Answer:
17
Step-by-step explanation:
We can split the expression:
3² + 2³
into two terms:
3² and 2³
We can evaluate each term individually, then add them at the end.
First, we can evaluate 3²:
3² = 3 × 3 = 9
Remember that an exponent specifies how many times a number should be multiplied by itself.
Next, we can evaluate 2³.
2³ = 2 × 2 × 2 = 8
Finally, we can add these two terms.
9 + 8 = 17
what is the value of y?
write the equation of the ellipse graphed in the image:
The equation of the ellipse graphed in the image is given as ((x-4)²/16) + ((y-6)²/4) = 1.
The standard form equation of an ellipse with center (h,k), horizontal axis of length 2a, and vertical axis of length 2b is,
((x-h)²/a²) + ((y-k)²/b²) = 1
Since the center is given as (4, 6), we have h = 4 and k = 6. The vertex is given as (0, 6) which means the horizontal distance from the center to the vertex is a = 4. Also, the co-vertex is given as (8, 6) which means the vertical distance from the center to the co-vertex is b = 2. Therefore, substituting these values in the equation of an ellipse, we get,
((x-4)²/4²) + ((y-6)²/2²) = 1
Simplifying, we get the equation of the ellipse,
((x-4)²/16) + ((y-6)²/4) = 1
Thus, the equation of the ellipse with center (4, 6), vertex at (0, 6), and co-vertex at (8, 6) is ((x-4)²/16) + ((y-6)²/4) = 1.
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Compute the amount in an account after 5 years if 1900 is invested at an annual interest rate of 6% compounded quarterly. Round to two decimal places. Use A=P(1+r/n)^nt
Evaluating the exponential equation we can see that after 5 years, the account has 2559.02
How to find the amount in the account?Here we need to use the formula:
A=P(1+r/n)^nt
Where P is the initial amount.
r is the percentage in decimal form, in this case 0.06
n is how many times it is compounded, in this case 4
t is the variable, in this case years.
Replacing all that we get:
A = 1900*(1 + 0.06/4)^(4t)
Now we want to evaluate this in t = 5, we will get:
A = 1900*(1 + 0.06/4)^(4*5)
A = 2559.02
That is the amount.
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Three man can do
piece of work in 10
days. After three
days one men left the work . And again after three days another man
left then in how many days the remaining
person will take to finish the work?
It will take the final worker 21 days to complete the task
To solve this problem
If a task can be completed by three men in ten days, the total work is:
3 men * 10 days = 30 man-days.
Let's suppose that each man has the same rate of production, allowing them to finish the work in equal amounts.
One worker left after three days, leaving just two men to do the job. They put in three more days of effort, so they finished the following amount of work in the first six days:
3 men multiplied by 3 days = 9 man-days.
One worker was left to do the job after another man departed after six days. The entire amount of work left is:
30 man-days - 9 man-days = 21 man-days
One man will need to put in 21 man-days of labour, which will need him to:
A man's day is equal to 21 man-days.
Therefore, it will take the final worker 21 days to complete the task
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70-40=30 using number line questions
Answer:
30
Step-by-step explanation:
70
40
Take out the zero
Then 7 - 4 then add a o to get 30
A company wants to determine a confidence interval for the average CPU time of its teleprocessing transactions. A sample of 70 random transactions in milliseconds is given below. Assume that the transaction times follow a normal distribution with a standard deviation of 600 milliseconds. Use Excel to determine a 98% confidence interval for the average CPU time in milliseconds. Round your answers to the nearest integer and use ascending order.
Time
6690
6160
5140
7210
5570
7320
5190
5770
8390
6730
6820
5340
6690
5560
6680
7270
5670
6650
6180
5570
5410
6160
6600
6910
6400
4960
5660
6360
5760
6270
6810
5860
5700
6730
4850
6160
6490
6790
6680
6160
5500
5490
5240
7020
5930
6280
5980
6380
5140
6270
6200
5770
5480
6090
6060
6380
4910
4170
6630
5990
4720
6510
5860
6610
5370
6510
5800
5660
5760
6110
We can say with 98% confidence that the true average CPU time of the teleprocessing transactions falls between 5751 and 6278 milliseconds.
What is average?
In mathematics, the average is a value that represents the typical or central value of a set of numbers. It is also known as the mean and is calculated by adding up all the values in a set and then dividing by the number of values in the set.
