hi
10/9 - 11/3 = 10/9 - 33/9 = -23/9
Answer:
-23/9
Step-by-step explanation:
You would need to find a common denominator which would be 9.
The next step would be to combine the top 10-11 (times)3 over 9
Then you multiply -11 by 3 tp get 10 -33 /9
The last and final step would be tp subract 33 from 10 to get 33 -10
Which will led you to your final awnser which is -23/9
Find the exact value of cos J in simplest radical form. I √82 4 J H V98
Answer:
We can start by using the Pythagorean identity to simplify the expression for cos J:
cos^2(J) + sin^2(J) = 1
Since we are given the value of sin J, we can substitute and solve for cos J:
cos^2(J) + (4/√82)^2 = 1
cos^2(J) + 16/82 = 1
cos^2(J) = 66/82
cos(J) = ±√(66/82)
We want to express cos J in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:
cos(J) = ±√[(2311)/(2*41)]
cos(J) = ±(√2/2) * (√33/√41)
Since J is in the first or second quadrant (based on the given value of sin J), we know that cos J is positive, so we can drop the negative sign:
cos(J) = (√2/2) * (√33/√41)
Therefore, the exact value of cos J in simplest radical form is (√2/2) * (√33/√41).
Question 11(Multiple Choice Worth 2 points)
(Circle Graphs LC)
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 54°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
If a circle graph were created using the findings, A. Kayaking would be the lake activity with a central angle of 54°.
Explain about the central angle:A central angle is one having endpoints on the perimeter and a vertex in the centre of a circle. The two arms of the circle's two radii intersect the circle's arc at two separate locations. A circle can be divided into sectors by using the central angle.
The proportion of the entire number of campers in degrees is used to calculate the central angle from each lake activity.There are 360 degrees in a circle. This sum is proportionately split amongst the lake programs according to the amount of campers having participated.Lake Activity Number Degrees
of Campers
Kayaking 15 (15/100 x 360°) = 54°
Wakeboarding 11 (11/100 x 360°) = 40°
Windsurfing 7 (7/100 x 360°) = 25°
Waterskiing 13 (13/100 x 360°) = 47°
Paddleboarding 54 (54/100 x 360°) = 194°
Total number 100
Thus, Kayaking hence has a 54° central degree when viewed proportionately.
Know more about the central angle
https://brainly.com/question/10945528
#SPJ1
Can someone help me with this maths question?
Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.
Explain about the factorization method:To factor is to identify the terms that make up an expression when they are multiplied together.
Expressions are made up of different words. A term may have specific components, such as coefficients, variables, and constants.While factoring in algebra, we seek out the most significant factors that the terms in an equation have in common. The only reasonably prime numbers we have are 7 and 9, thus we cannot factor out either constants.Given quadratic equation:
p² + 14p + 48 = 0
Find the factors of 48 such that on addition 14 will come:
48 = 6*8
So,
p² + 6p + 8p + 48 = 0
Taking p common first two terms:
p(1 + 6) + 8p + 48 = 0
Now, taking 8 common from last two terms
p(p + 6) + 8(p + 6) = 0
taking (p + 6) from both .
(p + 6)(p + 8) = 0
Now,
p + 6 = 0
p = -6 and
p + 8 = 0
p = -8
Thus, the two factors of the given quadratic equation is found as: p = - 6 and p = -8.
Know more about the factorization method:
https://brainly.com/question/25829061
#SPJ1
Correct question:
Solve the given quadratic equation using the factorization method:
p² + 14p + 48 = 0
sketch three solutions, with initial values y(0) > 0, y(0) = 0, and y(0) < 0.
To sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we'll need to use a differential equation or system of differential equations. So, to sketch three solutions with initial values y(0) > 0, y(0) = 0, and y(0) < 0, we would first draw a slope or direction field for our differential equation. Then, we would start at the point (0, y(0)) and follow the direction of the slope or arrow to sketch the solution for each initial value.
To sketch three solutions with the given initial values, follow these steps:
1. Determine the differential equation you're working with. For example, let's consider the equation y'(t) = y(t). This is just an example, and the process will be similar for other differential equations.
2. Solve the differential equation to obtain a general solution. In our example, the general solution is y(t) = C * e^t, where C is an arbitrary constant.
