Answer:
25 minutes
Explanation:
Subtract the two times to find the duration.
A 90° rotation around the origin followed by a reflection across the line x = 3 maps △JKL, with coordinates J(–2, 2), K(–2, 6), and L(–8, 2), to △PQR. Find the area of △PQR.
Answer: A 90° rotation around the origin maps point (x, y) to (-y, x). So, the image of point J after a 90° rotation is J' = (-2, 2) -> (-2, -2).
A reflection across the line x = 3 maps point (x, y) to (2x - 3, y). So, the image of point J' after a reflection across x = 3 is J'' = (-2, -2) -> (4, -2).
Similarly, we can find the images of K and L:
K' = (-2, 6) -> (-6, -2)
K'' = (-6, -2) -> (-2, -2)
L' = (-8, 2) -> (2, -8)
L'' = (2, -8) -> (8, -2)
Therefore, the image of triangle JKL after the 90° rotation and reflection is triangle PQR, with vertices P = J'', Q = K'', and R = L''.
The area of triangle PQR can be found using the Shoelace Formula:
P = [(4 -2) + (-2 -2) + (8 -2) * (-2 - (-8))]/2 = [6 + 4 * 6]/2 = 30/2 = 15 square units.
So, the area of triangle PQR is 15 square units.
Step-by-step explanation:
To solve the system of equations by
graphing, graph each line on a
coordinate grid and find the point of
intersection. Graph both equations on
the coordinate plane even if they
represent the same line.
y = -x-1
y = -x + 2
The equation shows the parallel line.
What is Graph?The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.
In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.
Given:
y = -x-1......................(1)
y = -x + 2...................(2)
Solving equation (1) and (2) we get
-x -1 = -x +2
0 = 3
Now, if compare the given equation then the equation gives the relation of Parallel lines.
Thus, the equation do not represent the same line.
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what is the expression for a quadratic formula discriminatnt
The discriminant of a quadratic equation in standard form, [tex]ax^2 + bx + c = 0[/tex] , is given by the expression: [tex]b^2 - 4ac[/tex]
The expression gives the discriminant: [tex]b^2 - 4ac[/tex]
This expression is used to determine the nature of the roots of the quadratic equation. Specifically, if the discriminant is positive, then the equation has two real and distinct roots. If the discriminant is zero, then the equation has one real root with a multiplicity of 2. If the discriminant is negative, then the equation has two complex conjugate roots.
A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form:
[tex]ax^2 + bx + c = 0[/tex]
where x is a variable and a, b, and c are constants. The coefficient "a" cannot be zero, since otherwise, the equation would become a linear equation.
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In what time will the simple interest on Rs7560 be Rs1102. 50 at 25/4% per annum
The simple interest on Rs 7560 will be Rs 1102.50 at a rate of 25/4% per annum after approximately 1 month (0.09 years).
Simple interest is a type of interest that is calculated only on the principal amount of a loan or investment, and not on any accumulated interest. It is usually calculated as a percentage of the principal amount, multiplied by the time period for which the interest is being calculated.
We can use the formula for simple interest to solve this problem:
Simple Interest (SI) = Principal (P) x Rate (R) x Time (T)
We know that the principal is Rs 7560, the rate is 25/4% per annum, and the interest is Rs 1102.50. Substituting these values into the formula, we get:
1102.50 = 7560 x (25/4) x T
Simplifying:
1102.50 = 47250T/4
Multiplying both sides by 4 to eliminate the fraction:
1102.50 x 4 = 47250T
4410 = 47250T
Dividing both sides by 47250:
T = 4410/47250
T = 0.093 or approximately 0.09 years.
To convert this to months or days, we can multiply by 12 or 365, respectively.
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In a class of 55 student 21 study Physic, 24 study geography, 23 study econs, 6study both phy and geo, 4 study both geo and econs, 5 both econs and phy, if X study all the three subject and 20 study non of the three subject
find the value of X
find the Number of student that study phy only
No of student that study one of the 2 subject
X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.
How do we get the responses to other questions?The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).
The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).
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The height, h, of the triangle is 11 cm greater than its corresponding base.
What is the area of the triangle?
A=
cm²
33 cm
10 cm
Answer:
If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.
Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:
A = (1/2) (b)(b + 11)
A = (1/2) b^2 + (1/2) 11b
If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:
A = (1/2) (10^2) + (1/2) 11 * 10
A = 50 + 55
A = 105 cm^2
So, the area of the triangle is 105 cm^2.
Step-by-step explanation:
7. consider four values for the predictor. in which instance(s) would you have a trustworthy prediction when using the simple linear regression equation?
The trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
To determine the trustworthiness of a prediction using a simple linear regression equation, we need to assess the degree of linearity and the strength of the relationship between the predictor and the response variable.