To find the 98% confidence interval for the average CPU time, we can use the formula:
CI = [tex]\bar{x}[/tex] ± t_(α/2,n-1) * (s/√n)
where:
[tex]\bar{x}[/tex] = sample mean
t_(α/2,n-1) = critical value from the t-distribution with n-1 degrees of freedom and a significance level of α/2
s = sample standard deviation
n = sample size
First, we need to calculate the sample mean, sample standard deviation, and the critical value. Using Excel, we can find:
[tex]\bar{x}[/tex] = 6014.9
s = 996.4
t_(α/2,n-1) = T.INV.2T(0.02, 69) ≈ 2.660
Plugging in these values into the formula, we get:
CI = 6014.9 ± 2.660 * (996.4/√70)
CI ≈ 6014.9 ± 263.5
Rounding to the nearest integer and putting the interval in ascending order, we get:
CI ≈ (5751, 6278)
Therefore, we can say with 98% confidence that the true average CPU time of the teleprocessing transactions falls between 5751 and 6278 milliseconds.
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Find the value of x
32.
(3x + 2)
(x+5)
(2x+1)
2x
Answer: 44
Step-by-step explanation:
Sum of external is 360 So add all up and make equal to 360
3x+2+2x+x+5+2x+1 = 360
8x + 8 =360
8x=352
x=44
Need help will give brainliest and 5 stars!
An equation for the transformed logarithm shown below, that passes through points (0, 0) and (-5, 2) is f(x) = 2log₆(x + 1).
How to write an equation for the transformed logarithm?By critically observing the logarithmic graph (see attachment) that models the logarithm function, we can logically deduce that it was reflected across the y-axis.
In Mathematics, the general form of a logarithm function is represented by the following mathematical equation:
f(x) = alog(±x + c)
Where:
a represent the scale factor of the logarithmic graphc represent a horizontal translation or vertical translation.x represent the base.Note: The vertical asymptote is at x = 1.
Next, we would determine the value of c and a by using the points (0, 0) and and (-5, 2):
0 = alog(0 + c) .....equation 1.
2 = alog(-(-5) + c) .....equation 2.
By solving equations 1 and 2 simultaneously, we have:
1 = 0 + c
c = 1.
For the value of a, we have:
2 = alog(5 + c)
2 = alog(5 + 1)
2 = alog(6)
a = 2/log(6)
In conclusion, the required logarithm function in compact form is given by:
f(x) = alog(±x + c)
f(x) = 2/log(6) × log(-x + 1)
f(x) = 2log₆(-x + 1)
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Which of the following sentences is written in subjunctive mood?
Turn the lights off when you leave the room.
If you're leaving the room, then turn the lights off.
I wish you'd turn the lights off when you leave the room.
Will you turn the lights off when you leave the room?
The sentences that is written in subjunctive mood is C. I wish you'd turn the lights off when you leave the room.
What is subjunctive mood ?The subjunctive mood can be regarded as the hypothetical scenario that is been used in English, it can can be considered as the one that is been used to express a wish.
In some cases be used in the process of making that recommendation, or demand, in the option C it can be seen that it is used to express wishes and this is the reason why it is been considered as a subjunctive mood.
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Answer: I wish you'd turn the lights off when you leave the room.
Using a fair coin and a fair six-sided number cube, what is the probability of tossing tails and rolling a multiple of 2?
Answer:
1/4
Step-by-step explanation:
The probability of tossing tails on a fair coin is 1/2. The probability of rolling a multiple of 2 on a fair six-sided number cube is 1/2 (since there are three multiples of 2: 2, 4 and 6). Since these two events are independent, the probability of both events happening is the product of their individual probabilities: (1/2) * (1/2) = 1/4.
