Answer:
Step-by-step explanation:
Triangle ABC is similar to triangle DEF,
Therefore we can use the property of similarity to find the length of DF.
By definition of similar triangles, corresponding sides are proportional. Therefore, we have:
AB/DE = AC/DF = BC/EF
We are given the lengths of AB, AC, and BC in triangle ABC. We need to find the length of DF in triangle DEF.
To find the length of DF, we can rearrange the equation AB/DE = AC/DF to get:
DF = AC * DE / AB
Substituting the values given, we get:
DF = 7.6 * 3.3 / 11 = 2.28
Therefore, the length of DF is 2.28.
Tentor, Inc., purchases disposable coffee cups on which to print logos for sporting events, proms, birthdays, and other special occasions. The owner received a large shipment of 861 cups this afternoon, and to ensure the quality of the shipment, he selected a random sample of 410 cups and identified 353 as defective.
What is the estimated proportion of defectives in the population? (Round the final answer to 3 decimal places.)
Answer
What is the standard error of the sample proportion? (Round your answer to 3 decimal places.)
Answer
What are the upper and lower bounds for a 98% confidence level? (Round the final answers to 3 decimal places.)
Upper bound is Answer
Lower bound is Answer
It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to√(0.861(1.0.861)/410) = 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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It is estimated that 0.861 percent of the population is faulty. The sample proportion's standard error is 0.022. A 98% confidence level has an upper bound of 0.910 and a lower bound of 0.812.
What is a proportion?
The comparative relationship between two or more things in terms of their size, amount, or number is referred to as a "proportion." Either a ratio or a fraction can be used to express it. The term "proportion" in statistics refers to the division of the total number of events by the frequency of each event.
The formula p = x/n, where p is the estimated proportion of defectives in the population, x is the number of defectives in the sample, and n is the sample size, can be used to determine the estimated proportion of defectives in the population.
When we substitute values, we obtain:
p = 353/410 = 0.861
As a result, the population's estimated defectiveness rate is 0.861.
The formula SE = √(p(1-p)/n), where SE is the standard error and n is the sample size, can be used to get the standard error of the sample percentage.
When we substitute values, we obtain:
SE is equal to[tex]\sqrt{\frac{0.861(1.0.861)}{410)}[/tex]= 0.022.
As a result, the sample proportion's standard error is 0.022.
Using the following formula, the upper and lower bounds for a 98% confidence level can be determined:
Lower bound = z*SE - p
Upper bound = z*SE + p
where z is the z-score for a 98% degree of confidence.
We discover that the z-score corresponding to a 98% confidence level is roughly 2.33 using a z-table or calculator.
When we substitute values, we obtain:
Lower bound is equal to 0.861 - 2.33*0.022, or 0.812.
Upper bound is equal to 0.861 + 2.33 * 0.022 = 0.910.
Consequently, the range of a 98% confidence level is as follows:
Maximum: 0.910
Upper limit: 0.812
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A retail manager constructs a 95% confidence interval to estimate the mean amount of money each customer spends per visit to the retail store. Assume that all conditions have been met. The one-sample t-interval is ($10.53, $31.89). The owner of the retail store will issue the manager a bonus if the customers spend $35, on average, per visit. Is it reasonable to believe this manager will receive a bonus? No. Because a different sample might give different results, no conclusion can be drawn. No. Because the interval does not contain $35, the manager would not be issued the bonus. Yes. Because the interval representing the mean amount customers spend per visit is entirely below $35, it is reasonable to believe the manager will be issued a bonus. Yes. Because the interval representing the mean amount customers spend per visit does not contain $35, it is reasonable to believe the manager will be issued a bonus.
The correct option is: No. Because the interval does not contain $35, the manager would not be issued the bonus.
What is an interval?An interval refers to a range of values between two points on a numerical scale. It can be represented by two numbers, called endpoints, and includes all the values that lie between these endpoints.
The two common types of intervals are closed intervals and open intervals.
According to the given information:
In a confidence interval, the range of values within which the true population parameter (in this case, the mean amount of money each customer spends per visit) is likely to fall is estimated. A 95% confidence interval means that there is a 95% probability that the true population parameter falls within the interval.
