Answers
the answer is "EF = 3.16". According to condition of Similar triangles.
How to solve these problem?
To solve this problem, we will use the property of similar triangles, which states that corresponding angles of similar triangles are equal, and their corresponding sides are proportional.
First, we need to find the ratio of the sides of the two triangles. We can do this by dividing the length of one side of triangle ABC by the corresponding side of triangle DEF. Let x be the length of EF, then:
AB/DE = BC/EF = CA/DF
Substituting the given values, we get:
11/4.4 = 7.9/x = 7.6/(DE + x)
Solving for x, we get:
x = 3.16
Therefore, EF = 3.16.
Hence, the answer is "EF = 3.16".
Note that we can also check our answer by verifying that the corresponding sides of the two triangles are proportional using the ratios we found:
AB/DE = 11/4.4 = 2.5
BC/EF = 7.9/3.16 = 2.5
CA/DF = 7.6/(4.4+3.16) = 2.5
Since the ratios are all equal, we can conclude that the triangles are similar.
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Related Questions
Based on historical data, it takes students an average of 48 minutes with a standard deviation of 15 ninutes to complete the Unit 5 test. What is the probability that your class of 20 students will have a mean Completion time greater than 60 minutes on the Unit test?
Answers
The probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
What is probability ?
Probability cam be defined as ratio of number of favorable outcomes, total number of outcomes
We can solve this problem by using the central limit theorem. According to the theorem, if we have a large enough sample size, the distribution of sample means will be approximately normal, regardless of the underlying distribution of the population.
The mean of the sample means will be equal to the population mean, and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size.
In this case, we have a sample size of 20, which is not very large, but we can still use the central limit theorem as an approximation. The population mean is 48 minutes, and the population standard deviation is 15 minutes. The standard error of the sample mean is:
SE = σ / sqrt(n) = 15 / sqrt(20) = 3.354
To find the probability that the mean completion time for the sample is greater than 60 minutes, we need to standardize the sample mean using the formula:
z = (x - μ) / SE
where x is the sample mean, μ is the population mean, and SE is the standard error of the sample mean.
Plugging in the values, we get:
z = (60 - 48) / 3.354 = 3.57
We can now look up the probability of getting a z-score greater than 3.57 in a standard normal distribution table (or use a calculator). The probability turns out to be very small, approximately 0.0002 or 0.02%.
Therefore, the probability that your class of 20 students will have a mean completion time greater than 60 minutes on the unit test is very low.
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A consulting company has a project to launch, Project MI, and two potential consultants that will take over the project as project leaders, Jim and Joe. The project will succeed with probability 0.8 if Jim is the project leader, and with probability 0.6 if Joe is the project leader. The manager of the company said that Jim or Joe would lead the project with probabilities 0.4 and 0.6, respectively. Two months later, we have been told that the project has succeeded. What is the probability that Jim was the project leader?
Answers
Answer:
Jim was the project leader given that the project has succeeded is approximately 0.57.
A chef need to 12 pound of sliced carrots. This preparation of carrots has a yield percent of 86. What he peed quantity of carrots does the chef need to pull from the walk-in?
Answers
The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
What is quantity?Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.
In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:
Quantity Needed = 12 lb / 0.86 (yield percent)
Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
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The chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
What is quantity?Quantity is the amount or magnitude of something. It can be measured in terms of units, such as length, weight, volume, area, speed, temperature and time. Quantity also refers to the size or number of something, such as the number of items in a package or the number of people in a room. In mathematics, quantity is usually represented by a number or symbol.
In order to calculate the quantity of carrots the chef needs to pull from the walk-in, we can use the following formula:
Quantity Needed = 12 lb / 0.86 (yield percent)
Therefore, the chef would need to pull 14.07 lb of carrots from the walk-in in order to have 12 lb of sliced carrots after preparation.
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Which of the following measurements could be the side lengths of a right triangle?
A.
24 in, 32 in, 40 in
B.
24 in, 36 in, 40 in
C.
24 in, 32 in, 48 in
D.
