m∠f to the nearest degree is 83°.
The Law of Cosines is used to find an angle when all triangle sides are known.
f² = d² +e² -2de cos(F)
To find angle ∠F, we need to find the value of cos(∠F), which we can do by rearranging the Law of Cosines as follows:
cos(F) = (d² +e² -f²) / (2de)
cos(F) = (20² + 25² - 30²) / (2 × 20 × 25)
cos(F) = (400 + 625 - 900) / (1000)
cos(F) = 125/1000
∠F = arccos(1/8)
∠F = 82.8°
Rounding to the nearest degree
∠F = 83°
Hence, m∠f to the nearest degree is 83°.
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Raymond wants to know the costs of buying different numbers of songs for his mp3 player. The cost of each song is the same.
To determine the cost of buying different numbers of songs for his mp3 player, Raymond needs to know the cost of a single song and the total number of songs he wants to buy, as well as consider bulk purchasing options like buying an album.
Assuming the cost of a single song is $1, if Raymond wants to buy 10 songs, the cost would be 10 x $1 = $10. Similarly, if Raymond wants to buy 20 songs, the cost would be 20 x $1 = $20. In general, the cost of buying n songs would be n x $1.
If the cost of a single song is not $1, then Raymond would need to adjust his calculations accordingly. For example, if the cost of a single song is $0.99, then the cost of buying 10 songs would be 10 x $0.99 = $9.90, and the cost of buying 20 songs would be 20 x $0.99 = $19.80.
Raymond could also consider purchasing songs in bulk, such as by buying an album, which typically offers a discounted price compared to purchasing individual songs. In this case, the cost of buying different numbers of songs would depend on the number of songs in the album and the cost of the album.
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Complete Question:
Raymond wants to know the costs of buying different numbers of songs for his MP3 player. The cost of each song is the same.
• Let s represent the possible number of songs Raymond could buy.
• Let d represent the amount of money, in dollars, Raymond would need to buy the songs.
Fill in the table for all missing values of s and d.
Number of songs, s
Amount of money ($), d
2
2.58
5.16
7
11
21.93
Find the missing number so that the equation has infinitely many solutions.
-5x +_____= -5x − 7
The monthly demand function for a product sold by a monopoly is p = 2104 – (1/3)x^2 dollars, and the average cost is C = 1000 + 22x + x2 dollars. Production is limited to 1000 units and x is in hundreds of units. (a) Find the quantity (in hundreds of units) that will give maximum profit. (b) Find the maximum profit. (Round your answer to the nearest cent.)
a) The quantity (in hundreds of units) that will give maximum profit: [tex]x^{2}[/tex] + 6x - 3022 = 0
b) The maximum profit is approximately $202,573.42.
What is Equation?An equation is a mathematical statement that shows that two expressions are equal. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
(a) To find the quantity that will give maximum profit, we need to find the level of output at which marginal revenue equals marginal cost.
The total revenue function for the monopoly is TR = px, where p is the price and x is the quantity sold. The marginal revenue is the derivative of the total revenue with respect to x, which is MR = d(TR)÷dx = p + x(dp÷dx).
To find the marginal revenue function, we differentiate the demand function with respect to x:
dp÷dx = -(2÷3)x
So, the marginal revenue function is:
MR = (2104 - (1÷3)[tex]x^{2}[/tex]) - (2÷3)[tex]x^{2}[/tex]
To find the marginal cost function, we differentiate the average cost function with respect to x:
dC÷dx = 22 + 2x
So, the marginal cost function is:
MC = 22 + 2x
To find the level of output at which MR = MC, we set the two functions equal to each other:
(2104 - (1÷3)[tex]x^{2}[/tex]) - (2÷3)[tex]x^{2}[/tex] = 22 + 2x
Simplifying this equation, we get:
[tex]x^{2}[/tex] + 6x - 3022 = 0
(b) Using the quadratic formula, we find that:
x = (-6 ± √( 36- 4(1)(-3022))) / 2(1)
x = (-6 ± √(36444)) / 2
x = (-6 ± 190.81) ÷ 2
x ≈ -98.4 or x ≈ 92.4
Since we can't produce a negative quantity, we choose x ≈ 92.4 as the quantity that will give maximum profit.