In this case, the confidence interval is ($10.53, $31.89), which means that we are 95% confident that the true mean amount customers spend per visit falls between $10.53 and $31.89. Since the interval does not contain $35, it is not reasonable to believe that the manager will receive a bonus, as the estimated mean amount spent per visit is below $35 according to the confidence interval.
The correct answer is: No. Because the interval does not contain $35, the manager would not be issued the bonus.
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Question 1 of 5
Which expression is equivalent to?x1/3
Answer:
[tex]\frac{?x1}{3}[/tex] is the answer as in ?x1/3 the ?x1/3 is = to ÷3.
so therefore the answer could also be [tex]\frac{?x1}{3}[/tex].
( please note that the [tex]\frac{x}{above}[/tex] symbolises ×by )
Hope this helps and gets brainliest.
Good luck with studies.
what is the surface area of this figure ?
The surface area of this figure is determined as 980.5 m².
What is the surface area of the figure?
The total surface area of the figure is the sum of all the area of the six faces and it is calculated as follows;
Area of top face = 12.7 m x 11 m = 139.7 m²
Area of bottom face = 9.5 m x 16 m = 152 m²
Area of far right face = 12.7 m x 14 m = 177.8 m²
Area of far left face = 9.5 m x 14 m = 133 m²
Area of front face = 16 m x 14 m = 224 m²
Area of back face = 11 m x 14 m = 154 m²
Total surface area = 139.7 m² + 152 m² + 177.8 m² + 133 m² + 224 m² + 154 m²
= 980.5 m²
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How long did Lizzie practice on Thursday and Friday altogether?
J
P
D
Lizzie's Drum Practice
P
S
P
D
P
S
S
Monday Tuesday Wednesday Thursday Friday
= 5 minutes
DONE
0
minutes
7 8
4
00
5
1 2
0
9
6
3
Answer:
Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
On Thursday, she practiced for 5 minutes according to the table.
On Friday, she practiced for 9 minutes according to the table.
Adding these two times together, we get:
5 minutes + 9 minutes = 14 minutes
Therefore, Lizzie practiced for a total of 14 minutes on Thursday and Friday combined.
Determine the domain and range of the graph of this function.
x ≤ 4, -2≤ y ≤ 2 are the domain and range of the graph of this function.
What is the domain and domain of the function in the graph?
Another way to identify domains and feature sets is with graphs. Domain refers to the set of possible input values, so a chart's domain consists of all input values displayed on the x-axis.
A range is the set of possible output values plotted on the y-axis. To find the domain and domain of the equation y = f(x), find the value of the independent variable x for which the function is defined.
y = f(x)
according to the graph value of y
x ≤ 4,
-2≤ y ≤ 2
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
Describe Volume?In general, volume refers to the amount of space occupied by a three-dimensional object. In physics, volume is a measure of the amount of space an object takes up, typically measured in cubic meters (m³) or cubic centimeters (cm³).
In mathematics, volume is often used to refer to the measure of the size of a solid object or region in three-dimensional space. This measure can be calculated using various methods depending on the shape of the object or region, such as integration, formulae, or counting.
For example, the volume of a cube can be calculated by multiplying its length, width, and height together. The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius of the sphere.
In finance, volume can also refer to the number of shares or contracts traded in a particular market or stock exchange over a given period of time. High trading volume often indicates a more active market, while low trading volume may indicate less interest or activity in a particular security or market.
The formula for calculating the volume of air passing through a filter is:
Volume = Filter Area x Airflow Velocity
Given that the airflow velocity is 100 ft/min and the dimensions of the filter are 4 ft x 2 ft, we can calculate the filter area as:
Filter Area = Length x Width
Filter Area = 4 ft x 2 ft
Filter Area = 8 square feet
Now we can substitute the values into the formula:
Volume = Filter Area x Airflow Velocity
Volume = 8 sq ft x 100 ft/min
Volume = 800 cubic feet per minute (CFM)
Therefore, the volume of air passing through the HEPA filter is 800 cubic feet per minute (CFM).
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Find the inradius of triangle ABC.
Find the circumradius of triangle ABC.
The sides of the triangle are 5, 29, and 42.
