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Answer:
(a) 21
Step-by-step explanation:
The product of the lengths to the near and far circle intercepts are the same for the two lines. For the tangent, the near and far intercepts are the same point, so we have ...
(36)(36) = (27)(27+x)
48 = 27+x . . . . . . . . . . divide by 27
x = 21 . . . . . . . . subtract 27
What is the future value of $500 to be received 3 years from now if the discount rate is 10%?
A cyclist rides her bike at a speed of 30 kilometers per hour. What is this speed in kilometers per minute? How many kilometers will the cyclist travel in 2
minutes? Do not round your answers.
Answer:
0.5 km/min and 1km
Step-by-step explanation:
30 km in an hour
30 km in 60 mins, 30/60 km in one minute so she cycle 0.5km/min. They will cover 1 km in 2 minutes
Laura, Scott, and Joe served a total of 104
orders Monday at the school cafeteria. Joe served 3
times as many orders as Scott. Laura served 9
more orders than Scott. How many orders did they each serve?
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Answer:
Joe: 57Scott: 19Laura: 28Step-by-step explanation:
Let s represent the number of orders Scott served. Then we have Joe served 3s, and Laura served (s+9). The total of orders served is ...
3s +s +(s +9) = 104
5s = 95 . . . . . . . . . . . subtract 9 and collect terms
s = 19 . . . . . . . . . divide by 5
3s = 3×19 = 57
s+9 = 19+9 = 28
Joe served 57 orders, Scott served 19, and Laura served 28 orders.
Can anyone help with this math equation please?
Help please! Thanks!
Find the length of the segment indicated.
A. 3.1
B. 3.9
C. 3.4
D. 3.8
Answer:
C
Step-by-step explanation:
using the theorem of Pythagoras
x = sqrt * 10.2^2 - 9.6^2 *
using the calculator
x = 3.4 units
rounded to 1 decimal place
Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election. Assume the probability that a given registered voter will vote in the presidential election is 63%. Approximate the probability using the normal distribution. Round your answer to four decimal places
Answer:
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
153 voters:
This means that [tex]n = 153[/tex]
Assume the probability that a given registered voter will vote in the presidential election is 63%.
This means that [tex]p = 0.63[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 153(0.63) = 96.39[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97[/tex]
Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.
Using continuity correction, this is: [tex]P(X \geq 88 - 0.5) = P(X \geq 87.5)[/tex], which is 1 subtracted by the p-value of Z when X = 87.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{87.5 - 96.39}{5.97}[/tex]
[tex]Z = -1.49[/tex]
[tex]Z = -1.49[/tex] has a p-value of 0.0681.
1 - 0.0681 = 0.9319
0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.
Use the substitution method to solve the system of equations. Choose the correct ordered pair. x + y = 3 y = 9 A. (–12, 9) B. (–6, 9) C. (6, 9) D. (12, 9)
B(-6,9)is the answer
have a great dayyyy.
the sum of √12 and √3 is
Step-by-step explanation:
You're going to break√12 into ✓4 and √3 because 4*3 = 12. Square rooting 4 will give you two, and now you can add since the argument of the roots are the same.
3+(-2) is_units from 3, in ___ the
direction.
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Answer:
2 unitsnegative (left) directionStep-by-step explanation:
-2 is 2 units in the negative direction (left on a number line). When that is added to 3, the result is 2 units from 3 in the negative direction.
If contribution margin is $70000, sales is $120000, and net income is $50000, then variable and fixed expenses are
Variable Fixed
a) $190000 $70000
b) $50000 $20000
c) $50000 $70000
d) $20000 $50000
Answer:
c) $50000 $70000
Step-by-step explanation:
!!!!!!!
slobs for x, pls help asap ! thanks
Answer:
Option D, there are no solutions
Answer:
[tex]-6x+14<-28[/tex]
[tex]-6x<-28-14[/tex]
Add,
[tex]-6x<-42[/tex]
Divide both sides by 6
[tex]\frac{6x}{6}>\frac{42}{6}[/tex]
[tex]x>7[/tex]
[tex]3x+28\leq 25[/tex]
Subtract both sides by 28
[tex]3x\le \:-3[/tex]
Now, divide both sides by 3
[tex]x\le \:-1[/tex]
Answer:- [tex]x\leq -1\: or \: x>7[/tex]
OAmalOHopeO
What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answer:
B.17
Step-by-step explanation:
B.17
B.17
B.17
B.17
• What is the constant term in the expression 3x + 11?
