Answer: x = -1
Step-by-step explanation:
Step 1: Distribute. 6 + 3x - 2x = 11 + 4 + 10x
Step 2: Subtract like-terms. x + 6 = 10x + 15
Step 3: Leave x by itself. x + (6-6) = 10x + (15-6)
Step 4: Subtract 10x to x, and simplify. (x - 10x) = (10x - 10x) + 9
Step 5: Divide. -9x/9 = 9/9
The answer is x = -1. Hope this helps
Question
Jim's music store bought a guitar at the wholesale price of $1,200. Jim marked up the price 50%. Find the list price.
Answer: $1,800
Step-by-step explanation:
$4,500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years
The account balance after 3 years of continuous compounding at 10% annual interest is $6,074.32.
To solve this problem, we can use the formula for continuous compounding, which is:
[tex]A = Pe^{(rt)[/tex]
where A is the account balance after t years, P is the principal amount invested, r is the annual interest rate expressed as a decimal, and e is the mathematical constant approximately equal to 2.71828.
In this problem, P = $4,500, r = 0.10, and t = 3. Substituting these values into the formula, we get:
[tex]A = 4500 * e^{(0.10 * 3)[/tex]
[tex]A = 4500 * e^{(0.30)[/tex]
A = 4500 * 1.34986
A = $6,074.32 (rounded to the nearest cent)
Therefore, the account balance after 3 years of continuous compounding at 10% annual interest is $6,074.32.
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The complete question is :
If $4500 is invested at 10% annual interest, which is compounded continuously, what is the account balance after 3 years, assuming no additional deposits or withdrawals are made?
find the length of ab
Answer:
[tex]AB \approx 5.6 \text{ cm}[/tex]
Step-by-step explanation:
We can find the length of side AB using the trigonometric ratio cosine.
[tex]\cos(\theta) = \dfrac{\text{adjacent}}{\text{hypotenuse}}[/tex]
↓ plugging in the given values
[tex]\cos(62\°) = \dfrac{AB}{12}[/tex]
↓ multiplying both sides by 12
[tex]12 \cdot \cos(62\°) = AB[/tex]
↓ plugging into a calculator
[tex]\boxed{AB \approx 5.6 \text{ cm}}[/tex]
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
the final velocity is approximately 14.5 meters per second.
Define accelerationThe rate at which an object's velocity alters over time is known as acceleration. It is a vector quantity, which means it has both magnitude (a numerical value) and direction.
Using the formula: v² = u2 + 2as
We can plug in the values given:
u = 6 m/s (initial velocity)
a = 3 m/s² (acceleration)
s = 29 m (distance)
v² = (6 m/s)² + 2(3 m/s²)(29 m)
v² = 36 m²/s² + 174 m²/s²
v²= 210 m²/s²
To solve for v, we need to take the square root of both sides of the equation:
v = √(210 m²/s²)
v ≈ 14.5 m/s (rounded to one decimal place)
Therefore, the final velocity is approximately 14.5 m/s.
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The complete question is:
v²=u²+2as
Where v
is the final velocity (in m/s), u
is the initial velocity (in m/s), a
is the acceleration (in m/s²) and s
is the distance (in meters).
Find v
when u
is 6 m/s, a
is 3 m/s², and s
is 29 meters.
1. How many ways are there to get from the point (-3,2) to (-1,-1) if you only step down and to the right
2. How many ways are there to get from the point (-1,-2) to (4,0) if you only step up and to the right
calculated using the binomial coefficient:
6 choose 3 = 6! / (3! * (6-3)!) = 20 ways
The binomial coefficient can be used to compute the following:
7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.
1. We simply need to take three steps down and three steps to the right in order to move from (-3,2) to (-1,-1) by doing so. It doesn't matter in whatever sequence we do these stages.
As a result, the number of ways to select 3 steps out of a total of 6 steps is the number of ways to travel from (-3,2) to (-1,-1). The binomial coefficient can be used to compute the following:
6 select 3 is equal to 6!/(3!*(6-3)!) = 20 ways.
2. We need to take 5 steps to the right and 2 steps up in order to move from (-1,-2) to (4,0) by simply moving up and to the right. It doesn't matter in whatever sequence we do these stages.
