SIMPLIFY 1^99.................................
Answers
Answer:
1 to the power of 99 is 1
Step-by-step explanation:
Related Questions
Line H has a gradient of 7.
Line K is perpendicular to line H
What is the gradient of line K
Answers
The gradient of the line K that is perpendicular to the line H that has a gradient of 7 is -1/7
What is the perpendicular lines?Perpendicular lines are lines that form a right angle (90 degrees angle) at the point of their intersection, in which the slope of one of lines is the negative reciprocal of the slope of the other line.
The gradient of the line H = 7
The relationship between the lines K and line H is; Line K is perpendicular to the line H
The slope of a line a, which is perpendicular to another line b with slope m is; -1/m
Therefore, the slope of the line K is -1/7
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Determine whether each expression can be used to find the length of side RS.
Answers
ANSWER:
\(\begin{gathered} \sin (R)\rightarrow\text{ Yes} \\ \tan (T)\rightarrow\text{ No} \\ \cos (R)\rightarrow\text{ No} \\ tan(R)\rightarrow\text{ No} \end{gathered}\)STEP-BY-STEP EXPLANATION:
Since we know a side and the hypotenuse, we can rule out tangent and cotangent, since these are related to the two legs.
Therefore, if we want to know that side we must apply sine or cosine, just like this:
\(\begin{gathered} \sin \theta=\frac{\text{opposite }}{\text{ hypotenuse}} \\ \text{therefore, in this case:} \\ \sin R=\frac{21}{35} \\ \cos \theta=\frac{\text{adjacent}}{\text{ hypotenuse}} \\ \cos R=\frac{\text{unknown}}{35} \end{gathered}\)Therefore, the way to calculate the value of the missing side is by means of the sine of the angle R
A nurse supervisor found that staff nurses complete a certain task in 10 minutes, on average. If the times required to complete the task are approximately normally distributed with a standard deviation of 3 minutes, find:
a) The percentage of nurses completing the task in less than 5 minutes.
% (e.g. 15.55%)
b) The percentage of nurses requiring more than 10 minutes to complete the task.
% (e.g. 15.55%)
c) The probability that a nurse who has just been assigned the task will take between 8 and 12 minutes to complete it.
(e.g. 0.7512)
d) The slowest 20% are given additional training. What task times qualify staff nurses for such training?
min (e.g. 45.5 min]
Answers
A) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%. b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%
To solve this problem, we will use the properties of the normal distribution and z-scores. Given that the average completion time for the task is 10 minutes and the standard deviation is 3 minutes, we can proceed with the following calculations:
a) To find the percentage of nurses completing the task in less than 5 minutes, we need to calculate the z-score corresponding to a time of 5 minutes and then determine the area under the normal distribution curve to the left of that z-score.
The z-score formula is given by: z = (x - μ) / σ
where x is the time in question (5 minutes), μ is the mean (10 minutes), and σ is the standard deviation (3 minutes).
z = (5 - 10) / 3 = -5/3 ≈ -1.67
Using a standard normal distribution table or a calculator, we can find that the area to the left of -1.67 is approximately 0.0475 or 4.75%. Therefore, approximately 4.75% of nurses complete the task in less than 5 minutes.
b) To find the percentage of nurses requiring more than 10 minutes to complete the task, we calculate the z-score for a time of 10 minutes and find the area to the right of that z-score.
z = (10 - 10) / 3 = 0
The area to the right of z = 0 is 0.5 or 50%. Therefore, approximately 50% of nurses require more than 10 minutes to complete the task.
c) To find the probability that a nurse will take between 8 and 12 minutes to complete the task, we need to find the area under the curve between the z-scores for 8 and 12 minutes.
z1 = (8 - 10) / 3 = -2/3 ≈ -0.67
z2 = (12 - 10) / 3 = 2/3 ≈ 0.67
Using a standard normal distribution table or a calculator, we find the area to the left of z = -0.67 as approximately 0.2514, and the area to the left of z = 0.67 as approximately 0.7514. Therefore, the probability that a nurse will take between 8 and 12 minutes to complete the task is approximately 0.7514 - 0.2514 = 0.5 or 50%.
d) To find the task times that qualify staff nurses for additional training, we need to determine the z-score corresponding to the slowest 20% of completion times and then convert it back to the original time scale.
The z-score corresponding to the slowest 20% is found by locating the z-score that has an area of 0.2 to its left. Using a standard normal distribution table or a calculator, we find this z-score to be approximately -0.84.
Now, we can convert the z-score back to the original time scale:
z = (x - μ) / σ
-0.84 = (x - 10) / 3
Solving for x, we have:
-0.84 * 3 = x - 10
-2.52 = x - 10
x = 10 - 2.52
x ≈ 7.48
Therefore, the task times that qualify staff nurses for additional training are approximately greater than 7.48 minutes.