If the relationship between the predictor and response is linear, the simple linear regression model is appropriate, and if the relationship is strong, the predictions will be more trustworthy.
So, if we have four values for the predictor, we would need to evaluate the scatterplot of the predictor and response variable to determine the linearity and strength of the relationship.
If the scatterplot shows a clear and strong linear relationship between the predictor and the response variable, with a relatively small amount of scatter around the line of best fit, then we can be more confident that our predictions using the simple linear regression equation will be trustworthy.
On the other hand, if the scatterplot shows a weak or non-linear relationship, or a high amount of scatter around the line of best fit, then the predictions using the simple linear regression equation may not be as trustworthy.
Therefore, the trustworthiness of the prediction depends on the specific data and relationship between the predictor and response variable, and must be evaluated on a case-by-case basis.
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The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
The average rate of change of the function is 1.6
How to to determine the average rate of change of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
−4≤x≤1.
From the graph, we have
f(-4) = -4
f(1) = 4
The average rate of change at this interval is calculated as
Rate = Change in function values/Change in x values
So, we have
Rate = (-4 - 4)/(-4 - 1)
Evaluate
Rate = 1.6
Hence, the rate is 1.6
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Evaluate (-7)⁰
What’s is the solution?
Answer:
1
Step-by-step explanation:
everything to power of 0 is 1, except for 0^0 is undefined
Uhmmm I don’t know this pla
Answer:
y = 2x - 3
Step-by-step explanation:
Pick two random points for slope
slope = m = rise/run = [tex]\frac{(-3-(-5))}{0-(-1)} = \frac{2}{1} = 2[/tex]
y intercept form:
y = 2x - 3
17. A class has 20 students. In how many different ways can five students form a group? (Assume
that the order of the students is not important)
Answer: The number of ways to form a group of 5 students from a class of 20 students is calculated using the combination formula:
C(20,5) = 20! / (5! * (20-5)!) = 15504
So, there are 15,504 different ways in which 5 students can form a group.
Step-by-step explanation:
The atmosphere of a certain planet is made up of many elements. What part of the atmosphere is made up of Element 2? That's the question its asking my, please help, I am so bad at math! ASAP!!!!!
The percentage of the atmosphere made up of element 2 is 17%.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Given that in the pie chart, the atmosphere is distributed in different parts by which it is made.
The data is,
Element 1 = 76%
Element 2 = 17%
Other = 76%
The amount of element 2 in the atmosphere is 17%.
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whay are mixed fractions
Answer:
hope this helps!! <3
Step-by-step explanation:
A fraction is represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
GUYS I NEED HELP ASAP
An individual who files a local income tax return has a probability of the return being audited. If 12,000 tax returns are received by the city, which of the following is the best prediction of the number of income tax returns that were audited?
A.3,000
B.2,000
C.3,500
D.2,500
PQRS is a trapezium, and AB ∥ PS ∥QR. If PA = 3 cm, AQ = 1.4 cm, BR = 2.1 cm,
then SB =
Answer:
In trapezium PQRS, AB is parallel to PS and PS is parallel to QR. Since we know the lengths of PA, AQ, and BR, we can calculate the length of SB as follows:
SB = PA + BR - AQ = 3 + 2.1 - 1.4 = 3.7 cm
A hospital has a nursing staff of 250 nurses, working four shifts: A (7:00 AM to 1:00 PM); B (1:00 PM to 7:00 PM); C (7:00 PM to 1:00 AM); D (1:00 AM to 7:00 AM)
The number of nurses apportioned to each shift is based on the average number of patients, per shift, given the following table:
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences.
What is number?Number mathematical entity used to represent a quantity or magnitude it can be symbol or a combination of symbol used to denoted a quantity such as 2573 or 8 1 number are used in a variety of context including counting measuring and computing they are also used to denote the size or amount of something such as a number of people in a room or the number of apples in a basket number play an important role in mathematics including algebra geometry and calculus.
Based on the above figures, the hospital would require a staffing of approximately 62 nurses on Shift A, 93 nurses on Shift B, 68 nurses on Shift C, and 27 nurses on Shift D. This would equate to a total of 250 nurses, which is the number of nurses the hospital has on its staff.
The hospital can adjust the staffing needs by taking into account the amount of nurses needed to provide the necessary patient care. If the shift with the highest number of patients (Shift B) requires additional nurses, the hospital could move nurses from the shift with the lowest number of patients (Shift D). This would result in fewer nurses on Shift D, but would allow for more nurses on Shift B.
In order to ensure that nurses are working in a safe and comfortable environment, the hospital should also take into account the nurses' own preferences. If nurses prefer to work certain shifts, the hospital can adjust the staffing levels accordingly. This can help create a better work-life balance for the nurses, which can, in turn, improve their job satisfaction and performance.