Mitchell stood at the entrance of his school and polled 35 students as they were entering the
building regarding their favorite food. If 16 of the students indicated they would choose pizza, what
percent of the students he polled chose pizza? (Round to nearest tenth)
if given f(x)= 2x^(2) +5 and g(x)= 1/2x
whats:
f+g
f-g
fg
f/g
To find f+g, we need to add f(x) and g(x):
f(x) + g(x) = (2x^(2) +5) + (1/2x)
f+g = 2x^(2) + (1/2)x + 5
To find f-g, we need to subtract g(x) from f(x):
f(x) - g(x) = (2x^(2) +5) - (1/2x)
f-g = 2x^(2) - (1/2)x + 5
To find fg, we need to multiply f(x) and g(x):
f(x) * g(x) = (2x^(2) +5) * (1/2x)
fg = x + (5/2)x^(-1)
To find f/g, we need to divide f(x) by g(x):
f(x) / g(x) = (2x^(2) +5) / (1/2x)
f/g = 4x + 10x^(-1)
NEED HELP WILL GIVE BRAINLIEST AND 5 STARS I HAVE 20 MINUTES PLEASE HELP!
1-4 if you can do all that would be great.
1) The domain of the rational function: Any real number except x = - 3
2) The function is undefined at x = - 3.
3) The end behavior of the function is equal to 4.
4) x-Intercept: - 8, y-Intercept: 32 / 3.
How to analyze a rational function
In this problem we find the case of rational function, whose features must be analyzed. First, we need to determine the domain of the function:
m(x) = [4 · (x - 5) · (x + 8)] / (x² - 2 · x - 15)
m(x) = [4 · (x - 5) · (x + 8)] / [(x - 5) · (x + 3)]
m(x) = [4 · (x + 8)] / (x + 3)
The domain of the rational function is any real number except x = - 3.
Second, we analyze the function at x = - 3 by lateral limits:
[tex]4\cdot \lim_{x \to - 3^{-}}\frac{x+ 8}{x + 3}[/tex]
[(- 3 - e) + 8] / [(- 3 - e) + 3]
(5 - e) / e
5 / e - 1
[tex]4\cdot \lim_{x \to - 3^{+}}\frac{x+ 8}{x + 3}[/tex]
[(- 3 + e) + 8] / [(- 3 + e) + 3]
(5 + e) / e
5 / e + 1
Then, the function m(x) does not exist for x = - 3.
Third, determine the end behavior of the function by limits:
[tex]4\cdot \lim_{x \to + \infty}\frac{x+ 8}{x + 3}[/tex]
4
Fourth, find the intercepts of the function by algebra:
x-Intercept:
[4 · (x + 8)] / (x + 3) = 0
x + 8 = 0
x = - 8
y-Intercept:
m(0) = (4 · 8) / 3
m(0) = 32 / 3
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Assume the following information for the month of August. June sales= $40,000; July sales=$65,000; August sales= $52,850. All sales are on account and are collected as follows: 20% in thecurrent month. 50% in the month following, 25% in the second month following, and 5%uncollectible. The beginning cash balance is $14,670, with cash payment of $ 24,653. If theminimum cash balance is $50,000, what is the amount needed by the bank, or how much isavailable to pay towards the bank loan? Show the amount needed as positive number, and theamount to repay a loan as a negative number
Answer:
Step-by-step explanation:
To find the amount needed or available, we need to calculate the total cash collections and the total cash payments for the month, as well as the ending cash balance.
Total cash collections:
- For June sales: 20% collected in August = $40,000 x 0.2 = $8,000
- For July sales: 20% collected in August + 50% collected in September = $65,000 x 0.2 + $65,000 x 0.5 = $19,500
- For August sales: 20% collected in August + 50% collected in September + 25% collected in October = $52,850 x 0.2 + $52,850 x 0.5 + $52,850 x 0.25 = $31,710
- Total cash collections: $8,000 + $19,500 + $31,710 = $59,210
Total cash payments:
- Cash payment: $24,653
- Ending cash balance required: $50,000
- Total cash payments: $24,653 + $50,000 = $74,653
Ending cash balance:
- Beginning cash balance: $14,670
- Total cash collections: $59,210
- Total cash payments: $74,653
- Ending cash balance: $14,670 + $59,210 - $74,653 = -$735
Since the ending cash balance is negative, the company needs additional funds to cover its cash requirements. The amount needed by the bank is the absolute value of the ending cash balance:
Amount needed by the bank = $|-735| = $735
Since the company needs funds, the amount available to repay a loan is $0 - $735 = -$735, meaning that the company needs to borrow $735 to cover its cash requirements.
What is the percent of increase from 50 to 64?
Write your answer using a percent sign (%).
Submit
Marcus is going to spin the spinner 36 more times. He said that the
spinner will most likely land on 2 another 7 times. This is incorrect.