Answer:
11
Step-by-step explanation:
A constant term in an expression or equation contains no variables. In other words, it’s just number on its own. For example: f (x) = 2x2 + 3 (the constant term is 3). Other examples of constant terms: 5, -99, 1.2 and pi (π = 3.14…).
Answer: Constant = 11
Concept:
In an algebraic expression, there are three main kinds of terms:
Constants: an individual numberVariable: the unknown valueCoefficient: the number before a variableIf you are still confused, you may refer to the attachment below for a graphical explanation.
Solve:
Given expression: 3x + 11
As we know, the constant is defined as an individual number. Thus, as we can see from the given expression, 11 is the only number that is isolated and being an individual.
Hope this helps!! :)
Please let me know if you have any questions
find the length of the arc. round your answer to nearest tenth
41.9 mi
Step-by-step explanation:
First, we convert the angle from degree measure to radian measure:
[tex]\theta = 240°×\left(\dfrac{\pi}{180°}\right)= \dfrac{4\pi}{3}\:\text{rad}[/tex]
Using the definition of an arc length [tex]s[/tex]
[tex]s = r\theta[/tex]
[tex]\:\:\:\:=(10\:\text{mi})\left(\dfrac{4\pi}{3}\:\text{rad}\right)[/tex]
[tex]\:\:\:\:= 41.9\:\text{mi}[/tex]
solve the following system by any method
8x+9y=-5
-8x-9y=5
Here is your solution for the problem.
Thanks
A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%. The test statistic is a.1.44. b.1.25. c..95. d..80.
Answer:
a. 1.44
Step-by-step explanation:
We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 40%.
At the null hypothesis, it is tested if the proportion is of at most 40%, that is:
[tex]H_0: p \leq 0.4[/tex]
At the alternative hypothesis, it is tested if the proportion is of more than 40%, that is:
[tex]H_1: p > 0.4[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.4 is tested at the null hypothesis:
This means that [tex]p = 0.4, \sigma = \sqrt{0.4*0.6}[/tex]
A random sample of 200 people was taken. 90 of the people in the sample favored Candidate A.
This means that:
[tex]n = 200, X = \frac{90}{200} = 0.45[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.45 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{200}}}[/tex]
[tex]z = 1.44[/tex]
Thus the correct answer is given by option a.
PLEASE HELPP ASAP!!
5.(06.02 MC)
Line BC contains points B (4, -5) and C (3, 2). Line DE contains points D (2,0) and E (9, 1). Lines BC and DE are (1 point)
parallel
perpendicular
neither
Answer:
Answer: Option A.
Step-by-step explanation:
Hey there!
Given; The Line BC contains points B (4, -5) and C (3, 2).
And the Line DE contains points D (2,0) and E (9, 1)
Note: Use double point formula for finding the equation and then find slopes of both then put the condition for perpendicular lines and parallel lines.
From line BC;
The points are B (4, -5) and C (3, 2).
Using double point formula;
[tex](y - y1) = \frac{y2 - y1}{x2 - x1}(x - x1) [/tex]
Keep all the value;
[tex](y + 5) = \frac{2 + 5}{3 - 4} (x - 4)[/tex]
Simplify it;
[tex]y + 5 = - 7x + 28[/tex]
Therefore, the equation is y = -7x+23........(I)And slope(m1) is -7 {comparing the equation (I) with y=Mx+c}
Again;
The points D (2,0) and E (9, 1)
Using double point formula;
[tex](y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)[/tex]
Keep all values;
[tex](y - 0) = \frac{9 - 2}{1 - 2} (x - 2)[/tex]
[tex]y = - 7x + 14[/tex]
Therefore, the equation is y = -7x+14......(ii)And the slope (m2) is -7. {comparing the equation (ii) with y= mx+c}
Check:
For parallel lines:
m1= m2
-7 = -7 (true)
Therefore, the lines are parallel.
Hope it helps!
Which of the following situations describe the expression 3 / (4/5)?