3. Apply the initial values to find specific solutions:
a. For y(0) > 0, choose a positive value for C, such as C = 1. The specific solution is y(t) = e^t.
b. For y(0) = 0, choose C = 0. The specific solution is y(t) = 0.
c. For y(0) < 0, choose a negative value for C, such as C = -1. The specific solution is y(t) = -e^t.
4. Sketch the three solutions on the same graph:
a. For y(t) = e^t, draw a curve that starts at (0,1) and increases exponentially as t increases.
b. For y(t) = 0, draw a horizontal line at y = 0.
c. For y(t) = -e^t, draw a curve that starts at (0,-1) and decreases exponentially (toward 0) as t increases.
These three curves represent the solutions with the specified initial values. Note that this process assumes you have a specific differential equation in mind. If you have a different equation, just follow the same steps to find and sketch the solutions.
Learn more about differential equation here: brainly.com/question/2273154
#SPJ11
Which equation shows how to find p, the price mrs. Mersin paid for the car
An equation which shows how to find p, the price Mrs. Merson paid for the car include the following: B) 5500/p = 55/100.
What is price?In Mathematics and Science, a price can be defined as an amount of money which is primarily set by the seller of a product, and it must be paid by a buyer to the seller, so as to enable the acquisition of this product.
Based on the information provided about the amount of money that Mersin paid for the car, an equation which shows how to find the price (p) is given by;
55% of p = 5500
55/100 × p = 5500
5500/p = 55/100
Read more on price here: https://brainly.com/question/14463202
#SPJ1
Complete Question:
Mrs. Merson is selling her car. Her research shows that the car has a current value of $5,500,
which is 55% of the amount Mrs. Merson paid for the car. A buyer wants to know the price
Mrs. Merson paid for the car.
• Which equation shows how to find p, the price Mrs. Merson paid for the car?
A) 55/p = 5500/100
B) 5500/p = 55/100
C) p/5500 = 55/100
D) p/5 = 5500/100
Suppose that 20% of a group of people have hazel eyes, what is the probability that the eighth passenger boarding a plane is the third one having hazel eyes? assume that passengers boarding the plane form a randomly chosen group
Answer: This is called percent error this is how i solve.
8 20%
3 100%
800. 60 = 48000
A transformation T is linear if and only if T(c1v1 + c2v2) = c1T(v1) + c2T(v2) for all v1 and v2 in the domain of T and for all scalars c1 and c2.
a. true
b. false
"A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.
To understand why this statement is true, we need to first define what it means for a transformation to be linear.
A linear transformation is a function that satisfies two properties:
Additivity and homogeneity.
Additivity means that [tex]T(u + v) = T(u) + T(v)[/tex]for all vectors u and v in the domain of T, while homogeneity means that [tex]T(cv) = cT(v)[/tex] for all vectors v in the domain of T and all scalars c.
Let's look at the given statement. It states that [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2)[/tex] for all v1 and v2 in the domain of T and for all scalars c1 and c2.
This is equivalent to saying that T is both additive and homogeneous, since we can rewrite the statement as [tex]T(c1v1 + c2v2) = T(c1v1) + T(c2v2) = c1T(v1) + c2T(v2).[/tex]
A transformation satisfies the given statement, it is both additive and homogeneous, and hence it is linear.
On the other hand, if a transformation is linear, it must satisfy the given statement by definition.
The statement "A transformation T is linear if and only if [tex]T(c1v1 + c2v2) = c1T(v1) + c2T(v2[/tex]) for all v1 and v2 in the domain of T and for all scalars c1 and c2" is true.
For similar questions on Linear
https://brainly.com/question/28732353
#SPJ11
if f(x) = 3 - x^2, find f(-2)
Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
What is a domain?In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.
When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;
f(x) = 3 - x²
f(x) = 3 - (-2)²
f(x) = 3 - 4
f(x) = -1
Read more on function here: brainly.com/question/9795474
#SPJ1
Samuel starts saving for his first car by opening a savings account and depositing $100. He plans to make a deposit every month to continue saving. Each term The amount of money in Samuel's savings account can be modeled by the sequence 100, An An-1 + 75, where n is the number of months since his initial deposit. - Use the drop-down menus below to complete the statements about his savings account growth. The sequence modeling the amount of money in Samuel's savings account is ✓the previous term.
