Answers
Answer:
Set your calculator to degree mode.
x^2 = 4^2 + 10^2 - 2(4)(10)(cos 29°)
x^2 = 46.0304
x = 6.78
The number that belongs in the green box is 6.78.
Related Questions
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
PLEASE ANSWER!!
Answers
Answer:
Step-by-step explanation:
a. 2r + 5 = b because you have you have 5 more blue marbles than double the red *r= red and b=blue
b. to do the substitution you know that the red marbles plus the blue marbles add up to 77 so
b + r=77
now we can isolate for b and then substitute that value into the first equation
b=77-r and then this goes to 2r+5=77-r
c. now you just have to get like terms to their side of the equal sign
add r to both sides: 2r+r+5=77-r+r= 3r+5=77
and then you subtract 5 from both sides which makes 3r=72
to find r, divide both sides by 3
r=24
there are 24 red marbles
1/27^{4-x}=9^{2x-1}
Please if you could explain how you get your answer, that would be great.
Answers
The solution of the given equation is x = -10.
We are given that;
The equation 1/27^{4-x}=9^{2x-1}
Now,
This is an exponential equation that can be solved by using the properties of exponents and logarithms. Here are the steps to solve it:
Rewrite both sides of the equation using the same base. Since 27 and 9 are both powers of 3, we can use 3 as the base. We have:
(3(-3))(4-x) = (32)(2x-1)
Apply the power rule of exponents to simplify the expressions. The power rule states that (ab)c = a^(bc). We have:
3^(-12+3x) = 3^(4x-2)
Since the bases are equal, we can set the exponents equal to each other and solve for x. We have:
-12 + 3x = 4x - 2 -10 = x
Therefore, by the given equation the answer will be x = -10.
Learn more about equations;
https://brainly.com/question/10413253
#SPJ1
15x + 6 = 10x + 21
x = 3
x = 5
x = 5
x = -5
Answers
-10x -10x
5x + 6 = 21
-6 -6
5x = 15, divide both by 5
x=3
Learning Page
Computing expected value in a game of chance
QUESTION
Scott is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Scott spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner
stops on the number 3, and $7 if the spinner stops on the number 4. He loses $1.25 if the spinner stops on 5 or 6.
(a) Find the expected value of playing the game.
dollars
(b) What can Scott expect in the long run, after playing the game many times?
Scott can expect to gain money.
He can expect to win dollars per spin.
Start
Scott can expect to lose money.
He can expect to lose dollars per spin.
Scott can expect to break even (neither gain nor lose money).
00 EXPLANATION
0 0/5
Answers
Answer:$0.25
Step-by-step explanation:
To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.
Let's first find the probabilities of each outcome:
- Probability of spinning1:1/6
- Probability of spinning2:1/6
- Probability of spinning3:1/6
- Probability of spinning4:1/6
- Probability of spinning5 or6:2/6( or1/3)
Now let's calculate the expected value:
Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)
Expected value=$0.25
So the expected value of playing the game is$0.25 per spin.
In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.
What is an improper fraction for 1 3/4
Answers
Answer:
An improper fraction for 1 3/4 is 7/4.
Step-by-step explanation:
[tex]\frac{7}{4}[/tex]
To find the improper fraction of a mixed number fraction. You first have to remove the whole number from the fraction (the big one bending the fraction)
Do this by multiplying the denominator (4) by the whole number (1)
4 x 1 = 4
Then add this number with the numerator (top number) which is 3.
4+3 = 7
Seven is our new numerator, our denominator stays the same (4)
So our new improper fraction is:
[tex]\frac{7}{4}[/tex]
How many real and complex roots exist for the polynomial
F(x)= x³ +2x² + 4x+8 ?
OA. 2 real roots and 1 complex root
OB. 1 real root and 2 complex roots
C. 3 real roots and 0 complex roots
D. 0 real roots and 3 complex roots
Answers
The roots of the function F(x) = x³ + 2x² + 4x + 8 are given as follows:
B. 1 real root and 2 complex roots.
How to identify the zeros of the function?The function in this problem is defined as follows:
F(x) = x³ + 2x² + 4x + 8.
The function is of the third degree, hence the total number of zeros of the function is of 3.
From the graph, the function has only one x-intercept, which is given as follows:
x = -2.
Hence the two remaining roots are the complex roots, meaning that option B is the correct option for this problem.
More can be learned about the zeros of a function at brainly.com/question/16550963
#SPJ1
what is an example of "an extension of a function f"?
Answers
An example of an extension of a function f is adding additional input-output pairs beyond the original domain and range of f.
What is an example of "an extension of a function f"?The extension of a function f means new function that preserves the properties and behavior of the original function on its domain while adding new values or expanding its domain.