20 in, 32 in, 40 in
Answers
Answer:
A. 24 in, 32 in, 40 in
Step-by-step explanation:
To determine whether a set of measurements could be the side lengths of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the lengths of the other two sides.
Using this theorem, we can check each set of measurements:
A. 24 in, 32 in, 40 in
Here, 40 in is the longest side, so it could be the hypotenuse. If we square the other two sides and add them together, we get:
24^2 + 32^2 = 576 + 1024 = 1600
And if we square the length of the hypotenuse, we get:
40^2 = 1600
So this set of measurements satisfies the Pythagorean theorem and could be the side lengths of a right triangle.
B. 24 in, 36 in, 40 in
Again, 40 in is the longest side and could be the hypotenuse. Squaring and adding the other two sides gives:
24^2 + 36^2 = 576 + 1296 = 1872
And squaring the length of the hypotenuse gives:
40^2 = 1600
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
C. 24 in, 32 in, 48 in
Here, again, we can take 48 in as the hypotenuse. Squaring and adding the other two sides gives:
24^2 + 32^2 = 576 + 1024 = 1600
And squaring the length of the hypotenuse gives:
48^2 = 2304
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
D. 20 in, 32 in, 40 in
Once more, we can take 40 in as the hypotenuse. Squaring and adding the other two sides gives:
20^2 + 32^2 = 400 + 1024 = 1424
And squaring the length of the hypotenuse gives:
40^2 = 1600
So this set of measurements does not satisfy the Pythagorean theorem and cannot be the side lengths of a right triangle.
In conclusion:
A set of measurements that could be side lengths of a right triangle is A) {24in,32in,40in}. The other sets do not satisfy Pythagorean theorem and cannot be sides of a right triangle.
n 8.1 Homework
K
Part 1 of 2
Suppose that the local sales tax rate is 3% and you purchase a car for $21,100.
a. How much tax is paid?
b. What is the car's total cost?
Answers
This same car's purchase amount, which would include tax, is $21,733.
Which tax is this?A tax is a compulsory fee / financial charge imposed by a government on a person or an entity in order to raise money for public works projects that provide the greatest infrastructure and facilities.
a. To determine the amount of tax paid, multiply the cost of the car even by applicable sales tax rate.
3% times $21,100 is the amount of tax paid.
Taxes paid = 0.03 times $21,100.
Total tax paid: $633
Hence, $633 in taxes were paid on the vehicle.
b. To get the entire cost of the vehicle, we must add the purchase price and any applicable taxes:
Total price equals automobile price plus tax paid.
Cost in total is $21,100 plus $633.
Cost in total is $21,733
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The speed limit is 50miles per hour. Kyle driving to a baseball game that starts in 2 hours. Kyle is 130 miles away from the baseball field. If Kyle drives at the speed limit, will he arrive in time
Answers
Answer:
To determine whether Kyle will arrive in time for the baseball game, we need to calculate how long it will take him to travel the 130 miles to the baseball field.
Using the formula:
distance = rate × time
We can rearrange the formula to solve for time:
time = distance / rate
Plugging in the given values, we get:
time = 130 miles / 50 miles per hour
time = 2.6 hours
This means that it will take Kyle 2.6 hours to travel the 130 miles to the baseball field at the speed limit of 50 miles per hour.
Since Kyle has 2 hours to get to the baseball game, he will not arrive in time if he drives at the speed limit. He would need to drive faster than the speed limit to make it to the game on time. However, it's important to note that speeding is illegal and dangerous, so Kyle should not exceed the speed limit. He may need to consider leaving earlier or finding alternative transportation to ensure that he arrives at the baseball game on time.
Step-by-step explanation:
Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs 15. (Take p = 3.14). (show working too) stop copying from others
Answers
The required length of lace = 4.17m and the cos for lace of 4.17m is ₹ 70.65.
[tex]\text{Circumference of the circle}=2\pi r[/tex][tex]\text{Radius of circle}=\dfrac{\text{diameter}}{2}[/tex]
Step 1:
Find the radius, r of the circular table.