Answer: The sequence modeling the amount of money in Samuel’s savings account is a recursive sequence. Each term in the sequence is determined by adding $75 to the previous term. The first term in the sequence is $100, representing Samuel’s initial deposit. After n months, the amount of money in Samuel’s savings account can be calculated using the formula An = An-1 + 75, where An represents the amount of money in his account after n months and An-1 represents the amount of money in his account after n-1 months.
For example, after 1 month, the amount of money in Samuel’s savings account will be A1 = A0 + 75 = 100 + 75 = $175. After 2 months, the amount of money in his account will be A2 = A1 + 75 = 175 + 75 = $250. And so on.
the given curve is rotated about the y-axis. find the area of the resulting surface. y = 1/4 x^2 − 1/2 ln(x), 3 ≤ x ≤ 5
To find the area of the resulting surface when the given curve y = 1/4x^2 - 1/2 ln(x) is rotated about the y-axis, we can use the Surface of Revolution formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from a to b
Here, a = 3 and b = 5.
First, we need to find the derivative of y with respect to x (dy/dx):
y = 1/4x^2 - 1/2 ln(x)
dy/dx = (1/4 * 2x) - (1/2 * 1/x) = x/2 - 1/(2x)
Now, let's plug this into the Surface of Revolution formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + (x/2 - 1/(2x))^2)] dx from 3 to 5
We will now integrate the expression within the brackets with respect to x from 3 to 5. This might be challenging to solve analytically, so we may need to use a numerical integration method or a calculator to find the exact value.
Once the integration is completed, you will obtain the surface area of the curve when rotated about the y-axis.
Learn more about Surface of Revolution from : brainly.com/question/30561148
#SPJ11
to determine the relative effectiveness of different study strategies for the sat, suppose three groups of students are randomly selected: one group took the sat without any prior studying; the second group took the sat after studying on their own from a common study booklet available in the bookstore; and the third group took the sat after completing a paid summer study session from a private test-prep company. the means and standard deviations of the resulting sat scores from this hypothetical study are summarized below: since we are comparing more than 2 groups, we will use anova to test whether the data provide evidence that sat score is related to study strategy. one of the conditions that allows us to use anova safely is that of equal (population) standard deviations. can we assume that this condition is met in this case?
We have to make a suspicion based on the given data. The standard deviations of the three bunches are not given within the address, so we cannot straightforwardly decide whether the condition of equal standard deviations is met. Be that as it may, ready to make a few taught surmises based on what we know almost each gather.
The primary gather, which did not think about, is likely to have a bigger change in scores than the other two bunches since understudies with shifting levels of arrangement and capacity took the test. Subsequently, we might anticipate the standard deviation of this group to be bigger than that of the other two bunches.
It is conceivable that the condition of rise to standard deviations isn't met. In case the condition of equal standard deviations isn't met, we may require to utilize an altered adaptation of ANOVA, such as Welch's ANOVA, which does not expect a rise in changes.
To learn about standard deviations visit:
https://brainly.com/question/13905583
#SPJ4
mark took 30minutes to finish lunch describe the turn the minute hand made
The turn the minute hand made is about 180 degrees when Mark finished his lunch.
How to calculate time with angle?To calculate time with angle, you need to know the angle between the hour hand and the minute hand. With that, you can use the formula
θ = 30H - 11/2M
where H is the current hour and M is the current minute.
Once you calculate the angle, you can use the formula
t = θ/30 to find the elapsed time in hours and decimal fractions of an hour.
The minute hand of a clock makes a full revolution (360 degrees) in 60 minutes (1 hour). Therefore, in 30 minutes, the minute hand will turn half the way around the clock face, which is 180 degrees.
To know more about time calculation visit:
brainly.com/question/20416068
#SPJ1
The complete question is: "Mark took 30minutes to finish lunch describe the turn the minute hand made when he finished his lunch".
If f(1)=4 and f(n)=-3f(n-1) , then find the value of f(6).
the value of f(6) is -972.To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
How to solve the question?
We can use the recursive formula given to find the value of f(6). Let's start by calculating f(2):
f(2) = -3f(1) = -3(4) = -12
Next, we can calculate f(3) using the same formula:
f(3) = -3f(2) = -3(-12) = 36
We can continue this process for f(4) and f(5):
f(4) = -3f(3) = -3(36) = -108
f(5) = -3f(4) = -3(-108) = 324
Finally, we can use the formula to find f(6):
f(6) = -3f(5) = -3(324) = -972
Therefore, the value of f(6) is -972.