In summary:
a) The percentage of nurses completing the task in less than 5 minutes is approximately 4.75%.
b) The percentage of nurses requiring more than 10 minutes to complete the task is approximately 50%
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9
Given log 103=0.4771 and log 107 = 0.8451, find log 10
9
log 10 49
(Round to four decimal places as needed.)
without using a calculator.
Answers
Step-by-step explanation:
rules of the logarithm :
e.g.
log(a×b) = log(a) + log(b)
log10(9) = log10(3×3) = log10(3) + log10(3) =
= 0.4771 + 0.4771 = 0.9542
log10(49) = log10(7×7) = log10(7) + log10(7) =
= 0.8451 + 0.8451 = 1.6902
Solve the question below:
Answers
Answer:
x = 15
Step-by-step explanation:
3x+1+4x-3 = 103
7x = 105
x = 15
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answers
Answer:
To translate triangle ABC 3 units up, we need to add 3 to the y-coordinate of each vertex:
A' = (-3, 3 + 3) = (-3, 6)
B' = (0, 7 + 3) = (0, 10)
C' = (-3, 0 + 3) = (-3, 3)
Therefore, the coordinates of the vertices for the image triangle A'B'C' are A'(-3, 6), B'(0, 10), and C'(-3, 3).
So the correct answer is: A′(−3, 6), B′(0, 10), C′(−3, 3).
A recent survey reported that small businesses spend 24 hours a week marketing their business. A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing. The chamber conducts a survey of 93 small businesses within their state and finds that the average amount of time spent on marketing is 23.0 hours a week. Assuming that the population standard deviation is 5.5 hours, is there sufficient evidence to support the chamber of commerce’s claim at the 0.02 level of significance?
Step 1 of 3 :
State the null and alternative hypotheses for the test. Fill in the blank below.
H0: μ=24
Ha: μ ____ 24
Step 2 of 3:
What is the test statistic?
Step 3 of 3:
Do we reject the null hypothesis? Is there sufficient or insufficient evidence?
Answers
Answer:
Ha: μ < 24
The test statistic is z = -1.75.
The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.
Step-by-step explanation:
A recent survey reported that small businesses spend 24 hours a week marketing their business.
This means that the null hypothesis is:
\(H_0: \mu = 24\)
A local chamber of commerce claims that small businesses in their area are not growing because these businesses are spending less than 24 hours a week on marketing.
This means that the alternate hypothesis is:
\(H_a: \mu < 24\)
The test statistic is:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.
24 is tested at the null hypothesis:
This means that \(\mu = 24\)
The chamber conducts a survey of 93 small businesses within their state and finds that the average amount of time spent on marketing is 23.0 hours a week.
This means that \(n = 93, X = 23\)
The population standard deviation is 5.5 hours
This means that \(\sigma = 5.5\)
Value of the test-statistic:
\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z = \frac{23 - 24}{\frac{5.5}{\sqrt{93}}}\)
\(z = -1.75\)
The test statistic is z = -1.75.
Do we reject the null hypothesis? Is there sufficient or insufficient evidence?
The pvalue of the test is the probability of finding a sample mean below 23, which is the pvalue of z = -1.75.
Looking at the z table, z = -1.75 has a pvalue of 0.0401
The pvalue of the test is 0.0401 > 0.02, which means that we do not reject the null hypothesis, as there is insufficient evidence.
assuming an interest rate of 5.4 percent, what is the value of the following cash flows four years from today? year cash flow 1 $ 3,000 2 4,040 3 5,885 4 7,975 multiple choice $23,120.48 $21,291.46 $22,178.61 $22,609.26 $23,631.70
Answers
The value of the cash flows four years from today is $22,609.26.
The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.
The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.
The value of the cash flows four years from today is $22,609.26.
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if the letter l,o,g,ic are randomnly arranged to form word logic what is the probability that result will be woord logic
Answers
The probability of randomly forming the word "woord logic" is:Probability = 1 / (10! / (2!))
To calculate the probability of forming the word "woord logic" by randomly arranging the letters l, o, g, i, c, we need to consider the total number of possible arrangements and the number of arrangements that result in the desired word.
The word "woord logic" has 10 letters in total. Among these letters, there are 2 o's and the remaining letters appear only once.
The total number of possible arrangements is given by the factorial of the total number of letters:
Total arrangements = 10!
However, since the letter "o" appears twice, we need to divide by the factorial of the number of repeated letters:
Total arrangements = 10! / (2!)