Explain the error Marcus made and then give the best prediction.
Answer:
Step-by-step explanation:
Each time you spin your odds are always the same. Over time the odds may be predicted but each spin has the same odds
Mr Victor had 100 computes for sale. He sold w computers in the moming and (2w+3) computers in the afternoon. He had 7 computers left. How many computers did he sell in the morning?
Using an equation, the number of computers Mr. Victor sold in the morning is 30.
What is an equation?An equation is an algebraic statement that shows the equality or equivalence of two or more mathematical expressions.
Unlike mathematical expressions, equations include the equal symbol (=).
The number of computers Mr. Victor has for sale = 100
Let the number of computers sold in the morning = w
Let the number of computers sold in the afternoon = (2w+3)
Let the number of computers left = 7
Equation:The total number of computers, 100 = w + (2w+3) + 7
100 = 3w + 10
3w = 90
w = 30
Thus, since Mr. Victor sold w computers in the morning, w is equal to 30.
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A linear function is represented on the coordinate grid. What is the y- intercept of the graph of this function?
The y-intercept of the graph of this function is 5.
Given information:
The linear function passes through the points (0, 5) and (8, -2).
Here, we have to find the y-intercept.
For that, the definition of y-intercept is given as the point where the graph intersects the y-axis.
To find the y-intercept of the graph of this function, we need to identify,
the point where the graph intersects the y-axis.
The y-axis corresponds to the x-coordinate of 0.
Since the function passes through the point (0, 5), we know that the y-intercept is 5.
Therefore, the y-intercept of the graph of this function is 5.
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valuate the summation for the indicated value of the variable. 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!); m = 3
The answer of the given question based on the expression is , the value of the summation when m = 3 is 137.
What is Expression?In mathematics, an expression is a combination of numbers, variables, and operators that represents a value or a set of values. It can be a simple combination of numbers and variables or a more complex combination involving mathematical operations like addition, subtraction, multiplication, division, exponents, and roots. Expressions can be used to represent a wide range of mathematical concepts, from simple arithmetic to complex functions and equations.
To evaluate the summation 1(1!) + 2(2!) + 3(3!) + 4(4!) + m(m!), where m = 3, we substitute m = 3 and simplify:
1(1!)+2(2!) +3(3!) +4(4!) +3(3!)
= 1(1) + 2(2) + 3(6) + 4(24) + 3(6) (since n! = n(n-1)! for all positive integers n)
= 1 + 4 + 18 + 96 + 18
= 137
Therefore, the value of the summation when m = 3 is 137.
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I was doing this on my own and got confused, please help ):
Answer:
- 3 > - 7
1 < 4
- 6 < 6
Step-by-step explanation:
From ( - ) to ( + ), it becomes greater as you go right side
Note : -
( + ) > ( - )
This is always true.
Represent "sum of a number and five" algebraically? (Use n to represent "a number")
The algebraic representation of "sum of a number and five" can be written as
n + 5
Where n represents the "number".
In mathematics, an algebraic representation is a way of expressing a mathematical relationship or equation using symbols, letters, and mathematical operations. It is a symbolic representation of a mathematical expression or equation that allows us to work with abstract concepts and manipulate them according to certain rules.
For example, the equation y = 2x + 1 is an algebraic representation of a linear function, where y and x represent variables and 2x + 1 is an expression that relates them. Algebraic representations are often used in algebra, calculus, and other areas of mathematics to describe relationships between quantities, solve equations, and make predictions based on mathematical models.
Hence, the algebraic representation of "sum of a number and five" can be written as
n + 5
Where n represents the "number".
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Write an expression to represent: 1 more than the quotient of x and 4.
1+ X/4 Quotient= division also like fraction
What is the best answer for this
i need help! please, this is confusing
The cost of the 28 inches and 36 inches diagonal Smart TVs, based on the quadratic cost function are;
28 - inch diagonal; $134
36 - inch diagonal; $165
What is a quadratic function?A quadratic function is a function of the form f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
The cost of the Smart TV as a function of the diagonal length is C(d) = 0.322·d² - 16.776·d + 351.444
The above function indicates that the cost of a Smart TV that is 28 inches long is; C(28) = 0.322 × 28² - 16.776 × 28 + 351.444 ≈ 134
A Smart TV with a diagonal of 28 inches costa about $134The cost of a Smart TV with a diagonal of 36 inches is therefore;
C(36) = 0.322 × 36² - 16.776 × 36 + 351.444 ≈ 165
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A shipping container has a rectangular base with dimensions 8 feet by 40 feet. The volume of the shipping containers is 3040 cubic feet. How tall is the shipping container
The shipping container shaped like a cuboid is 9.5 feet tall.
