Answer:
4. <3 and <7
Step-by-step explanation:
Corresponding angles are any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal, and angles 3 and 7 were the only angles that matched this criteria.
Hope this helps :)
A store had a grand opening sale. During the sale, each person entering the store received
a coupon for 10% off their entire purchase. The table lists the number of people who received
a coupon.
What percent of the area underneath
this normal curve is shaded?
[?]%
Hint: Use the 68 - 95 - 99.7 rule.
Enter
The shaded area under the normal curve is determined using the 68 - 95 - 99.7 rule to be 68.27%
What is the 68 - 95 - 99.7 rule?The 68 95 99 rule, also known as the empirical rule in statistics, states that given normal distributions,
68% of observed data points will fall within one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.considering the figure and using the 68 - 95 - 99 rule, the shaded part is the reads 68% of the population and falls under the mean's 1 standard deviation.
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Alexander is a Stockbroker. He earns 11% commission each week. Last week, he sold $7,100 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
is this a rigid motion
The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.
The transformation for this problem has the rule defined as follows:
(x,y) -> (x + 2, -y).
The transformations are defined as follows:
x -> x + 2 is a translation right two units.y -> -y is a reflection over the x-axis.Neither transformation is a dilation, hence it is a rigid motion.
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between what two consecutive integers must log2(17) lie
Answer:
4 and 5
Step-by-step explanation:
For answering questions like this, it can be useful to remember a few of the powers of small integers:
2^4 = 16
2^5 = 32
Exponents and logarithmsA logarithm can be considered to be an exponent of the base.
\(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)
The ordering of powers of 2 relative to the number of interest (17) is ...
16 < 17 < 32
2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2
log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality
4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs
Log₂(17) lies between 4 and 5.
__
Additional comment
Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.
log₂(17) = log(17)/log(2) . . . . . . using logs to the same base
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°. What is the angle between the ground and steepest slope on the real rollercoaster?
The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.
A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?
To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.
The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.
The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.
That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)
The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.
That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,
the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°
The negative sign indicates that the angle is measured below the horizontal line.
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Can someone help me
Answer: its
12 4
_
7
Step-by-step explanation:
Answer:
12 4/7
Step-by-step explanation:
5 1/7 + 7 3/7 =
= 5 + 1/7 + 7 + 3/7
= 5 + 7 + 1/7 + 3/7
= 12 4/7
Answer: 12 4/7
An angle measures 8° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
41° and 49°
Step-by-step explanation:
Complementary angles are angles that sum up to 90°.
Let x represent the smaller angle, then the bigger angle will be represented with x + 8:
x + x + 8 = 90°
Add like terms.2x + 8 = 90°
Subtract 8 from both sides.2x = 82°
Divide both sides by 2.x = 41° this is the measure of smaller angle, then the bigger angle wpis 49°
The answer is:
⇨ 41 and 49Work/explanation:
If two angles are complementary, their measures add to 90°.
So we can set up an equation to find the angles. Let the unknown angle be w, and its complement will be w + 8:
w + w + 8 = 90
Combine like Terms
2w + 8 = 90
2w = 82
w= 41
The other angle measures 8° more than the measure of w:
41 + 8 = 49
Hence, the angles are 41 and 49°.Which inequality matches the graph?
Answer:
2n + 5 ≤ 7 The first choice
Step-by-step explanation:
2n + 5 ≤ 7 Subtract 5 from both sides.
2n + 5 - 5 ≤ 7 - 5
2n ≤ 2 Divide both sides by 2
\(\frac{2n}{2}\) ≤ \(\frac{2}{2}\)
n \(\leq\) 1
Answer:
2x +5 ≤ 7
I hope my answer helps you.
The mean of the heights of three buildings A,B and C is 14.2m. The mean of the heights of five buildings A,B,C, D and E is 14.8m. Find the mean of the heights of the buildings D and E.
========================================================
Work Shown:
s = sum of the heights of buildings A,B,C
s/3 = mean of the heights of buildings A,B,C
s/3 = 14.2
s = 3*14.2
s = 42.6
The buildings A,B,C have their heights add up to 42.6
--------------
r = sum of the heights of buildings A,B,C,D,E
r/5 = mean of the heights of buildings A,B,C,D,E
r/5 = 14.8
r = 5*14.8
r = 74
--------------
r-s = (sum of heights of A,B,C,D,E)-(sum of heights of A,B,C)
r-s = sum of the heights of buildings D and E
r-s = 74-42.6
r-s = 31.4
(r-s)/2 = mean height of buildings D and E
(r-s)/2 = 31.4/2
(r-s)/2 = 15.7 meters is the average height of buildings D and E.