To understand why f(6) is equal to -972, we can think of the recursive formula as a process that generates a sequence of numbers. Starting with f(1) = 4, we can apply the formula repeatedly to generate the sequence:
4, -12, 36, -108, 324, -972, ...
Each term in the sequence is obtained by multiplying the previous term by -3. We can see that the sequence alternates between positive and negative values, with the magnitude of each term growing rapidly. By the time we reach f(6), the magnitude has grown to 972, and the negative sign indicates that the term is negative. Thus, f(6) is equal to -972.
To know more about function visit :-
https://brainly.com/question/11624077
#SPJ1
A rectangle has a length of 9 cm and width of (3x-y)cm the area of the rectangle is 72cm^2
PQRS is a kite where PQ = 4xcm and QR = ycm
The perimeter of the kite PQRS IS 33cm
Calculate the values of x and y
You must show your working
Do not use a trial and improvement method.
Answer:
the value of x ia 7/2 and y is 5/2
HELP MEEEEEE PLEASEEEE
Answer: a=2 b= -2 c= -2
Step-by-step explanation: you replace y with a and you plug the x for them in so a= -1^2 -3 (-1) - 2 and you solve that to equal 2 then you solve for the others
solve pretty please with cherries on top <3
Answer:
D
Step-by-step explanation:
given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
then the x- coordinate of the turning point ( vertex ) is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 2x² + 4x - 3 ← is in standard form
with a = 2, b = 4 , then
[tex]x_{vertex}[/tex] = - [tex]\frac{4}{2(2)}[/tex] = - [tex]\frac{4}{4}[/tex] = - 1
substitute x = - 1 into the equation for corresponding y- coordinate
y = 2(- 1)² + 4(- 1) - 3 = 2(1) - 4 - 3 = 2 - 7 = - 5
turning point = (- 1, - 5 )
Answer:
The Correct answer is D
(-1,-5)
what do all circle theorems have in common (30 points)!!
A thief entered an orange garden and stole some oranges. The guard caught him. To get rid of him, the thief gave him half of the stolen oranges and two more oranges. The thief was left with only 9 oranges. How many oranges did he stole
The thief stole 22 oranges using algebraic equations.
To solve this problem, we need to use algebra. Let x be the number of oranges the thief stole.
According to the problem, the thief gave the guard half of the stolen oranges and two more. This means that he gave away (1/2)x + 2 oranges.
We also know that the thief was left with only 9 oranges. So we can set up the equation:
x - [(1/2)x + 2] = 9
Simplifying this equation:
(1/2)x - 2 = 9
(1/2)x = 11
x = 22
Therefore, the thief stole 22 oranges.
The problem presents us with a scenario where a thief entered an orange garden and stole some oranges. However, he was caught by the guard. In order to get rid of the guard, the thief decided to give him half of the stolen oranges and two more. As a result, the thief was left with only 9 oranges.
To solve this problem, we used algebraic equations. We let x be the number of oranges the thief stole. We also knew that the thief gave away (1/2)x + 2 oranges to the guard. Using this information, we were able to set up an equation where x - [(1/2)x + 2] = 9. Simplifying the equation, we were left with (1/2)x - 2 = 9. Solving for x, we found that the thief had stolen 22 oranges.
In conclusion, algebraic equations are a useful tool in solving mathematical problems. By setting up an equation and simplifying it, we were able to determine the number of oranges that the thief had stolen.
To learn more about algebraic equations, refer here:
https://brainly.com/question/953809#
#SPJ11
Need help completing this
Answer:
a) What is her GROSS pay for a week? 1,400
b) What is her GROSS pay for a year? 67,200
c) What are her TOTAL DEDUCTIONS for a week? 351.39
d) What is her NET pay for a week? 1,048.61
e) What is her NET pay for a year? 50,333.28
f) What does she pay in Income Tax per YEAR? 13,535.52
g) What does she pay in CPP contributions per YEAR? 2,537.28
h) What does she pay in El contributions per YEAR? 793.92
i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
Step-by-step explanation:
GROSS
without tax or other contributions having been deductedNET
Net pay means take-home pay or the amount employees earn after all payroll deductions are subtracted from their gross pay.There are 4 weeks in a month, 52 weeks in a year.