To calculate the number of arrangements that result in "woord logic," we consider that the arrangement of "woord logic" is unique and distinct. Thus, there is only one arrangement that matches the desired word.Simplifying this expression would yield the exact probability.
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Suppose that the function f:[a,b]-->R is bounded and that it is continuous except at one point x_0 in the open interval (a,b). Prove that f:[a,b]-->R is integrable.
Answers
Answer:
Step-by-step explanation:xn − xn−1 + xn−1 − xn−2 + ··· + x2 − x1 + x1 − x0. = xn − x0. = |I|. Suppose that f : [a, b] → R is a bounded function on the compact interval.
write each rational number as a repeating decimal -7/9
Answers
Answer:
0.777777777777777...
If it is 9:00 what time will it be 25 minutes earlier
Answers
Answer:
8:35
Step-by-step explanation:
Answer:
8:35
Step-by-step explanation:
-25+60=35
9h-1h(60 above)=8h
=8:35
Which of these shapes will tessellate without leaving gaps? A. Hexagon B. Octagon C. Pentagon D. Circle
Answers
The shape that can tessellate without leaving gaps is the hexagon (option A).
The shapes that can tessellate without leaving gaps are shapes that can be repeated to completely cover a flat surface without any overlaps or gaps. Among the options provided, the shape that will tessellate without leaving gaps is the hexagon (option A).
A hexagon is a six-sided polygon with equal sides and angles. It is a regular polygon, which means all of its sides and angles are equal. A regular hexagon can be arranged and repeated in a pattern to fill a plane without any gaps or overlaps. Bees' honeycombs are a real-world example of hexagonal tessellation.
On the other hand, octagons (option B) and pentagons (option C) do not tessellate by themselves without gaps. While they can be used in combination with other shapes to create tessellations, they cannot tessellate on their own.
A circle (option D) cannot tessellate without leaving gaps. A circle is a curved shape, and it cannot form a repeating pattern that completely covers a flat surface without overlaps or gaps.
In summary, the shape that can tessellate without leaving gaps is the hexagon (option A).
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What is the answer to 4x-6=3x+4?
Answers
Answer:
x = 10
Step-by-step explanation:
4x - 6 = 3x + 4
x - 6 = 4
x = 10
Answer:
x=10
Step-by-step explanation:
You want to isolate the x variable so x will equal to a numerical value.
4x-6=3x+4
4x-6-4=3x+4-4
4x-10=3x
-10=-x
10=x
Find the measure’s of the diagram .
Answers
Step-by-step explanation:
mr.beast.com he can give you a lot of money
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
The fence around a circular garden is 18 feet long.What is the area of the garden to the nearest square foot?Use 3.14 for pi.
Type the answer in the box
________ square feet
Answers
lmk if this helped :)
Robert can complete 10 inspections in 8 hours. Which represents the unit rate for the number of inspections he completes per hour?
Answers
Answer: 5 inspections in 4 hours, because if its 8 hours it would be 10 inspections
Step-by-step explanation:
Answer:
1.25
Step-by-step explanation:
10 ÷ 8 = 1.25
the sum of 3\4 and 18\19 is closest to
Answers
The sum of 3/4 and 18/19
\(\frac{3}{4}\text{ + }\frac{18}{19}\)3/4 = 0.75 which is close to 1
18/19 = 0.947 whis is very close to 1
so 3/4 + 18/19 is close to 1 + 1 = 2
order the fraction to least to greatest 2/3 3/7 4/8
Answers
find the approximate area of the sector
blank cm2
Answers
Answer:
If Im NOT MISTAKEN its 7.41
Step-by-step explanation:
Mrs. Helms's class can be divided into equal groups of 5 students or groups of 6
students. Which of the following is a possible size of her class?
Answers
Answer:
30
Step-by-step explanation:
5 times 6 equals 30
Graph the system of equations on your graph paper to answer the question.
{y=x−4y=−x+6
What is the solution for this system of equations?
Answers
Answer: (5 , 1)
Step-by-Step explanation:
hihi your problem is a system of question y = x-4 and y = -x+6 okay so graph them both normally and then find the point where they intersect which is gonna be a coordinate point, and that's your solution !!
y = x-4
the y intersect is going to be 4
the slope is a positive 1 , going up to the right, through the positive quadrant, line is facing to the right
y = -x+6
the y intersect is going to be -6
the slope is going to be a -1 , following up the opposite way the line is going to face the left
once you graph them both you'll see the point of intersection, the solution
make sure you drew your lines very clearly !!!!
the solution is x = 5 and y = 1 which is also (5 , 1)
hopefully this was helpful !
Emina took out a 5/1 variable-rate mortgage for $120,000. The interest rate
for the first period was fixed at 5.25%, and the loan was amortized over 30
years. At the end of the initial loan period, the interest rate was 6.75%, plus a
1.5% margin. What will the unpaid balance on her mortgage be after her initial
period expires?