Given that, Salma wants to put a lace on the edge of a circular table of diameter
Diameter of circle, d=1.5m
Radius of circle, [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex]
Step 2:
Find circumference of the circle.
Substitute [tex]\text{r}=\dfrac{1.5}{2}\text{m}[/tex] in formula
[tex]\text{Circumference of the circle}=2\pi r[/tex]
Take [tex]\pi =3.14[/tex]
[tex]=2\times3.14\times\dfrac{1.5}{2}[/tex]
[tex]=3.14\times1.5[/tex]
[tex]=4.71 \ \text{m}[/tex]
[tex]\text{Circumference of circle} = 4.71 \ \text{m}[/tex]
[tex]\text{The length of lace required is 4.71} \ \text{m}[/tex]
Step 3:
Find the cost of rope.
From step 2
[tex]\text{Length of lace required} =\it{4.17} \ \text{m}[/tex]
Given that, of the lace costs ₹ 15
From the above statement, form an equation.
Cost of 1m lace = ₹ 15
Therefore, cost of 4.17m lace
Required length of lace = 4.17m. Cost for lace of 4.17m is₹ 70.65.
Write a function rule P(m) to represent Evelyn’s profit per mask so that she can always find what her profits will be for any amount of masks (m) she sells.
Answers
By answering the presented question, we may conclude that Evelyn will equation need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
Initially, we must determine the entire cost of producing and transporting one mask:
Total cost per mask = $1.25 plus $2.15 for delivery = $3.40
Profit per mask is selling price minus total cost per mask, which equals $5 - $3.40 = $1.60.
As a result, Evelyn will profit $1.60 for each mask she sells. We may use the following calculation to calculate how many masks she needs to sell to recoup her $450 initial project costs:
Total beginning project expenditures / profit per mask = number of masks to sell
Total number of masks to be sold = $450 / $1.60 per mask = 281 masks
Evelyn will need to sell roughly 281 masks in order to cover her initial project expenditures and begin generating a profit.
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Evaluate the following using Cauchy Integral Theorem; The integral of 3z+1/(z(z-2)^2)
Answers
Hence, in response to the provided question, we can say that As a result, derivatives the integral has a value of -i/2.
what is derivative?In mathematics, the derivative of a function with real variables measures how sensitively the function's value changes in reaction to changes in its parameters. Derivatives are the fundamental tools of calculus. Differentiation (the rate of change of a function with respect to a variable in mathematics) (in mathematics, the rate of change of a function with respect to a variable). The use of derivatives is essential in the solution of calculus and differential equation problems. The definition of "derivative" or "taking a derivative" in calculus is finding the "slope" of a certain function. einsteinerupload of. Derivatives are rate of change metrics that apply to almost any function.
To use the Cauchy Integral Theorem to evaluate the integral (3z+1)/(z(z-2)2), we must first determine whether the function has any singularities in the region we are integrating across.
We can write the function to find the residue at z=0 as:
A/z + B/(z-2) + C/(z-2)2 = (3z+1)/(z(z-2)2)
3z+1 = A(z-2)^2 + Bz(z-2) + Cz
When we set z=0, we get:
1 = 4A
So, A = 1/4.
Set z=2 in the following equation and its derivative to determine B and C:
9 = 4B + 2C
3 = 4A - 2B - C
B = -1/2 and C = 7/4.
So, A=1/4 is the remnant at z=0, while B=-1/2 is the residue at z=2.
Applying the residue theorem, the integral is as follows:
dz = 2i [Res(z=0) + Res(z=2)] = 3z+1/(z(z-2)2
= 2πi [1/4 - 1/2]
= -πi/2.
As a result, the integral has a value of -i/2.
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What are the coordinates D1/2 (2,4) coordinates =
Answers
The cοοrdinates οf A′ fοr the dilatiοn D1.5(A) is A'(3, 6).
What are cοοrdinates?Cοοrdinates are a set οf numbers used tο lοcate the pοsitiοn οf a pοint οr an οbject in a space οr plane. They are typically used tο represent pοints in a Cartesian cοοrdinate system, which is a system that uses twο οr three perpendicular axes tο define the pοsitiοn οf a pοint.