For example, we will consider the function f(x) = x^2 defined on the interval [0, 1]. An extension of this function could be g(x) = x^2 for x in [0, 1] and g(x) = 0 for x outside [0, 1].
This extension maintains the quadratic behavior of f on [0, 1] while assigning a constant value of 0 to points outside that interval.
Read more about function
brainly.com/question/11624077
#SPJ1
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts. a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month? b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month? Be sure to include in your response: • the answer to the original question • the mathematical steps for solving the problem demonstrating mathematical reasoning
Answers
a. It will take 7 months to pay off the credit card.
b. it will take 4 months to pay off the credit card.
Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.
a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.
We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:
PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)
where:
PV is the present value of the debt
PMT is the payment amount per period
r is the monthly interest rate
n is the number of periods
Substituting the values, we get:
754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV ×r / PMT)) / log(1 + r)
n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)
n = 6.18
Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.
b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.
754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV × r / PMT)) / log(1 + r)
n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)
n = 3.43
Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.
Learn more about APR, visit:
brainly.com/question/13597527
#SPJ1
25% (iv) MP=Rs. 26600, Discount-10%
Answers
For an item with a marked price of Rs. 26,600 and a 10% discount, the discount price is Rs. 2,660. Therefore, the customer will pay Rs. 23,940 after applying the discount.
To calculate the amount of discount on an item with a marked price of Rs. 26,600 and a discount percentage of 10%, we can follow a simple formula.
First, let's calculate the discount amount. The discount percentage is 10%, which means we can find the discount amount by multiplying the marked price by the discount percentage:
Discount amount = Marked price × Discount percentage
= Rs. 26,600 × 10/100
= Rs. 2,660
So, the discount amount for the item is Rs. 2,660.
Now, let's understand what this means. A discount is a reduction in the original price of an item. In this case, the discount amount of Rs. 2,660 is the amount by which the price of the item is reduced. Therefore, after applying the discount, the customer would only need to pay Rs. 26,600 - Rs. 2,660 = Rs. 23,940.
It's important to note that the discount amount is not the final price the customer pays. The final price is the marked price minus the discount amount. So, in this scenario, the customer will receive a discount of Rs. 2,660, and they will pay Rs. 23,940 for the item.
Understanding how discounts work can be helpful when making purchasing decisions or comparing prices. It allows customers to evaluate the value they are receiving and make informed choices based on their budget and preferences.
For more such questions on discounted price
https://brainly.com/question/23865811
#SPJ8
Probable question:
What is the amount of the discount if the marked price of an item is Rs. 26,600 and the discount percentage is 10%?
factor completely using distributive law 25y-15z
Answers
Answer:
5(5y - 3z)
Step-by-step explanation:
25y - 15z ← factor out common factor of 5 from each term
= 5(5y - 3z)
What are the minimum and maximum values of the function?
Answers
The minimum value of [tex]f(x) = -2^3 \sqrt\(5-4x+3)[/tex] on the interval [1, 8] is -3 and the maximum value is 5. To find the minimum value, we can start by finding the critical points of the function.
The critical points are the points where the derivative of the function is equal to zero. In this case, the derivative of the function is
[tex]f'(x) = -2^3 \times (5-4x+3) ^(-3/2) \times (-4)[/tex]
The critical points of the function are x = 1 and x = 5.
We can now evaluate the function at each critical point and at the endpoints of the interval to find the minimum and maximum values. The values of the function at the critical points and at the endpoints are
x | f(x)
-- | --
1 | -3
5 | 5
8 | 9
For more such questions on interval
https://brainly.com/question/30460486
#SPJ8
Which route of delivery would be most appropriate for a patient with a bacterial sinus infection?
Answers
Goodluck!
A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)
Answers
An equation to represent this situation is y = 60x
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + b
Where:
m represent the slope or rate of change.x and y are the points.b represent the y-intercept or initial value.Based on the information provided above, we can logically deduce that the cheetah was clocked running 60 miles per hour over a 50-yard distance. This ultimately implies that, an equation that models this situation is given by:
y = 60x
Where:
y represents the distance.x represents the time in hours.Read more on equation here: https://brainly.com/question/1382184
#SPJ1
the ratio of women to men in a local book club is 7 to 3. whitch combanation of women to the total could the club have
Answers
The possible combinations of women to the total number of club members could be:
7 women out of 10 members.
14 women out of 20 members.
21 women out of 30 members.
28 women out of 40 members.
And so on, as long as "x" is a multiple of 10 that is divisible by 7.
The ratio of women to men in the local book club is 7 to 3. This means that for every 7 women, there are 3 men.
To find the possible combinations of women to the total number of club members, we can consider the total number of members as a multiple of 10 (since the ratio is given as 7 to 3). Let's assume the total number of club members is represented by the variable "x."