Hence, the variety of routes to and from The range of options for selecting 2 stages out of a total of 7 steps is from (-1,-2) to (4,0). The binomial coefficient can be used to compute the following:
7 select 2 is equal to 7 / (2! * (7-2)!) = 21 ways.
Describe the binomial coefficient?The number of possibilities to choose k things randomly from a set of n items is represented mathematically by the binomial coefficient. The formula: It is represented by the symbol "n pick k" or "C(n,k)" and can be calculated.
C(n,k) = n!/(k!*(n-k))!
where the factorial function is shown by "!" A non-negative integer's factorial is the sum of all positive integers that are less than or equal to that number. 5!, for instance, equals 5 x 4 x 3 x 2 x 1 = 120.
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The image of the point (8,1) under a translation is (9,2). Find the coordinates of
the image of the point (5,5) under the same translation.
Answer:
Since the translation has shifted the point (8,1) to (9,2), we can determine the displacement vector between these two points as:
(9,2) - (8,1) = (1,1)
This vector represents the amount and direction of the translation. To find the image of the point (5,5) under the same translation, we need to add this vector to the coordinates of the point:
(5,5) + (1,1) = (6,6)
Therefore, the image of the point (5,5) under the same translation is (6,6).
A sample of maximum pressure from 12 trials with a stamping machine yielded a mean of 7.2 thousand psi and a standard deviation of 1.2 thousand psi. The histogram of the sample data is approximately normal. Calculate a 90% confidence interval.
The 90% confidence interval for the mean pressure is calculated equivalent to (6.39, 7.99).
What is t-distribution table?A t-distribution table is a statistical table that lists critical values of the t-distribution for various levels of significance and degrees of freedom. The t-distribution is a probability distribution that is used when the sample size is small or when the population standard deviation is unknown.
The table is organized by degrees of freedom (df), which is calculated as n-1, where n is the sample size. It also lists different levels of significance, usually ranging from 0.01 to 0.5 or more. The critical values are listed in the table corresponding to the degrees of freedom and the significance level. To use a t-distribution table, you need to know the degrees of freedom and the level of significance.
To calculate the 90% confidence interval for the mean pressure, we can use the formula:
CI = X' ± Z*(σ/√n)
Where X' is the sample mean, σ is the sample standard deviation, n is the sample size, and Z is the critical value for a 90% confidence interval.
Since the sample size is 12, we need to use a t-distribution with 11 degrees of freedom to find the critical value, because we are estimating the population standard deviation from the sample. Using a t-distribution table or calculator, we can find that the critical value for a 90% confidence interval with 11 degrees of freedom is approximately 1.796.
Substituting the values into the formula, we get:
CI = 7.2 ± 1.796*(1.2/√12)
= 7.2 ± 0.81
Therefore, the 90% confidence interval for the mean pressure is:
(7.2 - 0.81, 7.2 + 0.81) or (6.39, 7.99)
So, we can say with 90% confidence that the true mean pressure of the machine lies between 6.39 thousand psi and 7.99 thousand psi.
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How to write this standard form? 2y=3x+5
The standard form of the equation is as follows:
3x -2y + 5 = 0
Define equations?A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is known as an equation. as in 3x + 5 Equals 15, for instance.
Equations come in a variety of forms, including linear, quadratic, cubic, and others.
In the question,
The given equation is: 2y = 3x + 5
Standard form: ax + by + c = 0
Now,
2y = 3x + 5
Subtracting 2y from both the sides:
0 = 3x + 5 - 2y
Rearranging the equation we get,
3x -2y + 5 = 0
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Why am I not getting correct anwsers on my geometry questions
Maybe you're bad at math.
But I don't think that's true.
Try reading the questions more carefully and properly reading/understanding the material.
If you have any future questions, please ask me! I would be glad to help with your geometry work.
X^2(4x-3)(5x-1)=0 solve for x
Answer:
x = 0, 3/4, 1/5
Step-by-step explanation:
This equation is already factored into 3 terms.
