adults. The receipts for admission totaled $752.75. How many children and how many adults swam at the public pool that day?
127 children and 264 adults swam at the public pool that day
Solution:
Let "c" be the number of children swam
Let "a" be the number of adult swam
Cost for each children = $ 1.25
Cost for each adult = $ 2.25
391 people used the public swimming pool
Therefore,
c + a = 391
a = 391 - c ------- eqn 1
The receipts for admission totaled $752.75
Therefore, we frame a equation as:
number of children swam x Cost for each children + number of adult swam x Cost for each adult = 752.75
[tex]c \times 1.25 + a \times 2.25 = 752.75[/tex]
1.25c + 2.25a = 752.75 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
1.25c + 2.25(391 - c) = 752.75
1.25c + 879.75 - 2.25c = 752.75
c = 879.75 - 752.75
c = 127
Substitute c = 127 in eqn 1
a = 391 - 127
a = 264
Thus 127 children and 264 adults swam at the public pool that day
what is the equation of the following line written in slope intercept form?
a. y= -11x-7
b. y= -7x+11
c. y= -7x-11
Answer:
C
Step-by-step explanation:
slope is change in y over the change in x
points on graph are (-1, -4) and (-2, 3)
-4-3/-1+2 = -7/1 = -7
y = -7x + b
put one of the points in for x and y to solve for b
3 = -7 x -2 + b
3 = 14 + b
subtract 14 from both sides.
b = -11
Answer:
c
Step-by-step explanation:
solve for x and y
−8y+9x=−5
8y+7x=−75
Answer:
-8y + 9x = -5
8y + 7x = -75
16x = -80
x = -5
8y + 7(-5)= -75
8y - 35 = -75
8y = -40
y = -5
(-5,-5)
Round the following numbers and estimate the product.
72.87 . 37
Martina runs 7 miles in 50 mins at the same rate how many miles will she run in 75 mins
Martina runs 10.5 miles in 75 minutes
Solution:
Given that,
Martina runs 7 miles in 50 minutes
Therefore, miles ran in 1 minute is:
[tex]Miles\ ran\ in\ 1\ minute = \frac{7}{50}\ miles[/tex]
At the same rate how many miles will she run in 75 mins
Thus, to find the miles ran in 75 minutes:
[tex]Miles\ ran\ in\ 75\ minute = \frac{7}{50}\ \times 75\\\\Miles\ ran\ in\ 75\ minute = 0.14 \times 75\\\\Miles\ ran\ in\ 75\ minute = 10.5[/tex]
Thus she runs 10.5 miles in 75 minutes
Please help! Will give Brainliest!
What is the area of this trapezoid? 175 in² 140 in² 129 in² 85 in² Trapezoid A B C D with parallel sides D C and A B. Point F and E are on side D C. Point F is connected to point A by a dotted segment. Point E is connected to point B by a dotted segment. A B E F is a rectangle. D F is 4 inches. E C is 6 inches. E B is 7 inches. A B is 15 inches.
Answer:
198
Step-by-step explanation:
Answer:
The answer is 140! brainilest please!
Step-by-step explanation:
Clare has $150 in her bank account. She buys a bike for $200. What is Claire's account balance now?
Cooldown
unit 5, lesson 4
4.4
Answer:
-50
Step-by-step explanation:
she only had 150, but spent 200 she overdrew
she has an overdraft of $50
Answer:-50
Step-by-step explanation:150-200=-50
Which graph is the result of reflecting f(x) = One-fourth(8)x across the y-axis and then across the x-axis? On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and incresaes into quadrant 1. It goes through the y-axis at (0, 0.25) and goes through (1, 2). On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases in quadrant 2. It crosses the y-axis at (0, 0.25) and goes through (negative 1, 2). On a coordinate plane, an exponential function approaches y = 0 in quadrant 3 and decreases into quadrant 4. It crosses the y-axis at (0, negative 0.25) and goes through (1, negative 2). On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25).
On a coordinate plane, an exponential function increases in quadrant 3 into quadrant 4 and approaches y tends to zero, which goes through (-1,-2) and crosses the y-axis at (0,-0.25).
What is a function?Function is a type of relation, or rule, that maps one input to specific single output.
Given that f(x) = 1/4[tex](8)^x[/tex]
The Reflecting f(x) across the y - axis,
[tex]g(x) = \frac{1}{4} 8^{-x}[/tex]
g(x) reflecting across the x-axis,
The given graph, where f(x) represented by red, g(x) represented by green and function h(x) represented by purple
We conclude that exponential function increases in quadrant 3 into quadrant 4 and approaches y tends to zero, which goes through (-1,-2) and crosses the y-axis at (0,-0.25).
Therefore; the answer is option D; On a coordinate plane, an exponential funtion increases in quadrant 3 into quadrant 4 and approaches y tends to zero, which goes through (-1,-2) and crosses the y-axis at (0,-0.25).