O
A. $102,164.09
B. $123,740.97
c. $110,579.39
D. $113,739.09
Answers
Answer:
$110,579.39 this is the right answer.
Please help!!
If you could explain how you solved this in detail it would be much appreciated.
When x^3+kx^2+2kx+6 is divided by (x-2), the remainder is 30. Find k.
Answers
Simplifying this equation, we get:
8 + 4k + 4k + 6 = 30
8k + 14 = 30
8k = 16
k = 2
Therefore, the value of k is 1.
What is polynomial?In mathematics, a polynomial is an expression consisting of variables (usually represented by x), coefficients, and non-negative integer exponents, which are combined using the operations of addition, subtraction, and multiplication. For example,
\(3x^2 + 2x - 1\)
is a polynomial with three terms, or a "trinomial," where the variable x is raised to the powers of 2 and 1, and the coefficients are 3, 2, and -1.
The degree of a polynomial is the highest power of the variable in the expression. For example, the polynomial above has a degree of 2, since the highest power of x is 2.
Polynomials are used in many areas of mathematics, including algebra, calculus, and geometry, and are used to model many real-world phenomena.
We can use the remainder theorem, which states that if a polynomial f(x) is divided by (x - a), then the remainder is equal to f(a). In this case, we know that when the polynomial\(l x^3 + kx^2 + 2kx\) + 6 is divided by (x - 2), the remainder is 30. So, we can set up the following equation:
\(x^3 + kx^2 + 2kx + 6 = (x - 2)q(x) + 30\)
where q(x) is the quotient when. \(x^3 + kx^2 + 2kx + 6\) is divided by (x - 2). We don't need to know what q(x) is, since we're only interested in finding k.
Now, let's substitute x = 2 into the equation above:
\(2^3 + k(2^2) + 2k(2) + 6 = (2 - 2)q(2) + 30\)
Simplifying the left-hand side, we get:
\(8 + 4k + 4k + 6 = 30\)
\(16k = 16\)
\(k = 1\)
OR
8 + 4k + 4k + 6 = 30
8k + 14 = 30
8k = 16
k = 2
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can someone explain this ??
Answers
Answer: I thnk you just break each number in half and then determine the ratio
Step-by-step explanation:
In Bridget's class, 35% of the students chose pizza as their favorite food. If 14 of the students chose pizza as their favorite food, how many students are in the class?
Answers
Answer:
40 students are in the class :)
Step-by-step explanation:
35%=14
1%=14/35=0.4
0.4*100=40=100%
hi what is 398÷45.
Answers
Answer:
8.84444444444
Step-by-step explanation:
Answer:
the answered would be 8.8444444
if points p and q are contained in a plane, then pq is entirely contained in that plain
Answers
When P and Q are combined, they will be completely contained in the plane if P and Q are already inside the plane. PQ would therefore be totally in the aircraft.
What are two or more points if they lie on the same line?A plane may contain a number of points. A plane is carrying P and Q. A two-dimensional figure that never ends, the plane. It implies that there is no end. It has a level surface. If we draw a line to join the two points P and Q, the line will also be in the same plane. since the plane never comes to an end.
Collinear points are a group of points that all lie on the same line.The right response to this question is that a segment is a finite portion of a line connecting two locations, including its two ends.Coplanar points are groups of at least four points that all lie on the same plane. Keep in mind that given any two points, they are always coplanar, as are given any three points.
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Im not sure on how to do this and its suppose to be done with substitution method
Answers
Answer:
1. -6
2. 0
Step-by-step explanation:
Toula owns the Pita Pan restaurant. She needs to order supplies for the upcoming weekend rush. She needs 150 bags of pita bread. The bread come in crates of 50, and each crate costs $15.00. She also needs 65 containers of hummus dip. There are 5 containers in a box, and each box costs $20.00 What expressions can Toula use to determine how much the pita bread and hummus dips will cost? What will the total be?
Answers
The total cost of the pita bread and hummus dips will be $305.00.
To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:
Cost of pita bread:
Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates
Cost of each crate = $15.00
Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00
Cost of hummus dips:
Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes
Cost of each box = $20.00
Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00
Therefore, the expressions Toula can use to determine the costs are:
Cost of pita bread = 3 crates × $15.00/crate
Cost of hummus dips = 13 boxes × $20.00/box
The total cost will be the sum of the costs of pita bread and hummus dips:
Total cost = Cost of pita bread + Cost of hummus dips
Total cost = $45.00 + $260.00
Total cost = $305.00
Therefore, the total cost of the pita bread and hummus dips will be $305.00.
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