For this expression to equal 0, any of the terms must be equal to 0. Set each factor equal to 0 and solve for x.
x^2 = 0
x = 0
4x - 3 = 0
4x = 3
x = 3/4
5x - 1 = 0
5x = 1
x = 1/5
The solutions are x = 0, 3/4, 1/5
Amy is making salt dough for an art project. Her recipe calls for cup of salt
for each batch of salt dough she makes. She has 3 cups of salt. How
many batches of salt dough can Amy make?
If Amy has 3 cups of salt and each batch of salt dough requires 1 cup of salt, then she can make:
3 batches = 3 cups of salt / 1 cup of salt per batch
So, Amy can make 3 batches of salt dough with the amount of salt she has.
Answer:
3 batches of salt dough
Step-by-step explanation:
Rita has coins worth $3.00. If the coins are all dimes, how many dimes does she have?
Answer:
300 dimes I believe because 3.00 is 100 dimes?
Step-by-step explanation:
4.) Ayana wants to be a marine biologist when she grows up. Her entire room is
ocean-themed, so she is painting her bed frame blue to match. She estimates
that she will need 800 milliliters of paint, but the hardware store only sells
paint in liters. If Ayana buys 1 liter of paint, how many milliliters will she have
left?
Answer:
200ml
Step-by-step explanation:
1000ml =1l
1000-800=200
work out the value of (√7^)^2
Answer:
Step-by-step explanation:
Puedo ayudarte con tu cálculo. (√7) 2 es lo mismo que √(7^2), que es igual a 7. Por lo tanto, el valor de (√7) 2 es 7.
What is the measure of angle P?
Enter your answer as a decimal in the box.
Round only your final answer to the nearest hundredth.
P = ___
Therefore, the measure of angle P is approximately 22.62 degrees (rounded to the nearest hundredth).
So, the final answer is P ≈ 22.62.
What is triangle?A triangle is a closed geometric shape that has three sides, three angles, and three vertices (or corners). It is one of the most basic and important shapes in geometry. The sum of the angles in a triangle is always 180 degrees, and the length of each side can be calculated using the Pythagorean theorem or other geometric formulas. Triangles can be classified into different types based on the length of their sides and the size of their angles, such as equilateral, isosceles, scalene, acute, obtuse, and right triangles. Triangles are used extensively in mathematics, science, engineering, and many other fields.
To find the measure of angle P, we can use the Pythagorean theorem and trigonometric functions. Here's the step-by-step solution:
From the given information, we know that one angle of the triangle is 90 degrees, and the lengths of the adjacent sides are 5 and 13.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = 5^2 + 13^2
c^2 = 194
c = sqrt(194)
c ≈ 13.93
So the length of the hypotenuse is approximately 13.93 units.
Now, we can use the trigonometric function sine to find the measure of angle P:
[tex]sin(P) = opposite / hypotenuse[/tex]
[tex]sin(P) = 5 / 13.93[/tex]
[tex]P = sin^{-1(5/13.93)}[/tex]
P ≈ 22.62 degrees
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The table shows the numbers of feet and the equivalent numbers of inches. Lionel painted a wall that is 12 feet long. How many inches long is the wall that Lionel painted?
A. 144
B. 122
C. 156
D. 132
The wall is 144 inches long that Lionel painted
What are unit cοnversiοns?Unit cοnversiοn is the prοcess οf cοnverting οne unit οf measurement tο anοther unit οf measurement that is equivalent tο the οriginal unit.
Given table:
Number οf feet's Number οs inches
3 36
5 60
8 96
10 120
Tο cοnvert feet tο inches, we need tο multiply the number οf feet by 12 since there are 12 inches in οne fοοt.
Fοr 12 feet, we have:
12 feet = 12 x 12 inches = 144 inches
Hence, the answer is A. 144.
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click (with your mouse) on the image that best represents a 0.02 correlation
Answer:
Step-by-step explanation:
it would be the third one
Area between curves questions
Answer:
16.739
Step-by-step explanation:
Pls help There is a 20% chance that a customer walking into a store will make a purchase. A computer was used to generate 5 sets of random numbers from 0 to 9, where the numbers 0 and 1 represent a customer who walks in and makes a purchase.