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Answer:
Your answer is D
Step-by-step explanation:
I'm being forced to redo a handful of my answers since they were deleted...
"On a coordinate plane, an exponential function increases in quadrant 3 into quadrant 4 and approaches y = 0. It goes through (negative 1, negative 2) and crosses the y-axis at (0, negative 0.25)."
what property can be used to solve x-3= -5
Answer:
-2
Step-by-step explanation:
x-3=-5
x=-5+3
x=-2
What is the y-intercept of the function f(x)=4 -- 5x?
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I apologize if you are offended by the "bad words" in the answer below. Brainly's censor got offended.
What is the correct answer???
Option D: [tex]\frac{2}{5}[/tex] is the x-coordinate
Explanation:
It is given that the coordinates of the line segment are A(3,2) and B(6,11).
Since, the line is partitioned by the point C by the ratio AC : BC = 2 : 3
The distance between the x-coordinates is 3 units.
To determine the value of the x-coordinate for point C, let us divide the value of x-coordinate from the ratio divided by the sum of ratio.
The value of x-coordinate from the ratio is 2.
Sum of the ratio is 2 +3 = 5
Thus,
The x - coordinate = value of x-coordinate from the ratio / Sum of ratio = 2/5
Substituting the values, we have,
The x - coordinate of the Point C = [tex]\frac{2}{5}[/tex]
Thus, Option D is the correct answer.
A certain drink is made by adding 4 parts water to 2.5 part drink mix. What percent of the mixture is water? Omit % sign in your answer. Round your answer to the nearest tenth.
The mixture contains 61.5% of water.
Step-by-step explanation:
Total parts = 4+ 2.5 = 6.5
Parts of water =4
parts of drink = 2.5
Percent of water in the mixture = 4 × 100/ 6.5
= 400/6.5
= 61.53%
It is rounded to the nearest tenth as 61.5%.
To find the percentage of water in the mix, we calculate the proportion of water (4 parts) to the total mixture (6.5 parts) and multiply by 100%, resulting in approximately 61.5%.
To determine what percent of the mixture is water when a drink is made with 4 parts water and 2.5 parts drink mix, we add together the parts of water and drink mix to find the total parts of the mixture. Then, we calculate the fraction of the mixture that is water and convert that to a percentage.
First, we find the total parts of the mixture:
Water: 4 parts
Drink mix: 2.5 parts
Total parts: 4 + 2.5 = 6.5 parts
Next, we calculate the percentage of the mixture that is water:
(Parts of water / Total parts) × 100%
(4 parts / 6.5 parts) × 100% \approximately 61.5%
Rounding to the nearest tenth, we get:
61.5
Gasoline is selling for $3.29 per gallon. It takes 28.25 gallons to fill up Bill's new pick-up truck. How much does he pay?
Answer:
approximately (put the approximately sign) $92.94
Step-by-step explanation:
Just multiply 28.25 by $3.29. Tjen, round the answer to the nearest hundredth.
If theta is an acute angle, solve the equation tangent theta equals four fifths
. Express your answer in degrees, rounded to one decimal place.
Answer:
[tex]\theta=38.7\degree[/tex]
Step-by-step explanation:
We want to solve [tex]\tan \theta=\frac{4}{5}[/tex] given that [tex]\theta[/tex] is acute.
We take tangent inverse of both sides to get:
[tex]\theta=\tan^{-1}(\frac{4}{5})[/tex]
Now set your calculator to degree mode and evaluate [tex]\tan^{-1}(\frac{4}{5})[/tex] to obtain:
[tex]\theta=38.6598\degree[/tex]
To one decimal place, we have;
[tex]\theta=38.7\degree[/tex]
To solve the equation 'tangent theta equals four fifths', we use the inverse tangent function, or arctan(4/5). Using a calculator in degree mode, the result is approximately 38.7 degrees.
Explanation:To solve the equation tangent theta equals four fifths, we need to find the angle whose tangent is 4/5. We can find this using the inverse tangent function (also known as arctan)
So, theta = arctan(4/5)
Use a calculator to find out the value of arctan(4/5). Make sure your calculator is in degree mode because the answer needs to be in degrees. The answer is approximately 38.7 degrees, rounded to one decimal place.
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lonnie bought 6 pieces of ribbon. Each ribbon was 2 and 3/4 yards long. How much ribbon did Lonnie buy in all
Answer:
14.04
Step-by-step explanation:
you mupltiy
Answer:
b
Step-by-step explanation:
2.34 x 6 = 14.04
so it would total up to 14.12
Please Help Me!
A sphere's center is located at (0,0,0). The point (4,9,-5) is located on the surface of the sphere. Find the length of the radius of the sphere. Round to the nearest tenth.