Tο find the cοοrdinates οf the dilatiοn D1/2(△XYZ), we need tο multiply the cοοrdinates οf each vertex οf the triangle by the scale factοr οf 1/2. This will result in a triangle that is half the size οf the οriginal triangle, but with the same shape and prοpοrtiοns.
The given cοοrdinate is A(2, 4).
It's impοrtant tο knοw that a dilatiοn implies a bigger figure than the οriginal. In this case, we have a factοr οf dilatiοn οf 1.5, which means each cοοrdinate must be multiplied by it.
Sο, using the factοr οf dilatiοn, we have
A(2, 4) ⇒ A((2 × 1.5),(4 × 1.5)) ⇒ A'(3, 6)
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Complete question:
The point A has coordinates A(2, 4). What are the coordinates of A′ for the dilation D1.5(A)?
Calculus(Question in picture)
Answers
The percentage error in the volume calculation is estimated to be 24%.
What is the percentage error?The formula for the volume of a sphere is V = (4/3)πr³
where;
r is the radius of the sphere.Since the diameter is given as 50 ± 4 cm, the radius can be calculated as:
r = (1/2)d = (1/2)(50 ± 4) cm = 25 ± 2 cm
The percentage error in the radius is:
Δr/r = (2 cm) / (25 cm) = 0.08
This means that the radius measurement has an error of 8%.
Using the formula for the volume of a sphere, we can calculate the volume as:
V = (4/3)π(25 ± 2)³ = (4/3)π(27 ± 18) × 10³ cm³
The percentage error in the volume calculation can be found by:
ΔV/V = (Δr/r) × 3
ΔV/V = 0.08 × 3 = 0.24 = 24%
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pls help! show work!
Answers
Answer:
6 cm
Step-by-step explanation:
Volume of the given cylinder is calculated using the formula
V = π r ² l
r = radius of the cylinder = diameter/2
Here r = 4/2 = 2 cm
V = 150 cm³
and we are asked to calculate l
Plugging in known values
150 = π · 2³ · l
switch side:
π · 2³ · l = 150
π · 8 · l = 150
l = 150/8π
= 5.96831 cm
To the nearest centimeter we would round this up to 6 cm (Answer)
The sum of two numbers is 8. The larger number is 23 more than twice the smaller.
Answers
Answer:
-5 and 13.
Step-by-step explanation:
We will kick off by calling the first unknown x.
To get the expression for the larger number:
'23 more than twice the smaller number'
twice the smaller number (x) = 2x.
Thus, the bigger number = 2x+23.
We were told that the sum of these two = 8
Therefore,
x+2x+23=8
=> 3x+23=8
3x=-15
x = -5 (smaller number).
The larger number is 2x+23
= 2(-5) + 23
= 13.
Hope this helps! :)
I will mark you brainiest!
The sum of the interior angles of an octagon is:
A) 1080º.
B) 180º.
C) 360º.
D) 720º.
Answers
Answer:
A) 1080º
Step-by-step explanation:
I remember learning this in math class. The octagon has 8 interior angles and 8 exteriors angle. The sum of the interior angles of an octagon is 1080º
Answer:
The sum of the interior angles of an octagon can be found using the formula: (n-2) x 180 degrees, where n is the number of sides of the polygon.
For an octagon, n = 8, so the sum of the interior angles is (8-2) x 180 = 6 x 180 = 1080 degrees.
Therefore, the correct answer is A) 1080º.
-5yz + yz +2yz simplify these expressions
Answers
Answer:
-2yz
Step-by-step explanation:
To simplify the expression -5yz + yz + 2yz, we can combine the yz terms that have the same coefficient:
-5yz + yz + 2yz = (-5 + 1 + 2)yz
Simplifying the coefficients gives:
= -2yz
Therefore, the simplified expression is -2yz.