Let's call the height of the shipping container "h".
As per the given information, the shipping container can be described as a cuboid.
We are aware that the container's volume is given by the formula:
V = lwh,
where l stands for length, w for width, and h for height.
Substituting the values provided yields:
3040 = 8 x 40 x h
Simplifying, we get:
3040 = 320h
Dividing both sides by 320, we get:
h = 9.5
Therefore, the height of the shipping container is 9.5 feet.
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The Ordered pairs in the table below represent a function. What is the slope of the function? -3,7 -9,-2
Answer:
m = 3/2
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Points (-3,7) (-9,-2)
We see the y decrease by 9, and the x decrease by 6, so the slope is
m = -9 / -6 = 3/2
If the triangle on the grid below is translated three units left and nine units down, what are the coordinates of C prime? On a coordinate plane, triangle A B C has points (negative 1, 0), (negative 5, 2), (negative 1, 2). (–4, –7) (–4, 2) (2, –7) (2, 11) Mark this and return
The coordinates of C prime are (-4, -7).
The coordinates of the vertices of triangle ABC are
A(-1, 0)
B(-5, 2)
C(-1, 2)
To find the coordinates of C prime, we need to translate the triangle three units left and nine units down. This means we need to subtract 3 from the x-coordinates of each vertex and subtract 9 from the y-coordinates of each vertex.
So, the new coordinates for each vertex are:
A'(-1 - 3, 0 - 9) = (-4, -9)
B'(-5 - 3, 2 - 9) = (-8, -7)
C'(-1 - 3, 2 - 9) = (-4, -7)
Therefore, the coordinates of C prime are (-4, -7).
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OPR is a sector of a circle,centre O and radius 9cm
Find perimeter of the sector.
Give your answers in terms of π
The perimeter of the sector in terms of π is (7π+18) cm.
What is a sector?
A sector is a shape that is bounded by an arc and two radius.
To calculate the perimeter of the sector, we use the formula below
Formula:
P = (2πr∅/360)+2r.................. Equation 1Where:
P = Perimeter of the sectorr = Radius of the circle from which the sector was formed∅ = Angle of the sectorFrom the question,
Given:
r = 9 cm∅ = 140Substitute these values into equation 1
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What is the answer to 1 &2
A compound inequality that represent example 5 is -2 < x ≤ 5.
A compound inequality that represent example 6 is -4 < x < 0.
What is a number line?In Mathematics and Geometry, a number line simply refers to a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Since the open circle and closed circle are located at -2 and 5 respectively, a compound inequality to represent this is given by;
x > -2
x ≤ 5
By combining, we have:
-2 < x ≤ 5.
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Find the Area of the figure below, composed of a rectangle with two semicircles removed. Round to the nearest tenths place.
to find the area of the shape we have to find the area of the rectangle first then subtract the area of the 2 semi circles from it. to find the area of the rectangle its 13*6=78. to find the area of a circle you have to do this: radius*radius*pi. the diametre of the circle is 6 so we know the radius is 3. then if we do 3*3*3.14 it will be 28.26. and since there are 2 equal semi circles it is equal to 1 full circle so the area of the 2 semi circles combined is 28.26. Then you just do 78-28.26=49.74 which can be rounded up to 50 cm squared. So the answer is 50 cm squared also pls mark as brainliest answer thx
To calculate the area of the shape, first calculate the area of the rectangle, then deduct the combined areas of the two semicircles. 13*6=78 is the answer to the rectangle's area. To determine a circle's area, follow these steps: radius*radius*pi. Since the circle's diameter is 6, its radius must be 3. therefore the result of 3*3*3.14 is 28.26. The area of the two semicircles combined is 28.26 since there are two equal semicircles, which equals one full circle. The next step is to simply calculate 78-28.26=49.74, which can be rounded up to 50 cm2. The response is 50 cm squared.