Therefore, the level of output that will maximize profit is 924 units (in hundreds of units).
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The mean of data set A is 42. The mean of data set B is 47. The mean absolute deviation (MAD) of both data sets is 2. 5. What is the difference of the means as a multiple of the MAD?
The difference of the means is ______ times the MAD.
The difference in the means is two times the MAD.
To find the difference between the means as a multiple of the MAD, follow these steps:
Difference of the means = |mean of A - mean of B|
Multiplying the result by 1/MAD will give us the difference of the means as a multiple of the MAD.
1. Determine the difference between the means of the two data sets: Mean of data set A is 42, and the mean of data set B is 47.
Difference = 47 - 42 = 5.
2. Divide the difference of the means by the MAD: The MAD of both data sets is 2.5.
Multiple = Difference / MAD = 5 / 2.5 = 2.
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reiko drove from point a to point b at a constant speed, and then returned to a along the same route at a different constant speed. did reiko travel from a to b at a speed greater than 40 miles per hour?
Answer:
Step-by-step explanation:
Unfortunately, I cannot answer this question without additional information about the distances traveled and the time taken by Reiko to travel from point A to point B and back to point A.
The speed at which Reiko traveled is calculated as distance divided by time. Therefore, we need to know both the distance and time for each leg of the journey to determine the speed.
Without this information, it is not possible to determine whether Reiko traveled from A to B at a speed greater than 40 miles per hour.
please help me
a gift box is in the shape of a trapezoidal prism with base lengths of 7in by 5in by 4in the height of the gift box is 8in what is the volume?????
The volume of the trapezoidal prism is 192 in³
What is volume of a prism?A prism is a solid shape that is bound on all its sides by plane faces.
The volume of a prism is expressed as;
V = base area × height
The base of the prism is a trapezoid
area of trapezoid = 1/2(a+b)h
A = 1/2( 7+5) 4
A = 1/2 × 12 × 4
A = 12 × 2
A = 24 in²
Therefore the volume of the prism is
V = 24 × 8
V =192 in³
Therefore the volume of the trapezoidal prism is 192 in³
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Kai bought 5 bags. In each bag there is bottle of Gatorade that cost 3$ and two pacIs of gum. If Kai spent 55$ all together how much did each pack of gum cost?
If Kai spent 55$ all together then each pack of gum cost $4.
To solve this question follow the steps given below:
Calculate the total cost of Gatorade.
Since there are 5 bags and each bag has a bottle of Gatorade that costs $3, the total cost for Gatorade is 5 * $3 = $15.
Calculate the total cost of gum.
Since Kai spent $55 in total, we need to subtract the cost of Gatorade to find the total cost of gum. $55 - $15 = $40.
Calculate the total number of gum packs.
Each bag contains 2 packs of gum, and there are 5 bags. So, there are 2 * 5 = 10 packs of gum.
Calculate the cost of each pack of gum.
To find the cost of each pack of gum, divide the total cost of gum by the number of gum packs. $40 / 10 = $4.
So, each pack of gum cost $4.
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need help with this and the writing part
Hunter made a mistake in calculating the volume of the rectangular prism, hence he may have chosen the wrong formula.
How to obtain the volume of a rectangular prism?The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:
Volume = length x width x height.
The dimensions for this problem are given as follows:
2m, 3m and 5m.
Hence the volume of the prism is given as follows:
V = 2 x 3 x 5
V = 30 m³.
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The diagonal of rectangle ABCD is 42. 3 cm, and it forms an angle of 53° with the shorter side AD of the rectangle
Using trignometric functions the shorter side AD has length a ≈ 25.75 cm and the longer side AB has length b ≈ 34.25 cm.