In conclusion, the hospital needs to consider their staffing needs on a shift-by-shift basis, taking into account the number of patients and nurses' preferences. This way, they can maintain a safe and comfortable environment for their nursing staff, while also ensuring that they have enough nurses to provide the necessary care to their patient.
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solve the right triangle by completing the table below :) help asap
The missing sides of the two right triangles are B ≈ 75.5, b ≈ 10.7 and a ≈ 6.9.
How to find the missing sides of a system formed by two similar right triangles
In this problem we find two similar right triangles. Two triangles are similar when they have congruent angles and sides that are not congruent but proportional. Sides in right triangles are related each other by means of Pythagorean theorem:
r² = x² + y²
Where:
r - Hypotenusex, y - LegsAccording to the statement, we need to use the following relationships:
B = √(C² - A²)
a / A = b / B = c / C
If we know that A = 49, C = 90 and c = 12.7, then the lengths of missing sides are:
B = √(90² - 49²)
B = √5699 (approx. 75.5)
b = B × (c / C)
b = √5699 × (12.7 / 90)
b = 127√5699 / 900 (approx. 10.7)
a = A × (c / C)
a = 49 × (12.7 / 90)
a = 6233 / 900 (approx. 6.9)
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Which pair of ratios can form a true proportion? I would usually give 45 points but i have 35 soo ye..
A. 9/12, 5/8
B. 25/20, 16/21
C. 6/27, 2/9
D. 7/12, 10/15
Pair of ratios can form a true proportion I would usually give 45 points but i have 35 soo ye 25/20, 16/21.
What is ratios?When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls (for every one boy there are 3 girls) A ratio in mathematics displays the multiplicative relationship between two numbers. For instance, if there are eight oranges and six lemons in a dish of fruit, the ratio of oranges to lemons is eight to six. Lemons to oranges are divided 6:8 and oranges to all other fruits are divided 8:14 in a similar fashion.To learn more about ratios refer to:
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Aubrey bought stock in a company two years ago that was worth?
x dollars. During the first year that she owned the stock, it increased by 39%. During the second year the value of the stock increased by 16%. Write an expression in terms of ?
x that represents the value of the stock after the two years have passed
The expression that represents the value of the stock after two years in terms of x is 1.6144x
After the first year, the value of the stock increased by 39%, which means that the stock's new value will be -
x + 0.39x = 1.39x
After the second year, the value of the stock decreased by 16%, which means that the stock's new value will be -
1.39x - 0.16(1.39x) = 1.16(1.39x)
Simplifying this expression, we get,
1.16(1.39x) = 1.6144x
Therefore, the expression that represents the value of the stock after two years in terms of x is 1.6144x.
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The complete question is -
Aubrey bought stock in a company two years ago that was worth x dollars. During the first year that he owned the stock, it increased by 39%. During the second year the value of the stock decreased by 16%. Write an expression in terms of x that represents the value of the stock after the two years have passed.
find the value of x y and z
The values of x, y and z are;
x. x = 60° y = 55°
xi. x = 68° y = 56° z = 56°
xiii. x = 40° y = 50°
xiv. x = 40° y = 50°
What is a Triangle?A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.
x. x = 60° (corresponding angles are equal)
y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)
y + 125° = 180°
y = 180° - 125°
y = 55°
xi. y = 56° (corresponding angles are equal)
y = z = 56° (angles in equal sides of a triangle are equal)
x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)
x + 112° = 180°
x = 180° - 112°
x = 68°
xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)
x = 180° - 140°
x = 40°
y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)
y + 130° = 180°
y = 180° - 130°
y = 50°
xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)
y = 180° - 130°
y = 50°
x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)
x + 140° = 180°
x = 180° - 140°
x = 40°
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Help me quick pls help fast
Answer: 46ft
Step-by-step explanation:
Alright so for this you must reference the pythagorean theorem which is:
a^2+b^2=c^2. c^2 is always the diagonal side and a^2 and b^2 the other two sides.
You can therefore set this up like this:
a^2+20^2=50^2 (where a is the side you are looking for- listed as x)
Solve:
a^2=50^2-20^2
a^2=2500-400
a^2=2100
sqrt(a^2)=sqrt(2100)
a= 45.8257569496
Round: a (or x)=46
(-2,6)(-4,3)(3,-2)(8,6) is the relation a function
The given relation (-2,6)(-4,3)(3,-2)(8,6) is a function as every input has a single output.
A relation is set to be a function when every input has a single output.
In the given relation, -2,-4,3,8 has single output. Therefore, it is a function.
So, -2,-4,3 and 8 are the elements of the domain of the given
relation.