a) What is her GROSS pay for a week? 1,400
The amount of money she makes per hour × the amount of hours she works per week35 × 401,400b) What is her GROSS pay for a year? 67,200
The amount of money she earns in a month × 12(The amount of money she makes per week × 4) × 12(1,400 × 4) × 125600 × 1267,200c) What are her TOTAL DEDUCTIONS for a week? 351.39
Income Tax + CPP + El281.99 + 52.86 + 16.54334.85 + 16.54351.39d) What is her NET pay for a week? 1,048.61
Her gross pay for a week - Her total deductions for a week1,400 - 351.391,048.61e) What is her NET pay for a year? 50,333.28
Her gross pay for a year - Her total deductions for a yearHer gross pay for a year - ([Her total deductions for a week × 4] × 12)Her gross pay for a year - ([351.39 × 4] × 12)67,200 - ([351.39 × 4] × 12)67,200 - (1,405.56 × 12)67,200 - 16,866.7250,333.28f) What does she pay in Income Tax per YEAR? 13,535.52
Income tax per month × 12(Income tax per week × 4) × 12(281.99 × 4) × 121,127.96 × 1213,535.52g) What does she pay in CPP contributions per YEAR? 2,537.28
CPP per month × 12(CPP per week × 4) × 12(52.86 × 4) × 12211.44 × 122,537.28h) What does she pay in El contributions per YEAR? 793.92
El per month × 12(El per week × 4) × 12(16.54 × 4) × 1266.16 × 12793.92i) What percentage of her yearly Gross Pay is the yearly Income Tax she pays? 20.14%
(Her yearly Income Tax ÷ Her yearly Gross Pay) × 100(13,535.52 ÷ 67,200) × 1000.20142... × 10020.142...% or 20.14%33. Find the surface area of the rectangular prism.
7 cm
12 cm
1.6 cm
Answer: 228.8cm
Step-by-step explanation:
Hope this helps! :)
exploratory data analysis 1. when considering the research question, identify the two variables predictor (explanatory) variable: response variable: 2. use minitab to first create a scatterplot. minitab> graph > scatterplot how would you characterize the association between these two variables? a. linear or nonlinear? b. negative, none, or positive?
Identify the predictor and response variables, then create a scatterplot in Minitab. Characterize the association between the variables as linear or nonlinear and negative, none, or positive.
In exploratory data analysis, the first step is to identify the research question and the two variables of interest. The predictor variable (also known as the explanatory variable or independent variable) is the one that is used to explain or predict the outcome of the response variable (also known as the dependent variable).
After identifying the two variables, one can use software such as Minitab to create a scatterplot of the data. The scatterplot helps to visualize the relationship between the two variables.
To characterize the association between the two variables, we would first determine if the relationship appears to be linear or nonlinear. If the relationship is roughly linear, we would then determine if it is negative (meaning that as one variable increases, the other tends to decrease), positive (meaning that as one variable increases, the other tends to increase), or none (meaning that there is no clear trend).
Learn more about linear or nonlinear.
https://brainly.com/question/31510530
#SPJ4
What is
lim sin(x) in the graph shown?
Therefore, we can say: limit sin(x) as x approaches pi/2 does not exist lim sin(x) as x approaches 0 = 0.
What is the sinx x wiki's maximum size?Although the function (sin x)/x is not defined at zero, it approaches 1 arbitrarily close as x approaches zero. In other words, when x gets closer to zero, the limit of (sin x)/x = 1.
Why does Sinx have no limit?We can put g(x) equal to -1/x and h(x) equal to 1/x because sin(x) is always between -1 and 1. As x approaches either positive or negative infinity, we know that the limit of both -1/x and 1/x is zero, and as a result, the limit of sin(x)/x is also zero.
To know more about limit visit:-
https://brainly.com/question/12207558
#SPJ1
determine if the following is a supervised or unsupervised model. a local restaurant sends a 20% off coupon to its email subscribers. based on past data, what area around the restaurant contains the customers that spend the most when using the coupon?
The model of local restaurant which sends a 20% off coupon to its email subscribers, based on past data is an example of supervised model.
Supervised model is defined by its use of labeled datasets to train algorithms based on classification of data or predict outcomes accurately. While the accuracy of supervised learning models is more than unsupervised learning models. Supervised, as we are using past data. Classification, as we are trying to classify the customers into categories to study which ones will use the coupons. We have a local restaurant which send
a 20% off on a coupon to its email subscribers. It is based on past data. Using the above definition the predicted model for the provide example is supervised model.