In the given scenario, we have a rectangle with sides AD and AB. The length of AD is represented as 'a' and is approximately 25.75 cm, while the length of AB is denoted as 'b' and is approximately 34.25 cm. The diagonal AC of the rectangle has a length of 42.3 cm and forms an angle of 53° with AD.
To find the lengths of sides a and b, we can utilize trigonometric functions, specifically cosine and sine. Since we have the length of the diagonal AC and the angle it forms with AD, we can set up the following equations:
cos(53°) = a/42.3
sin(53°) = b/42.3
By rearranging the equations, we can solve for a and b:
a = 42.3 * cos(53°) ≈ 25.75 cm
b = 42.3 * sin(53°) ≈ 34.25 cm
By substituting the given values into the equations, we can determine that the length of AD (a) is approximately 25.75 cm, and the length of AB (b) is approximately 34.25 cm.
These calculations allow us to find the side lengths of the rectangle based on the given information about the diagonal length and angle. Understanding trigonometric relationships enables us to solve geometric problems involving angles, sides, and diagonals in various shapes and configurations.
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does the residual plot indicate that the regression equation is a good model or a bad model of the data? why or why not?
The residual plot can provide valuable insights into the adequacy of the regression model, and whether any modifications or alternative models may be needed to better explain the data.
A residual plot is a visual tool for evaluating a regression model's goodness-of-fit. The residuals—that is, the discrepancies between the observed and expected values—are plotted against the predicted values.
The residuals should be randomly dispersed around zero and the plot should show no clear patterns or trends if the regression equation accurately models the data.
The residuals may show patterns or trends in the plot if the regression equation is a poor model of the data, which would indicate that the model is failing to account for some crucial characteristics of the data.
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Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups of water. How many quarts of water will she need?
She will need 4 quarts of water.
Given Hannah decided to make finger gelatin for a huge children’s party. She had to make 8 packs of gelatin. Each pack needed 2 cups of water.
Since each pack of gelatin requires 2 cups of water, Hannah will need a total of:
8 packs x 2 cups/pack = 16 cups of water
To convert cups to quarts, we need to divide the number of cups by 4 (since there are 4 cups in a quart):
16 cups ÷ 4 cups/quart = 4 quarts
Therefore, Hannah will need 4 quarts of water to make 8 packs of finger gelatin for the children’s party.
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As Nancy's small insurance agency has grown, the spreadsheets they use to track income and expenses have become increasingly complex. Which feature of an AIS (Accounting Information System) would help Nancy to better manage income and expenses?
The income statement and Accounting Information System, along with the balance sheet and cash flow statement, help you understand your company's financial health.
MIS employs non-financial data, but AIS exclusively uses financial data.
MIS indirectly to other external users.
The income management account is most likely affected by Selling, General, and Administrative Expenses.
In accounting, an instrument that provides the data needed to effectively manage an organization and make decisions is a management information system (MIS).
It is used to locate, collect, process, and distribute economic data about a company to a variety of users (AIS).
MIS concentrates on the financial and accounting aspects of a business, diagnosing problems and proposing solutions. The former management system, that occasionally relied on intuition and unscientific approaches and was arbitrarily constructed, has been replaced with MIS.
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The cone and the sphere shown have the same volume. The diameter of the cone is 24 cm, and the diameter of the sphere is 18 cm. What is the height h of the cone?
40.50 cm
2.25 cm
6.75 cm
20.25 cm
Answer:
i think the answer is 20.25
Step-by-step explanation:
Make d the subject of the formula t=4b²/21(d-3b/5)
The formula for d is d = (t * 21/4b² + 3b)/5
To make d the subject of the formula t=4b²/21(d-3b/5), we need to isolate d on one side of the equation and simplify.