Answer:
[tex]-2yz[/tex]
Step-by-step explanation:
[tex]-5yz + yz + 2yz = (-5 + 1 + 2)yz[/tex]
[tex](-5 + 1 + 2)yz = -2yz[/tex]
Therefore, the simplified expression is:
[tex]-2yz[/tex]
Which graph shows the solution to the system of linear equations? y= 2x y=X- 2
Answers
(-2, -4)
Step-by-step explanation:Systems of equations are sets of two or more equations that share the same variables.
Graphing
To graph a system of equations, simply graph each line individually. Both of the equations given are linear. Attached is a graph of both equations. As you can see the graphs intersect at (-2, -4).
Solutions to Systems of Equations
The solution to a system of linear equations is the coordinate point that the lines intersect. This is the point where the x and y-values make both equations true. To check the answer, plug the values into the equations. If both remain true, the answer is correct.
First, y = 2x
-4 = 2(-2)-4 = -4This is true. Next, y = x - 2
-4 = -2 - 2-4 = -4This is also true; thus the answer is (-2, -4).
13 ) Skyler mows lawns in the summer. The function f(x) is used to
model the amount of money earned, where x is the number of lawns
completely mowed. A reasonable domain for this function would be
(1) real numbers
(2) rational numbers
(3) irrational numbers
(4) natural numbers
Answers
URGENT ! 100 POINTS !
Mali is preparing for a competition that involves running and biking. This past weekend, they ran and biked for a total of 34 miles in 3.5 hours. Their average speed
for running was 6mph, and for biking it was 12.5mph.
If "x" represents the total hours Mali ran, and "y" represents the total hours Mali biked....
Which equation is a representation of the TOTAL TIME Mali spent training?
A. x+y = 3.5
B. 6x +12.5y = 34(3.5)
C. 6x +12.5y = 3.5
D. x+y=34
E. 12.5x+6y= 3.5
Answers
A. x + y = 3.5 equation is a representation of the TOTAL TIME Mali spent training
What is distance?An amοunt οf space between twο things οr peοple
The tοtal distance Mali cοvered can be expressed as the sum οf the distance run and the distance biked, which is equal tο 34 miles:
distance run + distance biked = 34
We can express the distance run and the distance biked in terms οf their speeds and the time spent running and biking, respectively:
distance run = 6x (where x is the time spent running in hοurs)
distance biked = 12.5y (where y is the time spent biking in hοurs)
Using the fοrmula distance = rate × time, we can write twο equatiοns fοr the time Mali spent running and biking:
6x + 12.5y = 34 (tοtal time equatiοn)
x + y = 3.5 (tοtal time equatiοn)
Optiοn A, x + y = 3.5, is a representatiοn οf the tοtal time Mali spent training, but οptiοn B, 6x + 12.5y = 34(3.5), is nοt a representatiοn οf the tοtal time Mali spent training, but rather a representatiοn οf the tοtal distance cοvered by Mali in terms οf their speeds and time spent training. Optiοns C, D, and E are nοt cοrrect representatiοns οf the tοtal time Mali spent training either. Therefοre, the cοrrect answer is:
A. x+y = 3.5
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What is the area of the triangle in the coordinate plane?
(A) 36 units²
(B) 38 units²
(C) 66 units²
(D) 72 units²
_______________________________
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(giving brainliest to correct answers)
_______________________________
Answers
Area of a triangle = 1/2(bh)
base = 11-3 = 8
height = 12-3 = 9
9 • 8 = 72
72/2 = 36
The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.
What is the area of the triangle?Assume 'h' is the height of the triangle and 'b' be the base of the triangle. Then the area of the triangle is given as,
[tex]\text{A} = (\dfrac{1}{2} ) \times h\times b[/tex]
From the graph, the length of the height of the triangle is 9 units and the length of the base of the triangle is 8 units. Then the area is given as,
[tex]\text{A} = (\dfrac{1}{2} ) \times 9\times 8[/tex]
[tex]\text{A = 36 square units}[/tex]
The area of the triangle in this coordinate plane will be 36 square units. Then the correct option is A.