Based on the given ratio, we can calculate the number of women in terms of "x" by multiplying the ratio of women (7/10) by the total number of members:
Number of women = (7/10) * x
Since we're looking for possible combinations, the number of women must be a whole number. Therefore, "x" must be a multiple of 10 that is divisible by 7.
Let's explore some possible combinations:
If x = 10, the number of women = (7/10) * 10 = 7, which satisfies the ratio.
If x = 20, the number of women = (7/10) * 20 = 14, which satisfies the ratio.
If x = 30, the number of women = (7/10) * 30 = 21, which satisfies the ratio.
If x = 40, the number of women = (7/10) * 40 = 28, which satisfies the ratio.
As you can see, the possible combinations of women to the total number of club members could be:
7 women out of 10 members.
14 women out of 20 members.
21 women out of 30 members.
28 women out of 40 members.
And so on, as long as "x" is a multiple of 10 that is divisible by 7.
For such more questions on Ratio of Women:Men
https://brainly.com/question/15252151
#SPJ8
Need help with this equation 8x²+10x-3
Answers
Answer:
Step-by-step explanation:
You have to use the quadratic formula
x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]
and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2
you usually have to reject an answer but since there is no equal sign in the question, you should be fine
Can someone please help me wit this?
Answers
Answer:
6.6
Step-by-step explanation:
I’ve done this before. The original answer I did was 6.63 but it says round to the nearest tenth so yep…
complete the table , starting with the lowest class limit
Answers
The frequency distribution table would be:
Class ______ Freq ___ Midpoint __R/Freq__ C/Freq
0 - 9 _______ 4 ______ 4.5 ______ 0.2 _____ 4
10-19 _______ 5 ______ 14.5 _____0.25 _____9
20-29 ______ 4 ______ 24.5_____ 0.2______ 13
30-39_______3 ______ 34.5 _____0.15______ 16
40-49_______4 ______ 44.5 _____ 0.2 _____ 20
The data ranges from 0 - 49 . we had to use a class interval of 10 since we were interested in having just 5 classes.
The midpoint is the average value of the upper and lower class.
Relative frequency is the ratio of the class frequency to the total number of data in the distribution.
Cumulative Frequency is the running sum of frequencies in the distribution table.
Therefore, the frequency distribution captures all the information required.
Learn more on frequency distribution table :https://brainly.com/question/27820465
#SPJ1
Solve the following equations. Check the solutions. 8x^2 + 11 = 191 + 3x^2, 7x^2 - 15 = 49 + 3x^2, 14x^2 - 157 = 333 + 4x^2
Answers
The solutions to the equations are:
x = 6, x = 4, x = 7.
1. 8x² + 11 = 191 + 3x²
Rearranging the equation:
8x² - 3x² = 191 - 11
5x² = 180
Dividing both sides by 5:
x² = 36
Taking the square root of both sides:
x = ±6
Checking the solution:
8(6)² + 11 = 191 + 3(6)²
288 + 11 = 191 + 108
299 = 299
The solution x = 6 satisfies the equation.
2. 7x² - 15 = 49 + 3x²
Rearranging the equation:
7x² - 3x² = 49 + 15
4x = 64
Dividing both sides by 4:
x² = 16
Taking the square root of both sides:
x = ±4
Checking the solution:
7(4)² - 15 = 49 + 3(4)²
112 - 15 = 49 + 48
97 = 97
The solution x = 4 satisfies the equation.
3. 14x² - 157 = 333 + 4x²
Rearranging the equation:
14x² - 4x^2 = 333 + 157
10x² = 490
Dividing both sides by 10:
x² = 49
Taking the square root of both sides:
x = ±7
Checking the solution:
14(7)² - 157 = 333 + 4(7)²
686 - 157 = 333 + 196
529 = 529
The solution x = 7 satisfies the equation.
Therefore, the solutions to the equations are:
x = 6, x = 4, x = 7.
Learn more about Quadratic Equation here:
https://brainly.com/question/30098550
#SPJ1
What means killogram?
Answers
Answer:
1,000 grams
noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.
Henry has $21.50 to ride the trolley around San Francisco this week. It will cost him $0.50 every time he rides. Identify the dependent variable and the independent variable in this scenario.
Answers
Dependent variable: Total cost of riding the trolley
Independent variable: Number of times Henry rides the trolley.
In this scenario, the dependent variable is the total cost of riding the trolley, and the independent variable is the number of times Henry rides the trolley.
The dependent variable, the total cost of riding the trolley, depends on the independent variable, which is the number of times Henry rides the trolley. As Henry rides the trolley multiple times, the total cost will vary based on the number of rides.