Irene y Alejandro tienen 73 libros irene tiene el doble que Alejandro mas 1 cuantos libros tiene cada uno?
Irene has 49 Books, and Alejandro has 24 books.
Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:
1. Irene has twice as many books as Alejandro plus 1:
x = 2y + 1
2. The total number of books between Irene and Alejandro is 73:
x + y = 73
We can now solve this system of equations to find the values of x and y.
Substituting the value of x from equation (1) into equation (2), we have:
(2y + 1) + y = 73
3y + 1 = 73
3y = 72
y = 24
Now, we can substitute the value of y into equation (1) to find x:
x = 2(24) + 1
x = 49
Therefore, Irene has 49 books, and Alejandro has 24 books.
To verify our solution, we can check if the sum of their books equals 73:
49 + 24 = 7
So, our solution is correct.
In conclusion, Irene has 49 books, and Alejandro has 24 books.
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a light flashes every 2 minutes, a second light flashes every 3.5 minutes and a third light flashes every 4 minutes. if all three lights flash together at 8 p.m what is the next time of the day they will all flash together?
Answer:
take the LCM of the three numbers. Since 2 is a multiple of 4, you can ignore the two and just take the LCM of 4 and 3.5. Since 3.5 is a decimal, the LCM is just 3.5*4 which is 14. That is how many minutes after 8:00 they will flash together again.
Step-by-step explanation:
what is it plz help me with it
Answer:
isk
Step-by-step explanation:
Answer:
A) cards 1 and 2
Step-by-step explanation:
8/20 is equal to 2/5 and is also equal to 40%
Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about 3 inches. Assume men’s heights follow a normal curve.
a) (2 pts) What percentage of adult males are under 64 inches tall? Use the 68-95-99.7 and draw a picture that illustrates your rationale.
b) (2 pts) What percentage of adult males are between 64 and 73 inches tall? Use the 68-95-99.7 and draw a picture that illustrates your rationale.
Using the Empirical Rule, it is found that:
a) 2.5% of adult males are under 64 inches tall.
b) 81.5% of adult males are between 64 and 73 inches tall.
What does the Empirical Rule state?It states that, for a normally distributed random variable, approximately:
68% of the values in the distribution are within 1 standard deviation of the mean.95% of the values in the distribution are within 2 standard deviations of the mean.99.7% of the values in the distribution are within 3 standard deviations of the mean.For item a, we have that 64 is two standard deviations below the mean, hence, considering the symmetry of the normal distribution:
2.5% of adult males are under 64 inches tall.
As shown by the first graph at the end of the answer.
For item b, we have that 64 is two standard deviations below the mean, while 73 is one above, hence, considering the symmetry of the normal distribution:
P = 0.5 x 95 + 0.5 x 68 = 81.5%.
As shown by the two blue sections, plus the left brown section, in the second graph.
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Please answer this and show the work/explain
2/7m - 1/7 = 3/14
(2/7)m - (1/7) = 3/14
2m/7 =(3/14) + (1/7)
2m/7 = (3/14) + 2(1/7)
here we are multiplying 2 with 1/7 to make the denominator same for addition.
2m/7 = (3/14) +(2/14)
2m/7 = (3 + 2)/14
2m/7 = 5/14
2m = (5 *7)/14
2m = 35/14
2m = 5/2
m = 5/4
m = 1.25
So the value of "m" is 1.25
Please answer all parts as I know the answers but need the work to go with them. Thus, I believe that some answers are correct. Thank you!
The number of the sample that is necessary is 171. The number of employees that would be selected if E is 30 = 476
How to solve for the number of the sampleThe standard deviation = 398
error E = 50
Alpha is = 1-0.90 = 0.10
a. We are to find the value of the size of the sample
Z∝/2 = Z0.05
= 1.645
sample size,n >= [Za/2 *(sigma/E)]^2
n >= [1.645 * (398/50)] ^2
n >= 171.46
n = 171
b.
error,E = 30
n >= [1.645 * (398/30)] ^2
n >= 476.27
n = 476
Complete questionA survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 90% confident that the sample mean is correct to within ±$50 of the population mean annual family medical expenses. A previous study indicates that the standard deviation is approximately $398. a. How large a sample is necessary?
b. If management wants to be correct to within ±$30, how many employees need to be selected?