Solve by using matrices.
2x -y + 3z = 180
-4x + 2y + 3z = 225
3x - 4y = 270
X
= -66, y = [?], z =
Enter
Solving the system of equations using matrices is : = -66, y = 163, and z = 11.
Solving the system of equations using matrices ?To solve this system of equations using matrices, we can write it in the form AX = B, where:
A = coefficient matrix
X = variable matrix (containing x, y, and z)
B = constant matrix (containing the constants on the right-hand side of each equation)
So, we have:
| 2 -1 3 | | x | | 180 |
| -4 2 3 | x | y | = | 225 |
| 3 -4 0 | | z | | 270 |
We can solve for X by multiplying both sides of the equation by the inverse of A:
X = A^-1 * B
First, we need to find the inverse of A. We can do this by using the formula:
A^-1 = (1 / det(A)) * adj(A)
where det(A) is the determinant of A and adj(A) is the adjugate (transpose of the cofactor matrix) of A.
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
det(A) = 2(20 - 3(-4)) - (-1)(-40 - 33) + 3(-4*(-1) - 2*3) = 16
| 2 -1 3 |
| -4 2 3 |
| 3 -4 0 |
The cofactor matrix is:
| 2 9 6 |
| 12 0 -2 |
| 13 -9 8 |
Taking the transpose of the cofactor matrix gives us the adjugate of A:
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
So, we have:
A^-1 = (1 / det(A)) * adj(A) = (1 / 16) *
| 2 12 13 |
| 9 0 -9 |
| 6 -2 8 |
Multiplying A^-1 by B gives us:
| x | | -66 |
| y | = | 163 |
| z | | 11 |
Therefore, x = -66, y = 163, and z = 11.
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given that log c3 = 0.914
PLEASE HELP MATH
Answer:
≈ 0.153
Step-by-step explanation:
using the rules of logarithms
log x - log y ⇔ log ([tex]\frac{x}{y}[/tex] )
[tex]log_{b}[/tex] b = 1
then
[tex]log_{c}[/tex] ( [tex]\frac{4}{c}[/tex] )
= [tex]log_{c}[/tex] 4 - [tex]log_{c}[/tex] c
= 1.153 - 1
= 0.153
HELPPP PLEASEEE!!! Geometry checkpoint
The shaded region, the closest answer choice (B) is 20 square units.
What is the circumference in the definition of a circle?The circumference of a circle is the length of the edge of the circle. If we cut the circle and straighten it, the length of the border is the circumference of the circle.
The central angle of sector AOB is 2*35 = 70 degrees (because the central angle is twice the circumferential angle). The remaining angle of triangle AOB is (180 - 70)/2 = 55 degrees. Using trigonometry, we find that the length of AB is:
AB = 2 * 8 * sin(55/2) ≈ 11.96 units
The shaded area can be divided into two parts: a sector with a central angle of 70 degrees and a triangle with base AB and height 8 units (the radius of the circle).
The area of sector is
(70/360) * π * 8² ≈ 12.57 square units
The area of the triangle is:
(1/2) * AB * 8 ≈ 47.82 square units
Therefore, the total area of the shaded area is approximately:
12.57 + 47.82 ≈ 60.39 square units
Therefore, for the shaded region, the closest answer choice (B) is 20 square units.
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16. Mandy solved this system of equations using elimination. She says that the system has no solutions. Is her statement true or false? 9x + 15y = 6 5y=-3x+2 A True B False
Answer: We can solve this system of equations using elimination as follows:
9x + 15y = 6
5y = -3x + 2
To eliminate y, we can multiply the second equation by -3 and add it to the first equation:
9x + 15y = 6
-15y = 9x - 6
Simplifying the second equation, we get:
-5y = 3x - 2
Now we have two equations in terms of x and y:
9x + 15y = 6
-5y = 3x - 2
If we multiply the second equation by -3 and add it to the first equation, we get:
9x + 15y = 6
15y - 9x = 6
Simplifying, we get:
6y = 2
Dividing by 6, we get:
y = 1/3
Substituting y into the second equation, we get:
5(1/3) = -3x + 2
Simplifying, we get:
-3x = -13/3
Dividing by -3, we get:
x = 13/9
Therefore, the solution to the system of equations is (x, y) = (13/9, 1/3).