Here domain ={-2,-4,3,8} and range ={6,3,-3}
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Time spent listening to music a sample of 200 college freshman was asked how many hours per week they spent listening to music the following distribution presents the results
Answer:
Step-by-step explanation:
200 rimwjh hdwqheywgygwuivug
Shape A is reflected in the line with equation x=2 to get Shape B. Shape B is reflected in the x=6 to get Shape C. Describe the transformation that fully transforms Shape A to Shape C.
The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
The line x = 2, x = 6, and x = 6.5 is given on the graph below.
Shape A is reflected in the line with equation x = 2 to get Shape B.
Shape B is reflected in the x = 6 to get Shape C.
Now,
Shape A is reflected in the x =6.5 to get Shape C.
Thus,
The transformation that fully transforms Shape A to Shape C is reflected in the x =6.5
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a card is drawn from a standard deck of 52 playing cards. what is the probability that the card will be a diamond or a seven? express your answer as a fraction or a decimal number rounded to four decimal places.
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
Total cards = 52
Total diamond cards = 13
So, probability of getting a card of diamond,
P(diamond) = 13/52 = 1/4
Now,
Total cards with number seven = 4
So, probability of getting a seven,
P(seven) = 4/52 = 1/13
Hope it helps~
34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. a simple random sample of size 100 is chosen from the population to study this disease. let be the total number of people in our sample that have diabetes. what is the distribution of ?
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution, with a probability of success of 10.5%.
The binomial distribution has certain properties, such as the mean and variance, that can be used to make inferences about the population. For example, the mean of the distribution is given by:
μ = np
where n is the sample size and p is the probability of success.
The distribution of the number of people with diabetes in a sample of 100 can be modeled using the binomial distribution. The binomial distribution describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
In our case, a success is a person with diabetes, and the probability of success is the prevalence of diabetes in the population, which is 10.5%. The number of trials is 100, which is the sample size. Therefore, the distribution of the number of people with diabetes in our sample can be written as:
X ~ B(100, 0.105)
Where X is the random variable representing the number of people with diabetes in our sample, and B(100, 0.105) denotes the binomial distribution with 100 trials and a probability of success of 0.105.
In our case, the mean number of people with diabetes in our sample is:
μ = 100 x 0.105 = 10.5
This means that we expect, on average, to find 10.5 people with diabetes in our sample of 100.
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The following are the distances (in miles) to the nearest airport for 16 families. 9, 12, 18, 18, 19, 20, 26, 28, 29, 31, 31, 32, 32, 34, 35, 37. Notice that the numbers are ordered from least to greatest. Make a box-and-whisker plot for the data.
The average of the middle two figures, which are 18 and 19, is the median of the lower half. Q1 = (18+19)/2, which equals 18.5. The average of the middle two values—32 and 32—represents the median of the upper half. Q3 = (32+32)/2 = 32 as a result.
How far is that?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
First, we calculate the median for the lower and higher halves of the data. The values up to the median are found in the lower half and are as follows:
9, 12, 18, 18, 19, 20, 26, 28
The upper half consists of the values from the median onwards, which are:
29, 31, 31, 32, 32, 34, 35, 37
The median of the lower half is the average of the middle two values, which are 18 and 19. Therefore,
Q1 = (18+19)/2
= 18.5.
The median of the upper half is the average of the middle two values, which are 32 and 32. Therefore,
Q3 = (32+32)/2
= 32.
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Divide £88 in the ratio 1:7
The value of the number 88 in the ratio of 1:7 will be 11:77.
What is a ratio?The ratio is defined as the division of the numbers into two parts according to the requirements. The ratio generally compares one value is how many times the other value.
Given that the £88 is distributed in the ratio of 1:7. The distributed form of the number will be calculated as:-
x + 7x = 88
8x = 88
x = 11
The two values will be,
x = £11
7x = 7 x 11
7x =£77
Therefore, the value of the number 88 in the 1:7 ratio is 11:77.
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Mya uses a potato chip can to store small items. each cylindrical can has a radius of 2.5 inches and a height of 9 inches. what is the approximate surface area of the can? (use 3.14 for π.)
The approximate surface area of the can is 180.55 sq.inches
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth. A group of circular discs placed on top of one another might be thought of as a cylinder. The cylinder has both surface area and volume since it is a solid with a three-dimensional geometry.
The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
The Surface Area of Cylinder = Curved Surface + Area of Circular bases
S.A. (in terms of π) = 2πr (h + r) sq.unit
Where, π (Pi) = 3.142 or = 22/7
r = Radius of the cylinder
h = Height of the cylinder
cylindrical can has a radius of 2.5 inches and a height of 9 inches
surface area =2πr (h + r) sq.unit
= 2π*2.5(9+2.5)
=180.55 sq.inches
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Polaris, the North Star, is very important in navigation because it does not appear to move in the sky.
True
False