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Solve the indefinite integral (linear):
Answers
Answer:
[tex] \rm \: a. \: \displaystyle \int \rm \: (3 {x}^{2} + 4x)dx[/tex]
[tex] = \displaystyle \int \rm 3 {x}^{2} dx + \displaystyle \int \rm4x \: dx[/tex]
[tex] \rm = 3 \displaystyle \int \rm {x}^{2} \: dx + 4\displaystyle \int \rm \: x \: dx[/tex]
[tex] \rm \: = 3 \times \dfrac{ {x}^{3} }{3} + 4 \dfrac{ {x}^{2} }{2} + c[/tex]
[tex] \boxed{\rm = {x}^{3} + 2 {x}^{2} + c}[/tex]
[tex]b. \displaystyle \int \rm \bigg( \dfrac{1}{ {t}^{2} } + \sqrt{t} \bigg)dt[/tex]
[tex] = \displaystyle \int \rm \frac{1}{ {t}^{2} } dt + \displaystyle \int \rm \sqrt{t} \: dt[/tex]
[tex] = \displaystyle \int \rm \: {t}^{ - 2} dt \: +\displaystyle \int \rm {t}^{ \frac{1}{2} } dt[/tex]
[tex] \rm \: = \dfrac{ {t}^{ - 1} }{ - 1} + \frac{ {t}^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ [/tex]
[tex] \rm = - \dfrac{1}{t} + \dfrac{2}{3} {t}^{ \frac{3}{2} } + c \\ [/tex]
[ In Second question I used dt instead of dx ]
Express the perimeter of the following triangle in simplest form: 3a + 8 4a +2b + 7 5a + b
Answers
The perimeter of the triangle when expressed in simplest form is 12a + 3b + 15
How to express the perimeter of the triangleThe dimensions of the triangle are given as
3a + 8 4a +2b + 7 5a + b
Perimeter refers to the total length of the boundary or outer edge of a two-dimensional shape.
The perimeter is measured in linear units such as centimeters, meters, feet, or inches.
The formula for finding the perimeter of a shape depends on the type of shape
For the triangle, we have
Perimeter = 3a + 8 + 4a +2b + 7 + 5a + b
Evaluate
Perimeter = 12a + 3b + 15
Hence, teh perimeter is 12a + 3b + 15
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Find an equation for the graph.
Answers
Answer:
y=4sin(1/2πx)
Step-by-step explanation:
A = 4
Period for y=sin(x) is 2pi
Since the graph shows the period is 4. Then b must be 1/2pi
Some researchers claim there is an association between taking vitamins and gaining weight. They took a random sample of people living in Boston, Massachusetts, and recorded whether they took vitamins and whether they gained weight. The results are shown in the following two-way table:
A student reading the results stated that more than half of the study participants are taking vitamins. Determine if the student is correct.
A) Yes, because 23.5% take one vitamin and 48.2% take more than one vitamin, which is a total of 71.7% taking vitamins.
B)Yes, because 27.4% take one vitamin and 49.5% take more than one vitamin, which is a total of 76.9% taking vitamins.
C) No, because 11.4% take one vitamin and 23.5% take more than one vitamin, which is a total of 34.9% taking vitamins.
D) No, because 16% take one vitamin and 26% take more than one vitamin, which is a total of 42% taking vitamins.
Answers
Option D is correct as 16% and 26% results in a percentage of 42%, in line with percentages in the "At least one vitamin" row of the table of random sample.
In random sample:
The student is incorrect. To determine the proportion of participants taking vitamins, we need to add up the percentages in the "At least one vitamin" row of the table. Adding 23.5% and 48.2%, we get a total of 71.7%, which is not more than half. Therefore, option A is incorrect.
Option B is also incorrect, as adding 27.4% and 49.5% gives a total of 76.9%, which is more than half but does not match the percentages in the table.
Option C is incorrect, as adding 11.4% and 23.5% gives a total of 34.9%, which is lower than the percentages in the table.
Option D is correct, as adding 16% and 26% gives a total of 42%, which matches the percentages in the "At least one vitamin" row of the table. Therefore, the correct answer is D.
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23. If point P (4,11) is reflected across the line y = 1, what are the coordinates of its reflection image?