The independent variable, the number of times he rides, determines the value of the dependent variable, the total cost.
for such more question on variable
https://brainly.com/question/19803308
#SPJ8
Absolute value of 2.
Answers
log base 4 of 9
HELPPPPPPPP
Answers
Answer:
1.58 ish
Step-by-step explanation:
For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007
A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the high-quality version is 4.2 MB.
Yesterday, there were 1380 downloads of the song, for a total download size of 4716 MB. How many downloads of the standard version were there?
Answers
There were 600 downloads of the standard version.
How many downloads were there?An equation means the formula that expresses the equality of two expressions by connecting them with the equals sign.
Let x represents the number of downloads of the standard version.
Given:
Size of the standard version = 2.4 MB
Size of the high-quality version = 4.2 MB
Total download size = 4716 MB
Total downloads = 1380
We will set up the following equation:
2.4x + 4.2(1380 - x) = 4716
2.4x + 5796 - 4.2x = 4716
-1.8x + 5796 = 4716
-1.8x = 4716 - 5796
-1.8x = -1080
x = 600
Read more about equation
brainly.com/question/29174899
#SPJ1
Simplify the rational expression
7x/14x^6
Answers
The simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
To simplify the rational expression (7x)/(14[tex]x^6[/tex]), we can reduce the numerator and denominator by their greatest common factor.
In this case, the greatest common factor is 7x.
Dividing both the numerator and denominator by 7x, we get:
(7x)/(14[tex]x^6[/tex]) = (7x)/(7x × 2[tex]x^5[/tex])
Canceling out the common factor of 7x, we have:
= 1/(2[tex]x^5[/tex])
Therefore, the simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
for such more question on rational expression
https://brainly.com/question/28832980
#SPJ8
If 15% of the customers total is $98,880, then the sum total equals what
Answers
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
Learn more about percent here:
https://brainly.com/question/11549320
#SPJ1
What is the instantaneous rate of change y=sqrtx of at x = 2? Responses negative 1 over 2 negative 1 over 4 negative 1 none of these none of these
Answers
The instantaneous rate of change of y = √x at x = 2 is √2 / 2.
To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.
Taking the derivative of y = √x using the power rule for differentiation, we have:
dy/dx = (1/2) × x^(-1/2)
Now, substituting x = 2 into the derivative expression:
dy/dx = (1/2) × 2^(-1/2)
= (1/2) × √2
= √2 / 2
Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.
None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.
for such more question on instantaneous rate
https://brainly.com/question/23377525
#SPJ8
Solve the equation below for x by graphing
3x =8_2x
Answers
The solution to the equation 3x = 8 - 2x is x = 1.6.
To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:
Express the equation in the form of y = f(x). Rearrange the equation:
3x + 2x = 8
5x = 8
x = 8/5 or 1.6
Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.
Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.
The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).
Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.
for such more question on equation
https://brainly.com/question/27870704
#SPJ8
Type the correct answer in the box.
Fill in the missing term in the equation.
(1 + 2)(2+1) + blank
= 5(2+i)
Answers
(1 + 2)(2 + 1) + blank
= 3(3) + blank
= 9 + blank
Expanding the right side of the equation:
5(2 + i)
= 10 + 5i
Since the left side of the equation (9 + blank) is equal to the right side (10 + 5i), we can deduce that the missing term should be equal to 1i.
Therefore, the missing term in the equation is "1i".
a tip of $10 is typically suitable for which kind of service?
a mover delivering furniture
a valet who parks your car
a waiter at a fast food restaurant
Answers
a new social media sit is increasing its user base by approximately 4% per month. If the site currently has 35.930 users, what will the approximate user base be 10 months from now?
Answers
Answer:
The approximate user base of the social media site 10 months from now would be approximately 52,374.
Step-by-step explanation:
To calculate the approximate user base of the social media site 10 months from now, considering a 4% increase per month, we can use the following steps:
1. Calculate the monthly growth factor: 1 + (4% / 100) = 1 + 0.04 = 1.04
2. Apply the growth factor to the current user base for each month:
Month 1: 35,930 * 1.04 = 37,387.2 (approx.)
Month 2: 37,387.2 * 1.04 = 38,868.49 (approx.)
...
Month 10: Previous Month * 1.04
By repeating this calculation for each month, we can determine the approximate user base 10 months from now.
Month 1: 37,387.2
Month 2: 38,868.49
Month 3: 40,391.33
Month 4: 41,957.61
Month 5: 43,569.34
Month 6: 45,228.24
Month 7: 46,936.32
Month 8: 48,695.44
Month 9: 50,507.45
Month 10: 52,374.40 (approx.)
Therefore, the approximate user base of the social media site 10 months from now would be approximately 52,374.