Mandy's statement that the system has no solutions is false. The system has a unique solution.
Step-by-step explanation:
Draw place value disk to represent the value of the following expressions
5 times 2=
When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.
What is number?Number is a mathematical concept used to quantify or measure a quantity. It is a symbol or group of symbols that stands for a quantity, such as 2, 4, 5, 10, and so on. Numbers are used to express amounts, to count, and to measure. They are also used to represent relationships between quantities and to compare quantities.
A place value disk can be used to represent the value of 5 times 2, which is equal to 10. The disk would have two sections, one representing the number 5 and the other representing the number 2. The number 5 would be represented by five single circles in the “ones” section, and the number 2 would be represented by two single circles in the “ones” section. When the two sections are combined, the total number of circles would be ten, representing the value of 5 times 2, which is 10.
The place value disk is a useful visual tool to help students understand the concept of multiplication. It allows them to clearly see how the number of circles in each section are multiplied to get the final answer. This can help them better understand the concept of multiplication and how it works.
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Complete questions as follows-
The number of potholes in any given 1 mile stretch of freeway pavement in Pennsylvania has a bell-shaped distribution. This distribution has a mean of 62 and a standard deviation of 11. Using the empirical rule (as presented in the book), what is the approximate percentage of 1-mile long roadways with potholes numbering between 51 and 84?
Find the gradients of lines A and B
I'm afraid you forgot to add a picture?
Given f(x)=3x2−2 and g(x)=7−1/2x2, find the following expressions.
(a) (f◦g)(4) (b) (g◦f)(2) (c) (f◦f)(1) (d) (g◦g)(0)
Answer:
To evaluate the composite functions (f◦g), (g◦f), (f◦f), and (g◦g), we need to substitute one function into the other and simplify the resulting expression.
(a) (f◦g)(4):
To find (f◦g)(4), we need to first find g(4) and then substitute it into f(x):
g(4) = 7 - 1/2(4)^2
= 7 - 8
= -1
Now we substitute g(4) = -1 into f(x):
(f◦g)(4) = f(g(4))
= f(-1)
= 3(-1)^2 - 2
= 1
Therefore, (f◦g)(4) = 1.
(b) (g◦f)(2):
To find (g◦f)(2), we need to first find f(2) and then substitute it into g(x):
f(2) = 3(2)^2 - 2
= 10
Now we substitute f(2) = 10 into g(x):
(g◦f)(2) = g(f(2))
= g(10)
= 7 - 1/2(10)^2
= -43
Therefore, (g◦f)(2) = -43.
(c) (f◦f)(1):
To find (f◦f)(1), we need to find f(f(1)):
f(1) = 3(1)^2 - 2
= 1
Now we substitute f(1) = 1 into f(x):
(f◦f)(1) = f(f(1))
= f(1)
= 1
Therefore, (f◦f)(1) = 1.
(d) (g◦g)(0):
To find (g◦g)(0), we need to find g(g(0)):
g(0) = 7 - 1/2(0)^2
= 7
Now we substitute g(0) = 7 into g(x):
(g◦g)(0) = g(g(0))
= g(7)
= 7 - 1/2(7)^2
= -17/2
Therefore, (g◦g)(0) = -17/2.
ZA =
Round your answer to the nearest hundredth.
Angle A equals 41.81°
c:
What is one third plus eight twelves
Answer:
1
Step-by-step explanation:
1/3 + 8/12 ⬅️(factor out by common factor, 4)
= 1/3 + 2/3
=1+2/ 3
=3/3 or 1
What is the equation of the circle with centre
(1/2, 0)and radius 2?
Responses (attached)
The equation of the circle is (x - 1/2)^2 + y^2 = 15/4.
How to calculate the equationThe equation of a circle with center (a,b) and radius r is given by the equation:
(x - a)^2 + (y - b)^2 = r^2
Using the given values, the equation of the circle with center (1/2, 0) and radius 2 is:
(x - 1/2)^2 + (y - 0)^2 = 2^2
Expanding and simplifying, we get:
(x - 1/2)^2 + y^2 = 4 - 1/4
Therefore, the equation of the circle is:
(x - 1/2)^2 + y^2 = 15/4
So, the equation of the circle is (x - 1/2)^2 + y^2 = 15/4.