For more information about supervised model, visit :
https://brainly.com/question/16872972
#SPJ4
The following data shows the grades that an 8th grade mathematics class received on a recent exam.
{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}
Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)
Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)
The resulting histogram would show the distribution of the grades on the exam, with the bins and frequency of data points clearly displayed. The title, axis labels, and scales would provide context for the graph and make it easy to interpret the data.
What is graph?In mathematics and computer science, a graph is a collection of points, called vertices or nodes, that are connected by lines, called edges or arcs. Graphs can be used to model and analyze relationships between objects or data, such as social networks, transportation systems, or web pages.
Here,
Part A:
The best graphical representation to display the given data is a histogram. A histogram is a bar graph-like representation of data that divides the data into intervals or bins and shows the frequency of each interval. Histograms are appropriate for displaying continuous data, which the grades on the exam can be considered as, and can also show the distribution of the data.
Part B:
To create a histogram of the given data, follow these steps:
Choose the number of bins or intervals. In this case, we can choose a reasonable number of bins, such as 6-8, to display the distribution of the grades.
Determine the range of the data. The lowest grade is 60 and the highest is 99, so the range is 99-60 = 39.
Calculate the bin size. The bin size is calculated by dividing the range by the number of bins. For example, if we choose 6 bins, the bin size would be 39/6 ≈ 6.5. Since it is difficult to have bins that are fractions of a point, we can round the bin size up to the nearest whole number to get a bin size of 7.
Create the bins. Starting from the lowest grade, create intervals or bins of size 7 that cover the range of the data. For example, the first bin would be 60-66, the second bin would be 67-73, and so on.
Count the frequency of data points that fall into each bin. For example, there are 2 data points in the first bin, 3 data points in the second bin, and so on.
Draw the histogram. On the horizontal axis, label and scale the bins. On the vertical axis, label and scale the frequency of data points in each bin. Draw a rectangle above each bin with a height equal to the frequency of data points in that bin.
Title: Grades on Recent 8th Grade Mathematics Exam
X-axis label: Grades
Y-axis label: Frequency
To know more about graph,
https://brainly.com/question/11950137
#SPJ1
If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I, find the value of tan(A−B).
If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.
What is the value of tan(A-B)?We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
From the given information, we have:
cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)
tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5
Now, we can use the definitions of sine and cosine to find tan A:
tan A = sin A / cos A = (7/25)/(24/25) = 7/24
Substituting the values we have found into the formula for tan(A - B), we get:
tan(A - B) = (tan A - tan B)/(1 + tan A tan B)
= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]
= (-13/72)/(25/72)
= -13/25
Therefore, tan(A - B) = -13/25.
Learn more about tan(A - B) here:https://brainly.com/question/24305408
#SPJ1
____ is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.
The quadratic formula x = (-b ± √ ( [tex]b^2[/tex] - 4ac) / (2a) is used to find the solutions (or roots) of a quadratic equation of the form [tex]ax^2[/tex] + bx + c = 0.
In this formula, "a", "b", and "c" are coefficients of the quadratic equation, and the ± symbol indicates that there are two possible solutions, one with a positive square root and one with a negative square root. By plugging in the values of "a", "b", and "c" from the given quadratic equation, one can use the quadratic formula to calculate the solutions for x that satisfy the equation.
Learn more about “ quadratic equation “ visit here;
https://brainly.com/question/17177510
#SPJ4
x = (-b ± √(b² - 4ac)) / (2a) is the formula x=-b±b2-4ac2a, used to find the solutions to a quadratic equation of the form ax2+bx+c=0.
The formula x = (-b ± √(b² - 4ac)) / (2a) is known as the Quadratic Formula, used to find the solutions to a quadratic equation of the form ax² + bx + c = 0.
The formula x=-b± b2 -4ac2a, is called the quadratic formula, which is used to find the solutions (or roots) to a quadratic equation of the form ax2+bx+c=0,
where a, b, and c are coefficients of the equation.
The term under the square root sign (b2-4ac) is called the discriminant and can tell you whether the quadratic equation has two real solutions (if the discriminant is positive), one real solution (if the discriminant is zero), or two complex conjugate solutions (if the discriminant is negative).
For similar question on quadratic.
https://brainly.com/question/30373079
#SPJ11
express the double integral d f (x, y) da as an iterated integral for the given function f and region d.