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW
Answer:
Choice D
Step-by-step explanation:
3 ÷ 4/5
We need to have 3 of something and divide it into 4/5
This eliminates choices B and C because those have 4/5 of something
Choice A is giving away which is subtracting
Choice D is 3 lbs divide into 4/5 lb groups
From a cuboidal cardboard box of dimensions 80cm×40cm×15cm,6 circles of radius 7 cm were cut from the front face.Find the surface area of remaining box.
Answer:
9076 cm²
Hope my answer helped you
find the measure of y
Answer:
Step-by-step explanation:
x = 90°-47° = 43°
y = x = 43°
Find the value of the trigonometric ratio. sin A
Answer:
sin A = 4/5
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin A = opp / hyp
sin A = 24/ 30
Dividing the top and bottom by 6
sin A = 4/5
sinØ=Perpendicular/Hypotenuse
sinA=BC/ACsinA=24/30sinA=4/520 POINTS PLEASE HELP
Answer:
2x^3+5x^2+2x
Step-by-step explanation:
x+2 x and 2x+1
The volume of a rectangular prism is solved by multiplying the height, width, and base. So to solve for the volume, it is (x^2+2x)*(2x+1) [just multiplies x+2 and x] 2x^3+5x^2+2x
Step-by-step explanation:
[tex]thank \: you[/tex]
What is the value of the logarithm below? (Round your answer to two decimal
places.)
log4 12
Answer:
1.68
Step-by-step explanation:
log(4)12=log(48)
log(48)=1.6812... or rounded, 1.68
simplify each expression below. Compare your answers with your classmates answers.
Answer:
1)17
2)33
3)9
4)27
5)1252
6)50
Step-by-step explanation:
Find perpendicular,hypotenuse and base
Step-by-step explanation:
In right angled triangle ABC,
Taking alpha as reference angle,
By pythagoras theorem,
p=BC,h=AB,b=AC
Taking thita as reference angle,
p=AC,h=AB,b=BC
Keep smiling and hope u are satisfied with my answer.Have a good day :)
For the following exercise, calculate the desired dose. Then calculate the amount to administer. Ordered: Pergolide mesylate 100 mcg PO tid On hand: Pergolide mesylate 0.05 mg tablets what is the Desired dose?
Answer:
was assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarismwas assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarism
Step-by-step explanation:
was assigned with this problem (the reference text is attached):
Which of the following, if included in a student's paper, would NOT be an example of plagiarism?
1. In the game of baseball, which is rather boring, the batter stands on home base (Hughes 1).
2. Baseball is rather surprisingly known as "America's Favorite Pastime."
3. Baseball is "a rather boring sport played between two teams of nine players" (Hughes 1).
4. All of these are plagiarism.
The answer tells that only the third choice is NOT a plagiarism. My question is, why is the first choice a plagiarism
Suppose a restaurant offers the following prix fixe menu:
Main course: prime rib, steak, chicken, filet of sole, shrimp
Side dish: soup, salad, crab cakes
Dessert: cheesecake, chocolate chip delight, ice cream.
Beverage: coffee, tea, milk
In how many ways can someone order a meal consisting of one choice from each category?
There are 135 ways someone can order a meal consisting of one choice from each category.
Permutation and combinationTo find the total number of ways someone can order a meal consisting of one choice from each category, we need to multiply the number of options in each category:
Number of options for the main course = 5
Number of options for the side dish = 3
Number of options for the dessert = 3
Number of options for the beverage = 3
Using the multiplication principle, the total number of ways to order a meal is:
5 x 3 x 3 x 3 = 135
Therefore, there are 135 ways someone can order a meal consisting of one choice from each category.
More on permutation can be found here: https://brainly.com/question/30557698
#SPJ1
Megan and Suzanne each have a plant. They track the growth of their plants for four weeks.
Whose plant grew at a faster rate, and what was the rate?
Suzanne’s at 2 inches per week
Suzanne’s at 1.5 inches per week
Megan’s at 3 inches per week
Megan’s at 2.5 inches per week
Answer:
Megan’s at 2.5 inches per week
Find the inequality represented by the graph.
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Answer:
y < 3x -4
Step-by-step explanation:
The boundary line has a slope (rise/run) of 3/1 = 3. It has a y-intercept of -4. The shaded area is below the line and the solution does not include the line. The relevant inequality can be written ...
y < 3x -4
16. How many different words can be formed with the letters of the word 'RAJARAM'? In how many of
these,
(i) have two R and J always together?
(ii) being with Rand end with J?