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please help meeeee. What is the value of k?
Answer:
k = 10
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ MYZ is an exterior angle of the triangle , then
4k + 5 + 6k + 10 = 115
10k + 15 = 115 ( subtract 15 from both sides )
10k = 100 ( divide both sides by 10 )
k = 10
Answer:
k = 10----------------------
Exterior angle of a triangle is equal to the sum of remote interior angles.
In the given picture, the exterior angle is 115°, and remote interior angles are (4k + 5)° and (6k + 10)°.
Set up equation and solve for k:
4k + 5 + 6k + 10 = 11510k + 15 = 11510k = 100k = 10Therefore the value of k is 10.
25. Find m/T. 0 (9x-17) T (4x + 28) S R
Answer:
The given expression is:
m/T = 0(9x-17) / (T(4x + 28)S R)
Since the numerator is multiplied by 0, the entire expression becomes 0, regardless of the value of the denominator. Division by 0 is undefined in mathematics, as it is not a valid operation. Therefore, the result of m/T in this case is undefined.
You can double check urself ;D
What is the value of k?
help pleaseeeee
The value of k in the given diagram is 10.
What is a linear pair?A linear pair refers to two adjacent angles that are created when two lines intersect. The defining characteristic of a linear pair is that the sum of their measures is always equal to 180 degrees, which makes them supplementary angles. Essentially, a linear pair is a type of angle pair where the two angles are not only adjacent to each other, but they also add up to a straight angle. Linear pairs are frequently found in various geometric shapes, including triangles, quadrilaterals, and polygons. They also have real-world applications in areas such as architecture and engineering.
We know that sum of angles of a triangle is 180.
So in tringle XYZ,
Angle ZXY + Angle XYZ + Angle YZX = 180
Given angle values ZXY = 6k+10, YZX = 4K+5 and ZYM = 115
We see that Angle XYZ + Angle ZYM = 180, since they are a linear pair.
This means Angle XYZ = 180 - Angle ZYM = 180 - 115 = 65
Hence, Angle ZXY + Angle XYZ + Angle YZX = 180
6k+10 + 65 + 4K+5 = 180
10k + 80 = 180
10k = 180 - 80 = 100
k = 100/10 = 10
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Please solve this asap.
Answer:
height= 3cm
Step-by-step explanation:
to find the base of each triangle just half the bottom to get 4cm
a^2+b^2=c^2
a^2+4^2=5^2
a^2+16=25
a^2=9
a=√9
a=3
please answer in detail
Answer:
y = 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 2x + 3 ← is in slope- intercept form
with slope m = 2
• Parallel lines have equal slopes , then
slope of line AB is m = 2
line AB crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 2x + 4 ← equation of line AB
is trigonometry hard?
Answer:
yes it is pretty hard but I believe I. you
50 Points! Write the expression x^4+5x^2-8 in quadratic form, if possible. Photo attached. Thank you!
The expression x^4 + 5x^2 - 8 in quadratic form is: (x^2 + 8)(x^2 - 1)
How to solve the expressionIt should be noted that to express the given expression x^4+5x^2 - 8 in quadratic form, we need to identify a suitable substitution that will allow us to rewrite the expression as a quadratic in a new variable.
One possible substitution is to let u = x^2, so that we can write:
x^4 + 5x^2 - 8 = u^2 + 5u - 8
We can then factor this quadratic expression as:
u^2 + 5u - 8 = (u + 8)(u - 1)
Substituting back u = x^2, we get:
x^4 + 5x^2 - 8 = (x^2 + 8)(x^2 - 1)
Therefore, the expression x^4 + 5x^2 - 8 in quadratic form is:
(x^2 + 8)(x^2 - 1)
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What are the answers to these questions?
A=?
B=?
f''(A)=?
f''(B)=?
Thus f(x) has a local max or min at A and a local max or min at B.
We can say that f(x) has a local maximum at A and a local minimum at B.