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Express the difference of 5.023 x 10^-2 and 4.6 x 10^-4 in scientific notation.
Complete the following sentence. Yevgeni works as an air conditioner repairman for a large company. He looks at his monthly paycheck and sees that $79.75 has been withheld for Medicare. Before withholdings, Yevgeni's monthly salary is
A. $3,250
B. $4,100
C. $5,500
D. $2,750
drew used these clues to describe a number he wrote.
One digit has a value of 7 x 100,000.
One digit has a value of 9 x 100
One digit has value of 8 x 0.01
Which could be the number Drew wrote?
The number that Drew wrote is 790,800.
What is number?Number is a mathematical object used to count, measure, and label. It is an abstract concept that can be represented with symbols, such as numerals, and words, such as "three" or "three hundred." Numbers can be used to represent quantities, distances, sizes, and other measurements. In mathematics, number theory is the study of the properties of numbers, such as addition, subtraction, multiplication, and division. Number theory is also used in other sciences, such as physics and computer science.
This is determined by taking the value of each digit and multiplying it by the exponential value that Drew described. The first digit has a value of 7 x 100,000, the second digit has a value of 9 x 100, and the third digit has a value of 8 x 0.01. Therefore, the number is 790,800.
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Write a Quadratic function in vertex form y - alx - h)2 + k that when compared to the parent function y * *? has the following Transformations.
No reflection over the x axis, shift right 9 units and has a vertical compression by a factor of 0.14.
Answer:
(02.02 HC)
The boxes described below have the same volume but different dimensions and surface area. Describe
the relationship between the surface area and the volume of a cell. Analyze the data and explain why cell
shapes can be beneficial.
future: a day, a week, or even a few months from now.
short-term goal
long-term goal
intermediate goal
specific goa
The graph of the function f(x)=log4(x) is stretched vertically by a factor of 2, reflected over the x-axis, reflected over the y-axis, and shifted down by 1 unit.Find the equation of the function g(x) described above.
Transformations on a lograrithmic function:
\(\begin{gathered} Reflections: \\ over\text{ x-axis: -}\log_bx \\ over\text{ y-axis:}\log_b(-x) \end{gathered}\)\(\begin{gathered} \text{Vertical stretching: }a\log_bx\text{ \lparen a is the factor of streatching\rparen} \\ \\ \end{gathered}\)\(Shift\text{ down k units:}\log_b(x)-k\)Then, the given function after the given transformations is:\(g(x)=-2\log_4(-x)-1\)When this net is folded into a cube, which
edge joins with edge X?
X
F
A
E
B
D
C
When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.
Explain about the cube?A cube is a solid shape with six square faces. Each side of a square has the same side length, so all faces are the same size.
A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.
Shape Properties of Cube
It is a three-dimensional square shape It has 6 faces, 12 sides and 8 vertices All faces are square All sides are of equal length Every vertex meets three faces and three sides Sides are square All sides are of equal length Each vertex meets three faces and three sides parallel to it All angles of a cube are right anglesThus, when edge D connects with edge X, this net is folded into a cube.
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How many solutions does this system have? no solutions one unique solution O O two solutions O or an infinite number of solutions
Answer:
no solutions
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 )
equation of blue line is y = x + 2 , in slope- intercept form
with slope m = 1
equation of red line is y = x - 3 , in slope- intercept form
with slope m = 1
• Parallel lines have equal slopes
then the blue and red lines are parallel.
the solution to the system is at the point of intersection of the 2 lines
since the lines are parallel then they do not intersect each other.
thus the system shown has no solution.
Gaurav was conducting a test to determine if the average amount of medication his patients were taking was similar to the national average. He wants to use a 5% significance level for his test to help ensure that his patients do not receive too little or too much medication. If Gaurav were to conduct a test, what probability value would indicate that his null hypothesis (that there is no significant difference between the amount of medication Gaurav's patients are receiving and the national average) would be rejected?
A probability value equal to or smaller than 0.05 would indicate that Gaurav's null hypothesis should be rejected at the 5% significance level.
In hypothesis testing, the significance level, denoted as alpha (α), is the predetermined threshold used to determine whether to reject the null hypothesis.