First, let's simplify the right side of the equation by multiplying the fraction by the LCD of 5:
t = 4b²/21(d-3b/5)
t = (4b²/21d) * 5d - 3b
Now, we can isolate d by dividing both sides of the equation by the coefficient of d on the right side:
t/(4b²/21) = 5d - 3b
Simplifying the left side, we get:
t * 21/4b² = 5d - 3b
Adding 3b to both sides of the equation, we get:
t * 21/4b² + 3b = 5d
Finally, we can divide both sides by 5 to isolate d:
d = (t * 21/4b² + 3b)/5
Therefore, the formula for d is:
d = (t * 21/4b² + 3b)/5
In words, to find the value of d, we need to multiply the value of t by 21/4b², add 3b to the result, and divide the sum by 5.
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HELP PLEASE BRAINLIEST + POINTS
Answer:
CD = 34 units--------------------------
Since CD is diameter, therefore the angle CAD opposite to it is a right angle.
We are given the lengths of two legs, AD = 16 and AC = 30.
Use Pythagorean theorem to find the length of the hypotenuse CD:
CD² = AD² + AC²CD² = 16² + 30²CD² = 1156CD = √1156CD = 345x2(x − 5) + 6(x − 5) =
write thé expression in completed form
Answer:
5x^3-25x^2+6x-30
Step-by-step explanation:
Answer:
Step-by-step explanation:
5x2(x − 5) + 6(x − 5)
Using the Distributive Law:
= 5x^3 - 25x^2 + 6x - 30
In factored form it is
(x - 5)(5x^2 + 6)
A repeated-measures study is done to measure the change in IQ test scores taken on a Monday versus those taken on a Friday. There were n = 9 participants in the study. The mean difference was MD = –5 points, and the standard error for the mean difference was = 0. 51. Construct a 95% confidence interval to estimate the size of the population mean difference
The 95% confidence interval for the population mean difference in IQ test scores between Monday and Friday is (-6.174, -3.826) points. This indicates that we are 95% confident that the true mean difference falls within this range.
We can use the formula for the confidence interval of the mean difference in a repeated-measures study:
CI = MD ± t* SE
where MD is the sample mean difference, SE is the standard error for the mean difference, and t is the critical value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%.
Substituting the given values, we get:
CI = -5 ± t(0.51)
We need to find the value of t. Since n = 9, we have 8 degrees of freedom. Using a t-table or calculator with a degrees of freedom of 8 and a confidence level of 95%, we find that t = 2.306.
Substituting t = 2.306, we get:
CI = -5 ± 2.306(0.51)
CI = -5 ± 1.174
Therefore, the 95% confidence interval for the population mean difference is (-6.174, -3.826). We can interpret this interval as follows: we are 95% confident that the true mean difference in IQ test scores taken on a Monday versus those taken on a Friday lies between -6.174 and -3.826 points.
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A department store buys 200 shirts at a cost of $ 3600 and sells them at a selling price of $ 20 each. Find the percent markup.
The value of the calculated percent markup of the shirt is 11.1%
Finding the percent markup of the shirtFrom the question, we have the following parameters that can be used in our computation:
A department store buys 200 shirts at a cost of $ 3600 and sells them at a selling price of $ 20 each.
This means that
Cost price = 3600/200
Evaluate
Cost price = 18
The percent markup of the shirt is then calculated as
Percentage = (20 - 18)/18
Evaluate
Percentage = 11.1%
Hence, the percent markup of the shirt is11.1%
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Kadeesha invested $900 in an account that pays 1. 5% interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Kadeesha
would have in the account 11 years after her initial investment. Round to the nearest
tenth (if necessary)
Kadeesha would have approximately $1187.80 in the account 11 years after her initial investment.
We can use the formula for compound interest to solve this problem. The formula is given by:
A = P(1 + r/n)^(nt)
where A is the amount after t years, P is the principal amount, r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, P = $900, r = 0.015, n = 1 (since interest is compounded annually), and t = 11. Plugging these values into the formula, we get:
A = $900(1 + 0.015/1)^(1*11) = $1187.7989
Rounding this to the nearest tenth, we get $1187.80. Therefore, Kadeesha would have approximately $1187.80 in the account 11 years after her initial investment.