What is Function?A function is a mathematical rule that assigns a unique output value to each input value. It describes the relationship between the input and output variables.
Critical numbers of a function are the values of the independent variable where the derivative is zero or undefined, indicating possible extrema or inflection points.
According to the given information:
To find the critical numbers of the function f(x), we need to find the values of x where f'(x) = 0 or f'(x) is undefined.
f(x) = cos(x) + √2/2
f'(x) = -sin(x)
Setting f'(x) = -sin(x) = 0, we get sin(x) = 0, which is true for x = nπ, where n is an integer. However, we only need to consider the values of x in the interval [0,2].
For n = 0, x = 0 is a critical number.
For n = 1, x = π is a critical number.
For n = 2, x = 2π is not in the interval [0,2], so we don't need to consider it.
Therefore, the critical numbers of f(x) in the interval [0,2] are A = 0 and B = π.
To find the nature of the critical points, we need to find the second derivative of f(x).
f''(x) = -cos(x)
Evaluating f''(x) at A and B, we get:
f''(A) = -cos(0) = -1, which means that f(x) has a local maximum at A.
f''(B) = -cos(π) = 1, which means that f(x) has a local minimum at B.
Therefore, we can say that f(x) has a local maximum at A and a local minimum at B.
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Jason bought 91.5 pounds of fruit for a class party. The class ate 0.2 pounds of the fruit. How much fruit is left?
91.3 pounds of fruit are left
Jason bought = 91.5 pounds
class ate = 0.2 pounds
You subtract the amount the class ate from the amount Jason bought to get the amount of fruit left.
91.5 - 0.2 = 91.3 pounds
A coordinate plane with 2 lines drawn. The first line is labeled f(x) and passes through the points (0, negative 2) and (1, 1). The second line is labeled g(x) and passes through the points (negative 4, 0) and (0, 2). The lines intersect at about (2.5, 3.2)
How does the slope of g(x) compare to the slope of f(x)?
The slope of g(x) is the opposite of the slope of f(x).
The slope of g(x) is less than the slope of f(x).
The slope of g(x) is greater than the slope of f(x).
The slope of g(x) is equal to the slope of f(x)
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
Where do the X and Y axes intersect on the coordinate plane, at position 0 0?The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.
We can use the slope formula to get the slopes of the lines f(x) and g(x):
slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3
slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2
The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.
Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).
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Answer:
B
Step-by-step explanation:
Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The answer are in angle m∠5+m∠6=180°,m∠2+m∠3=m∠6,m∠2+m∠3+m∠5=180°.
What is angle?Angle is a geometric concept that is used to describe the relationship between two lines or planes. It is measured in degrees, with a full circle being 360 degrees. Angles are used in mathematics to measure the size of a shape and the amount of turn between two lines. In physics, angles are used to describe the force of friction, the direction of a force, and the direction of light. Angles can also be used to describe the orientation of objects in space.
case A) we have
m∠5+m∠3=m∠4 ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary by angles
m∠4=180°-m∠3 ----> equation B
substitute the equation- B in equation A
m∠5+m∠3=180°-m∠3
m∠5+m∠3+m∠3=180°
This equation is true when m∠2=m∠3
therefore
Is not always true
case B) we have
m∠3+m∠4+m∠5=180° ----> equation A
we know that
m∠3+m∠4=180° -----> by supplementary to angles
m∠4=180°-m∠3 ----> equation B
substitute equation B in equation A
m∠3+(180°-m∠3)+m∠5=180°
m∠5=0°
This option is not true
case C) we have
m∠5+m∠6=180°
we know that
m∠5 and +m∠6 are supplementary angles
so
Their sum is always 180 degrees
therefore
This option is always true
case D) we have
m∠2+m∠3=m∠6 -----> equation A
we know that
m∠5+m∠6=180° ----> by supplementary angles
m∠6=180°-m∠5 ----> equation B
substitute equation B in equation A
m∠2+m∠3=180°-m∠5
m∠2+m∠3+m∠5=180°
Remember that the sum of any of tAnswer:
Step-by-step explanation:
he interior angles that of a triangle must be equal to 180 degrees
therefore
This option is true for sure
case E) we have
m∠2+m∠3+m∠5=180°.
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