Gaurav has specified a 5% significance level, which means he wants to control the probability of making a Type I error (rejecting the null hypothesis when it is true) at 5% or less.
If Gaurav were to conduct a test and calculate the p-value, he would compare it to the significance level of 0.05.
The p-value is the probability of observing a test statistic as extreme as the one obtained, assuming the null hypothesis is true.
If the p-value is less than or equal to the significance level (p ≤ α), it indicates that the observed difference is unlikely to occur by chance alone under the assumption of the null hypothesis.
Gaurav would reject the null hypothesis and conclude that there is a significant difference between the average amount of medication his patients are taking and the national average.
Conversely, if the p-value is greater than the significance level (p > α), it suggests that the observed difference could reasonably occur by chance, and Gaurav would fail to reject the null hypothesis.
This would imply that there is no significant difference between the average medication amounts of Gaurav's patients and the national average.
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3 over x minus 2 equals 1 over x
9514 1404 393
Answer:
x = 1
Step-by-step explanation:
As written, we must interpret your equation as ...
\(\dfrac{3}{x}-2=\dfrac{1}{x}\\\\\dfrac{2}{x}=2\qquad\text{add $2-\dfrac{1}{x}$}\\\\x=\dfrac{2}{2}=1\qquad\text{multiply by $\dfrac{x}{2}$}\)
The value of x is 1.
In physics, the current (I), potential difference (V), and resistance ® of an electrical circuit are known to stand in the following relation. i=V/R Which of the following is the same equation solved for V?A. V=IR B. V= I(1-R) C. V=I/R D.V=R/I
Answer:
Step-by-step explanation:
The current that flows through most substances is directly proportional to the voltage V applied to it. The German physicist Georg Simon Ohm (1787–1854) was the first to demonstrate experimentally that the current in a metal wire is directly proportional to the voltage applied: I∝V I ∝ V .
Ethan decides to type up some documents while waiting the meeting to start.He can type 2 pages every 1/8 hour.If the meeting started 3/4 hour later than the scheduled time,how many pages can he type before the meeting starts?
Answer: 4 pages
Step-by-step explanation:
To solve this problem, we need to use the formula:
Rate = Output/Time
Let's use "p" to represent the number of pages Ethan can type and "t" to represent the time he has before the meeting starts.
Rate = 2 pages/(1/8 hour) = 16 pages/hour
Since the meeting starts 3/4 hour later than the scheduled time, Ethan has t = 1 - 3/4 = 1/4 hour to type pages before the meeting starts.
Output = Rate * Timep = (16 pages/hour) * (1/4 hour) = 4 pages
Therefore, Ethan can type 4 pages before the meeting starts.
Answer: 4 pages
what's the inverse of f(x)=(x+3)^5
Answer:
The inverse is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x) = (x+3)^5
Finding the inverse,
\(f(x) = (x+3)^5\\or,\\y = (x+3)^5\)
We replace x with y and vice versa
so,
\(x = (y+3)^5\)
Solving for y,
the the 5th root,
\(\sqrt[5]{x} = y + 3\\y = \sqrt[5]{x} - 3\)
hence the inverse function is,
\(f^{-1}(x) = \sqrt[5]{x} - 3\)
Step-by-step explanation:
f(x)=(x+3)×5
Y=5X+15
now
interxchanging x and y we get,
x=5y+15
5y=x-15
y=x-15/5
therefor f~1(x)=x-15/5
K
A recipe for soup calls for 4 tablespoons of lemon juice and cup of olive oil. The given recipe serves 2 people, but a cook wants to make a larger batch that serves 20.
a) How many cups of lemon juice will the chef need for the larger batch?
b) How many pints of olive oil will the che need for the larger batch?
a) The chef needed
cups of lemon juice for the larger batch.
(Type a whole number, proper fraction, or a mixed number.)
Answer: A) 2 and a half B) 5 pints
Step-by-step explanation:
in 1 cup there are 16 table spoons.
a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp
40/16 =2.5
ANSWER A= 2 and a half cups of lemon juice.
in 1 pint there are 2 cups.
b)
1 cup = 1/2 a pint,
1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints
ANSWER B= 5 pints of olive oil
3.92 rounded to the nearest tenth
Answer: 3.9
Step-by-step explanation:
Since the one hundredth digit is below 5 the higher digits will stay as they are.