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The average number of hours of sleep Ms. Joe's classes is shown below. Which of the following statements is best supported by the data?
The statement that is best supported by the data is this: C. The range of data in Mr. Joe’s class is less than the range of data in Ms. Gambino’s class.
Which statement is true?The true statement about the data is that the range of data in Mr. Joe's class is less than the range of data in Ms. Gambino's class.
The range of data in Mr. Joe's class spans from 4 to 10 hours while the range of data in Ms. Gambino's class spans from 4 to 12 hours. So, the data range for the latter class is higher than the former.
Complete Question:
The average number of hours of sleep of Ms. Gambino’s and Mr. Joe’s classes is shown below. Which of the following statements is best supported by the data?
The image shows a line graph:
Mr. Gambino's Class: Range 4 - 12
Hours: 4 = 0
5 = 1
6 = 1
7 = 3
8 = 5
9 = 3
10 = 2
11 = 1
12 = 1
Mr. Joe's class: Range 4 -12
4 = 0
5 = 1
6 = 5
7 = 3
8 = 1
9 = 2
10 = 5
11 = 0
12 = 0
The median number of hours slept in Ms. Gambino’s class is less than the median number of hours in Mr. Joe’s class.
The data for Ms. Gambino’s class is symmetrical, while the data for Mr. Joe’s class is skewed right.
The range of data in Mr. Joe’s class is less than the range of data is Ms. Gambino’s class.
The mode of the data in Ms. Gambino’s class was equal to the mode of the data in Mr. Joe’s class.
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A card is drawn from a standard deck and replaced. After the deck is shuffled, another card is pulled.
What is the probability that both cards pulled are kings? (Enter your probability as a fraction.)
Answer:
1/169
Step-by-step explanation:
Lisandra was the center a towel bar on her door that is 29 inches wide she determines that the better distance from each of the towel bar to the end of the door is 7. 75 inches write and solve an equation to find the length of the towel bar.
The length of the towel bar is 13.5 inches.
Let's use the given information to write and solve an equation for the length of the towel bar.
We know that the door is 29 inches wide and that there is a 7.75-inch distance from each end of the towel bar to the respective end of the door. Let's denote the length of the towel bar as x.
So, the total width of the door can be expressed as the sum of the two distances and the length of the towel bar:
29 = 7.75 + x + 7.75
Now, let's solve for x:
29 = 15.5 + x
x = 29 - 15.5
x = 13.5 inches
Therefore, the length of the towel bar is 13.5 inches.
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What is the distance between the bakery (b) and the library (c)? explain using coordinate subtraction.
The distance between the bakery and the library is about 6.7 units.
To discover the distance among points using coordinate subtraction, we want to use the distance formula.
The distance formula is derived from the Pythagorean theorem, which states that during a proper triangle, the forecourt of the period of the hypotenuse( the longest aspect) is identical to the sum of the places of the lengths of the opposite two aspects.
the distance components is as follows
[tex]distance =\sqrt{((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]
in which [tex]( x_1, y_1)[/tex] and [tex]( x_2, y_2)[/tex] are the coordinates of the two factors.
In this example, let's anticipate that the equals of the bakery( b) are( 3, 5) and the equals of the library( c) are( 9, 2). applying the space formula, we get
[tex]distance = \sqrt{((9 - 3)^2 + (2 - 5)^2)[/tex]
[tex]distance = \sqrt{x(6^2 + (-3)^2)[/tex]
distance = [tex]\sqrt{( 36 9)[/tex]
distance = [tex]\sqrt{(45)[/tex]
distance ≈ 6.7082
hence, the distance between the bakery and the library is about 6.7 units.
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Fareed is making a rectangular garden in his backyard. He wants the length of the garden to be 5 feet longer then the width. which type of function can Fareed write to model the possible areas of his garden?
Answer:
Area = w(l) l = 5 + w
Step-by-step explanation:
X= 140×15²
write X as a product of powers of its prime factors
Answer:
X = 2² * 3² * 5³ * 7.