An iterated integral for the given function f and region d is [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].
What is integral?
An integral is the continuous equivalent of a sum in mathematics, where sums are used to compute areas, volumes, and their generalizations. One of the two basic operations in calculus, along with differentiation, is integration, which is the process of computing an integral.
Here, we have
Given: Consider the following F(x, y) = x + y YA (1,1) D 0 2 x
Equation of line passes through (2,0),(1,1)
= (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)
= (y - 0)/(1 - 0) = (x - 2)/(1 - 2)
= y/1 = (x-2)/(-1)
y = -x + 2
x = 2-y
∫∫F(x,y)dA = [tex]\int\limits^0_1 \int\limits^2_y {f(x,y)} \, dx dy[/tex]
∫∫F(x,y)dA = [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex]
Hence, an iterated integral for the given function f and region d is [tex]\int\limits^1_0 \int\limits^2_y {x+y} \, dx dy[/tex].
To learn more avbout the integral from the given link
https://brainly.com/question/27419605
#SPJ4
The perimeter of a rectangle is 80 inches. The
length of the rectangle is 12 inches.
Which equation could represent the width of the
rectangle, w?
Answer:
Step-by-step explanation:
Study the solutions of the three equations on the right. Then, complete the statements below.
There are two real solutions if the radicand is
There is one real solution if the radicand is
There are no real solutions if the radicand is
There are two real solutions if the radicand is positive.
There is one real solution if the radicand is zero.
There are no real solutions if the radicand is negative.
What is the radicand about?In mathematics, the radicand refers to the value inside a square root (√) symbol. In the given equations and solutions, we can see that there are square root symbols involved, and we can determine the nature of the solutions based on the sign of the radicand.
For the first equation, y = -16x² + 32x - 10, the solutions for x are given as x = (-32 ± √384) / -32. The radicand in this case is 384. Since 384 is positive, greater than 0, there will be two real solutions for x.
For the second equation, y = 4x² + 12x + 9, the solutions for x are given as x = (-12 ± √0) / 8. The radicand in this case is 0. Since the square root of 0 is 0, there is only one real solution for x in this case.
Therefore, For the third equation, y = 3x² - 5x + 4, the solutions for x are given as x = (5 ± √(-23)) / 6. The radicand in this case is -23. Since the square root of a negative number is not a real number, there are no real solutions for x in this case.
To know more about radicand here:
https://brainly.com/question/12224210
#SPJ1
See full text below
Study the solutions of the three equations on the right. Then, complete the statements below. There are two real solutions if the radicand is There is one real solution if the radicand is There are no real solutions if the radicand is 1. y = negative 16 x squared + 32 x minus 10. x = StartFraction negative 32 plus-or-minus StartRoot 384 EndRoot Over negative 32 EndFraction. 2. y = 4 x squared + 12 x + 9. x = StartFraction negative 12 plus-or-minus StartRoot 0 EndRoot Over 8 EndFraction. 3. y = 3x squared minus 5 x + 4. x = StartFraction 5 plus-or-minus StartRoot negative 23 EndRoot Over 6 EndFraction.
An advertising banner has four sections.two sections are congruent trapezoids with the bases as 1.75 and 2 with a height of 1,and two sections are congruent triangles with a width of 1.75 and a height of 1.25.
A measurement that is the best estimate of the area of the banner in square meters include the following: A. 6 m².
How to calculate the area of a trapezoid?In Mathematics and Geometry, the area of a trapezoid can be calculated by using this mathematical equation (formula):
Area of trapezoid, A = ½ × (a + b) × h
Where:
a and b represent the base areas of a trapezoid.h represent the height of a trapezoid.Based on the information provided about the two congruent trapezoid, we can logically deduce that they both have the same base area of 1 m.
This Means the total base of the entire triangle will be;
Base area = 1 + 1 ¾ + 1 + 1 ¾
Base area = 1 + 1.75 + 1 + 1.75
Base area = 5.5 m
Height of main triangle = 2 m
Area of banner = ½ × 5.5 × 2 = 5.5 ≈ 6.0 m²
Read more on trapezoid here: brainly.com/question/4758162
#SPJ1
Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Complete Question:
An advertising banner has four sections, as modeled below. Two sections are congruent trapezoids, and two sections are congruent right triangles. Which measurement is the best estimate of the area of the banner in square meters?
6 m²
15 m²
8 m²
10 m²