A two column table with title Customer Purchases is shown. The first column is labeled Trial and the second column is labeled Numbers Generated.
What is the experimental probability that at least one of the first three customers that walks into the store will make a purchase?
A) 60%
B) 13%
C) 40%
D) 22%
Answer:
it's D
Step-by-step explanation:
hope this helps lol.....
Multiply and simplify the following complex numbers: ( − 4 + 4 � ) ⋅ ( 3 + 2 � ) (−4+4i)⋅(3+2i)
Answer:
Step-by-step explanation:(−4+4i)⋅(3+2i);
= -4(3+2i)+4i(3+2i);
=-12-8i+12i-8;
= -20+4i
2 Al gives food pellets to the animals on the farm.
• Rabbits: 0.3 kilogram
• Chickens: 1,300 grams
• Ducks: 0.7 kilogram
How many more grams of pellets does Al give
the chickens than he gives the rabbits and
ducks combined?
A 1,000 g
B 2,300 g
C 3,000 g
D 300 g
By answering the presented question, we may conclude that As a result, inequality the correct answer is D) 300 g.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions and shows the relationship between them, usually using the symbols > (greater than), < (less than), ≥ (greater than or equal to), or ≤ (less than or equal to).
For example, "3 > 2" is an inequality that states that 3 is greater than 2. Similarly, "x ≤ 5" is an inequality that states that the value of x is less than or equal to 5.
Inequalities are used to represent ranges of possible values and are commonly used in algebra, calculus, and other branches of mathematics. They are often used to describe constraints in optimization problems, such as finding the maximum or minimum of a function subject to certain conditions.
To begin, we must convert the weights to the same units. We can convert rabbit weight to grammes as follows:
300 grammes = 0.3 kilos
We can also convert duck weight to grammes:
700 grammes = 0.7 kilos
We can now multiply the weights of rabbits and ducks:
300 grammes plus 700 grammes equals 1000 grammes
300 grammes plus 1300 grammes plus 700 grammes equals 2300 grammes.
To calculate how many more grammes of pellets Al feeds the chickens than the rabbits and ducks combined, subtract the total weight of pellets fed to the rabbits and ducks from the weight of pellets fed to the chickens:
1300 grammes minus 1000 grammes equals 300 grammes
As a result, the correct answer is D) 300 g.
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PLEASE ANSWER ASAP I NEED IT.
Answer:
[tex]\huge\boxed{\sf 18^{-3}}[/tex]
Step-by-step explanation:
Given expression:[tex]\displaystyle \frac{18^4}{18^7}[/tex]
According to exponent rule:[tex]\displaystyle \frac{a^m}{a^n} = a^{m-n}[/tex]So, the expression becomes:
= [tex]18 ^{4-7}[/tex]
= [tex]18^{-3}[/tex]
[tex]\rule[225]{225}{2}[/tex]
A water station table at a marathon starts with 200 plastic cups on it. Every minute, 15 cups are taken from the table. How many minutes could have passed if there are fewer than 65 cups on the table?
[tex]15x < 65[/tex]
Solve for x to get
[tex]x < 4.33[/tex].
So 4.33 minutes could have passed if there are fewer than 90 cups on the table.
Answer:
x=10
Step-by-step explanation:
Simplify the following
8⁶÷8
Answer: 8^5
Step-by-step explanation:
To simplify this expression, we can use the rules of exponents which state that when we divide two exponential terms with the same base, we can subtract their exponents. So we have:
8⁶ ÷ 8 = 8^(6-1) = 8^5
Therefore, the simplified expression is 8^5.
Mr. Apo Man borrowed K 2 000 from a bank to finance an extension to his home. He agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. a) What is the amount of each yearly payment? (2 marks)
If he agrees to pay back the loan in 8 yearly payments at 14% p.a. compound interest. The amount of each yearly payment is K 368.51.
How to find the yearly payment?To calculate the amount of each yearly payment, we can use the formula for the present value of an annuity:
PV = A * [(1 - (1 + r)^-n) / r]
where:
PV = present value of the loan
A = annual payment
r = interest rate per year
n = number of years of the annuity
In this case, Mr. Apo Man borrowed K 2 000 from the bank at an interest rate of 14% p.a. compound interest, and agreed to pay back the loan in 8 yearly payments.