Step-by-step explanation:
140 = 2*2*5*7
15^2 = 3*5*3*5
So X = 2² * 3² * 5³ * 7
To find the prime factorization of X, we first need to simplify the expression.
140 × 15² = 140 × 225Now, we can factor 140 and 225 into their prime factors:
140 = 2² × 5 × 7225 = 3² × 5²So,
X = 140 × 225= (2² × 5 × 7) × (3² × 5²)We can now use the distributive property to multiply these factors together:
X = 2² × 3² × 5³ × 7Therefore, the prime factorization of X is:
Therefore, the prime factorization of X is:X = 2² × 3² × 5³ × 7which graph represents the linear equation y= 1/2 x + 2
Answer:
The graph on the top right
Step-by-step explanation:
The slope-intercept form is y = mx + b
m = the slope
b = y-intercept
The equation is y = 1/2x + 2
The y-intercept in this equation is 2, meaning the graph has a point (0,2) on it. Looking at the options, the only graph that has a point (0,2) is the map on the top right, and that is the answer.
A thin wire has the shape of the first-quadrant part of the circle with center the origin and radius 5. If the density function is 8(x, y) = 2xy, find the mass of the wire.
The mass of the wire is 500.
To find the mass of the wire, we need to integrate the density function over the surface area of the wire.
First, we need to parameterize the curve. The equation of the circle with center at the origin and radius 5 is:
x^2 + y^2 = 25
We can parameterize this curve by letting:
x = 5cos(t)
y = 5sin(t)
where t varies from 0 to pi/2 (the first quadrant).
Next, we need to find the surface area element. We can do this using the formula:
dS = sqrt(1 + (dz/dx)^2 + (dz/dy)^2) dA
where dz/dx and dz/dy are the partial derivatives of the height function z = f(x,y) (in this case, z = 0 since the wire is a curve in the xy-plane).
Since dz/dx = dz/dy = 0, we have:
dS = dA
where dA is the area element in the xy-plane, which is given by:
dA = |(dx/dt)(dy/ds) - (dx/ds)(dy/dt)| dt ds
Plugging in our parameterization, we have:
dA = 5 dt ds
Now we can integrate the density function over the surface area of the wire:
m = ∫∫ 8(x,y) dS
= ∫∫ 2xy dA
= ∫[0,pi/2] ∫[0,5] 2(5cos(t))(5sin(t)) (5 dt ds)
= 500
Therefore, the mass of the wire is 500.
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select the equivalent expression (7/2)^8
5764801/256, is equivalent expression of [tex](7/2)^8[/tex] which is an exact value and cannot be simplified any further.
What is equivalent expression and How do you write an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. You can write equivalent expressions by combining like terms. Like terms are terms that have the same variables raised to the same powers.
We can simplify the expression[tex](7/2)^8[/tex]by raising both the numerator and denominator to the 8th power:
We get,
[tex](7/2)^8 = 7^8 / 2^8[/tex]
To solve this value, simplify the numerator and denominator separately:
So we get,
[tex]7^8[/tex]= 5764801
[tex]2^8[/tex]= 256
Therefore, [tex](7/2)^8[/tex] = 5764801/256, which is an exact value and cannot be simplified any further.
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A group of neighbors is holding an end of summer block party. They buy p packs of hot dogs, with 8 hot dogs in each pack. All together, they have 56 hot dogs for the party. Write an equation to describe this situation. How many packs of hot dogs did the neighbors buy
Step-by-step explanation:
8p= 56
p= 7
therefore, the neighbours bought 7 packets of hotdogs.
Let functions f and g be defined over the real numbers as f(x)=x+3 and g(x) = 4x. It follows that f(g(x)) = ?
F. 12x
G. 4x+3
H. 5x+3
J. 4x² +3
K. 4x² + 12x
Answer:
I think it is k
Step-by-step explanation:
x+3(4x)
4x^2 + 12x
I am sorry if this is wrong