Answers
Answer:
b
Step-by-step explanation:
The coordinates of its reflection are (4, -10)
What is Reflection of a point?A reflection over line is a transformation in which each point of the original figure (the pre-image) has an image that is the same distance from the reflection line as the original point, but is on the opposite side of the line.
Given that point P(4,11) is reflected across the line y=1,
Point P is on x = 4 which will not change after reflection, P is 10 units above line y = 3 so counting down 10 from y = 1, and then we will get on
y = -5'
Hence, the coordinates of reflection of point P = (4, -10)
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Use set-builder notation to indicate set numbers as described.
Answer
4
The set of all real numbers between 1 and 3, including 1
Answers
The set of all real numbers between 1 and 3, including 1 can be represented using set-builder notation as: { x ∈ R | 1 ≤ x ≤ 3 }
set-builder notation:
{ x ∈ R | 1 ≤ x ≤ 3 }
"The set of all x in the set of real numbers such that x is bigger than or equal to 1 and less than or equal to 3" can be understood from this notation. The word "such that" is denoted by the vertical bar "|," and the condition that follows lists the requirements that each element of the set must meet.
When the criteria is "more than or equal to 1" in this instance, the set contains 1. As they also meet the requirement of being "less than or equal to 3," the set also includes all real numbers between 1 and 3. Observe that no numbers outside of the range [1,3] are included in the collection.
In conclusion, the set of all real numbers between 1 and 3, including 1, may be written as x R | 1 x 3 in set-builder notation.
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Where is there a striking deviation in the dot plot above
Answers
The is a striking deviation at the value of 5.5.
This deviation is seen in the form of a cluster of dots that are significantly higher than the rest of the data points. This cluster of dots represents a group of observations that share a similar characteristic or variable that sets them apart from the rest of the data set.
The presence of this deviation at the value of 5.5 indicates that there is a unique factor or characteristic present in this group of observations that is not shared by the rest of the data set. This could be due to a number of factors, such as a different population, different data collection methods, or even measurement error.
It is important to note this deviation when analyzing the data set, as it can have a significant impact on any conclusions drawn from the data.
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What is the domain of the function
Answers
Answer: x[tex]\neq[/tex]6
Step-by-step explanation
The inverse function is f^-1(x)=1/x-4+6 and the domain is x[tex]\neq[/tex]6
Express f(x) as y
Swap the positions of x and y
Add 6 to both sides
Multiply both sides by y-4
Divide both sides by x + 6
Add 4 to both sides
Rewrite as: f-1(x)=1/x+6-4
Hence, the inverse function is 4 and the domain is x[tex]\neq[/tex]6
A passenger train has tickets available for 12 window seats and 8 aisle seats. The next person to buy a ticket will be randomly selected to one of those seats. What is the probability that the next passenger will be assigned to an aisle seat?
Answers
The answer is 2/5.
There is an 8/20 chance that the next person will receive a window seat. You simplify that probability to get your answer. 8/20 becomes 2/5. So the answer is 2/5.
Find the value of x. (Pic)
Answers
x+101+79+58=360
x=360-101-79-58
x=122
122°
Step-by-step explanation:
the formula is (n-2)180
n = the number of sides of a polygon
in this case (n-2)180;
=(4-2)180
=(2)180
=360 the total interior angle
add everything and minus them with the total interior angle to get your answer
Select the graph that correctly represents ƒ(x) = 1∕2(x – 3)^2 – 6.
Answers
Option (b) correctly represent the graph f(x) = 1/2 (x-3)² -6, we can find by coordinate geometry.
What is Coordinate geometry?
A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one (1) or more numbers, or coordinates.
In coordinate geometry, many geometric figures are described using graphs and coordinates. The coordinate plane must be described in a definition of coordinate geometry. The intersection of 2 number lines, referred to as axes, yields the coordinate plane, also known as the coordinate graph, which is a grid system.
In option (b), if we put x = 7 , we get y = 2.
and , if we put x =4, we get y = -5.5
Hence, the option (b) is correct.
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