So, we have:
r = 14% = 0.14
n = 8
PV = K 2 000
We can solve for A by rearranging the formula:
A = PV * r / [(1 - (1 + r)^-n)]
Substituting the values, we get:
A = K 2 000 * 0.14 / [(1 - (1 + 0.14)^-8)]
A = K 2 000 * 0.14 / 0.7598
A = K 368.51
Therefore, the amount of each yearly payment that Mr. Apo Man needs to make to repay the loan in 8 years at 14% p.a. compound interest is K 368.51.
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How much will I have by the end of the year if I clean the yards of roughly 6 houses for 25$ every month?
If you clean the yards of 6 houses for $25 every month, you will earn $1,800.
$25/month * 6 houses = $150/month . If you continue earning $150 every month for a year (12 months), then your total earnings for the year will be: $150/month * 12 months = $1,800
Therefore, you will have approximately $1,800 by the end of the year if you clean the yards of roughly 6 houses for $25 every month. However, please note that this assumes that you will be able to consistently clean the yards of all 6 houses every month for the entire year.
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pls pls help pls pls
The length of Jennifer's garden is 25 feet.
What is rectangle?A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length. It is a type of quadrilateral, a polygon with four sides. The length of the sides that are parallel to each other is called the base, and the length of the sides that are perpendicular to the base is called the height.
Let's suppose that the length of the garden is x feet.
We know that the width of the garden is 5 feet, so the total length of the edging required for the two widths is 2 x 5 = 10 feet.
The remaining edging is used for the two lengths of the garden, so we can write an equation based on the total length of the edging:
2(5 + x) = 60
Simplifying this equation, we get:
10 + 2x = 60
2x = 50
x = 25
Therefore, the length of Jennifer's garden is 25 feet.
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Hi i need help on this question please real answers!
Answer:
0.75
Step-by-step explanation:
0.75
or 3/4
Answer: 3/4
3/8x2= 3/4
Please help asap, i need it fast
After 13 years, the account will have a balance of $[tex]12,197.97[/tex].
Account balance or bank balance?The final cash amount for just a bank account that appears on the financial statements is known as the bank balance. When a query is made about the bank's records of the cash amount in an account, the bank balance may also be obtained at any time.
Can I utilize the balance on my account?Indeed, as your bank balance balance informs you of the amount of money in your account. That money serves a purpose when you remove or leave in situ, potentially in order to receive interest costs on it.
[tex]A = P (1 + r/n)^{nt}[/tex]
A = final amount
P = initial principal (or investment)
r = annual interest rate (as a decimal)
n = number of times the interest is compounded per year
t = time (in years)
Substituting the given values, we have:
[tex]P = 6,759[/tex]
[tex]r = 0.05[/tex]
[tex]n = 2[/tex]
[tex]t = 13[/tex] years
[tex]A = 6,759 (1 + 0.05/2)^{2*13}[/tex]
[tex]A = 6,759 (1.025)^{26}[/tex]
[tex]A = 6,759 (1.80611)[/tex]
[tex]A = 12,197.97[/tex]
Therefore, the account balance after [tex]13[/tex] years will be $[tex]12,197.97[/tex].
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rovide an appropriate response.
Determine the number of classes in the frequency table below.
tableau3 ( (Class Frequency)(23-24 7)(25-26 2)(27-28 6)(29-30 4)(31-32 1) )
2
5
6
20
There are 5 classes in the frequency table.
What is frequency table?The frequency of each data point or interval in a dataset is displayed in a frequency table. It is a technique for arranging data such that patterns and connections within the data may be examined. Two columns are normally present in the table: one for the intervals or data points (referred to as classes) and the other for the frequency of recurrence for each class. The classes may be intervals of equal size or they may be determined by the data's relevant categories or values.
From the given table we have:
Class 1: 23-24 (frequency of 7)
Class 2: 25-26 (frequency of 2)
Class 3: 27-28 (frequency of 6)
Class 4: 29-30 (frequency of 4)
Class 5: 31-32 (frequency of 1)
There are 5 classes in the frequency table.
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