Answer:
The length of the radius of the sphere is 11.0 units
Step-by-step explanation:
we know that
To calculate the radius of the sphere, we can use the distance formula
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}+(z_2-z_1)^{2}}[/tex]
where
d is the length of the radius
(x_1,y_1,z_1) is the center of the sphere
and
(x_2,y_2,z_2) is one point on the surface of the sphere
we have
[tex](x_1,y_1,z_1)=(0,0,0)[/tex]
[tex](x_2,y_2,z_2)=(4,9,-5)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-0)^{2}+(9-0)^{2}+(-5-0)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(9)^{2}+(-5)^{2}}[/tex]
[tex]d=\sqrt{122}[/tex]
[tex]d=11.0\ units[/tex]
therefore
The length of the radius of the sphere is 11.0 units
HELP QUICK I NEED TO KNOW THIS Three pirates named Ahab, Sparrow, and Davy play a game. The pirates have a total of 210 coins, and each pirate has a different number of coins. At the end of the game, Ahab has won 5 coins and Davy has won 7 coins. Now, the ratio of coins belonging to Ahab, Sparrow, and Davy is 4:5:6, respectively. How many coins did Sparrow have at the beginning of the game?
The number of coins Sparrow has at the beginning of the game is 92 coins.
How many coins did Sparrow have at the beginning of the game?
Total number of coins = 210.
Ratio of coins belonging to Ahab, Sparrow and Davy = 4 : 5 : 6
Let
x = multiplying factor
The number of coins to Ahab = 4x
The number of coins to Sparrow = 5x
The number of coins to Davy = 6x
Since, total number of coins = 210
So
4x + 5x + 6x = 210
15x = 210
Divide both sides by 15
x = 16
Therefore,
The number of coins to Sparrow = 5x
= 5 × 16
= 80 coins
At the end Ahab and Davy wins 5 and 7 coins respectively
So at the beginning of the game, the number of coins Sparrow has = 80 + 7 + 5
= 92
Which graph represents the solution for the equation -5/2x -1 = 4x + 2?
Answer:
D would be the best choice.
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
Did the test
5. Katie makes and sells scarves. Her monthly profit is given by P(s) = -s2 + 25s - 100, where "s" is the selling price. For what range of prices can Katie sell the scarves, in order to make a profit? (For what values of "s" will -s2 + 25s - 100 be greater than 0?)
Answer: s > 5
Step-by-step explanation:
-s² + 25s - 100 > 0
Coefficient of s² is -1, multiply the equation through by -1.
-1 × (-s² + 25s - 100)
s² — 25s + 100
ax² + bx + c
Then you get the factors x and y that gives x + y = b and xy = c
b = -25 and c = 100, x = -20 and y = -5
-20 × -5 = 100 and -20 + -5 = -25
Then
s² — 20s — 5s + 100 > 0
Factorising,
s (s — 20) — 5(s — 20) > 0
(s — 5)(s — 20) > 0
(s — 5) > 0 and (s — 20) > 0
s>5 and s>20
s > 5
Hope this Helps?
Which inequality is equivalent to
6. X+7
5x+3?
Step-by-step explanation:
(1/2x)+7 is a equation
Answer:
on edgenuit it's c
Step-by-step explanation:
-15x-53/x^2+8x+15
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
Answer:
12 m squared
Step-by-step explanation:
area of triangle is 1/2 base x height
base x height is 28 so 1/2 is 14
the area of the rectangle is base x height
1 x 2 = 2
14-2 = 12
brand A granola is 25% nuts and dried fruit and brand B granola is 10% nuts and dried fruit. how much of sweet item A and sweet item B should be mixed to form a 30-lb batch of sweets that is 22% nuts and dried fruit?
To create a 30-lb batch of sweets that is 22% nuts and dried fruit, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B.
To find the solution, we can set up a system of equations based on the percentages of nuts and dried fruit in each brand of granola and the desired final percentage.
Let x represent the amount of sweet item A (in pounds) and y represent the amount of sweet item B (in pounds) to be mixed.
The total weight of the mixture is x + y = 30 lbs.
The percentage of nuts and dried fruit in brand A is 25%, so the amount of nuts and dried fruit from A is 0.25x lbs.
The percentage of nuts and dried fruit in brand B is 10%, so the amount of nuts and dried fruit from B is 0.10y lbs.
The desired final percentage in the mixture is 22%, so we have the equation: (0.25x + 0.10y) / 30 = 0.22.
Now, we can solve this system of equations to find x and y.
First, we'll multiply the last equation by 30 to get 0.25x + 0.10y = 6.6.
Then, we can use substitution or elimination to solve for x and y.
In this case, it's simpler to use elimination, and we find that x = 12 lbs and y = 18 lbs.
Therefore, you should mix 12 lbs of sweet item A and 18 lbs of sweet item B to create the desired 30-lb batch with 22% nuts and dried fruit.
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