Answer:
The common ratio of the progression is 3/4Explanation:
A geometric progression is a sequence of terms in which the consecutive terms have a constant ratio; thus, each term is equal to the previous one multiplied by a constant value:
[tex]First\ term=a_1\\\\ Second\ term=a_2=a_1\times r\\\\ Third\ term=a_3=a_2\times r=a_1\times r^2\\\\n_{th}\ term=a_n=a_{n-1}\times r=a_1\times r^{n-1}[/tex]
A infinite geometric progression may have a finite sum. When the absolute value of the ratio is less than 1, the sum of the infinite geometric progression has a finite value equal to:
[tex]S_{\infty}=\frac{a_1}{1-r}[/tex]Thus, the information given translates to:
[tex]a_1=5\\ \\ S_{\infty}=20=\frac{5}{1-r}[/tex]
Now you can solve for the constant ratio, r:
[tex]1-r=\frac{5}{20}\\ \\ r=1-\frac{5}{20}\\ \\ r=\frac{15}{20}\\ \\ r=3/4[/tex]
The common ratio of the infinite geometric progression with the first term of 5 and a sum of 20 is 0.75.
The question pertains to finding the common ratio of an infinite geometric progression (GP) when given the first term and the sum of all its terms. The first term is known as 5, and the sum of the infinite GP is 20. To find the common ratio, we use the formula for the sum of an infinite GP, which is S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.
Plugging in the given values, we have:
20 = 5 / (1 - r)
We can solve for r by multiplying both sides by (1 - r) and then simplifying:
20(1 - r) = 5
20 - 20r = 5
15 = 20r
r = 0.75
Thus, the common ratio of the infinite GP with a first term of 5 and a sum of 20 is 0.75.
Can the positive integer p be expressed as the product of two integers, each of which is greater than 1?
Answer:
maybe
Step-by-step explanation:
If p is prime, then answer is NO. If p is not prime, the answer is YES.
__
Some positive integers are prime; some are not. We need to know more about p before we can give a better answer than this.
Unless otherwise posted, what is the speed limit for cars in a residential area?
Answer:
In general if speed limit is not posted it will be 25 mph in residential area
Step-by-step explanation:
When speed limit is not posted then it is 25 mph in residential area or school zones
But its also depend on the density of population in that area is density is very low then speed limit can go up to 35 mph and if density of population is high then speed limit will be restricted up to 25 mph
So in general if speed limit is not posted it will be 25 mph in residential area
A dealer sold 200 pairs of gloves. Some were sold at $6 per pair and the remainder were sold at $11 per pair. Total receipts from this sale were $1,600. How many pairs of gloves did he sell at $6 each
The dealer sold 120 pairs of gloves at $6 each.
Explanation:To find out how many pairs of gloves were sold at $6 each, we can set up a system of equations based on the given information.
Let's assume x represents the number of pairs of gloves sold at $6 each.
Since the dealer sold a total of 200 pairs, the number of pairs sold at $11 each would be 200 - x.
We can now set up the equation: 6x + 11(200 - x) = 1600.
Simplifying the equation, we get 6x + 2200 - 11x = 1600.
Combining like terms, we have -5x + 2200 = 1600.
Now, we can solve for x: -5x = 1600 - 2200.
-5x = -600.
x = -600 / -5 = 120.
Therefore, the dealer sold
120 pairs
of gloves at $6 each.
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So, the dealer sold 120 pairs of gloves at $6 each.
Let's denote the number of pairs of gloves sold at $6 per pair as [tex]\(x\)[/tex], and the number of pairs sold at $11 per pair as [tex]\(200 - x\)[/tex] (since the total number of pairs is 200).
The total receipts from selling [tex]\(x\)[/tex] pairs at $6 each and [tex]\(200 - x\)[/tex] pairs at $11 each is given by the equation:
[tex]\[ 6x + 11(200 - x) = 1600 \][/tex]
Now, let's solve for [tex]\(x\)[/tex]:
[tex]\[ 6x + 2200 - 11x = 1600 \][/tex]
Combine like terms:
[tex]\[ -5x + 2200 = 1600 \][/tex]
Subtract 2200 from both sides:
[tex]\[ -5x = -600 \][/tex]
Divide by -5:
[tex]\[ x = 120 \][/tex]
What is the chance that heads will come up more than 55 times in 100 flips of a fair coin?
Answer:
Step-by-step explanation:
50
Please help me with this problem
Answer:
domain: [0, 7]range: [-2, 4]is a function? YESStep-by-step explanation:
The domain is the horizontal extent, which is from x=0 to x=7.
The range is the vertical extent, which is from y=-2 to y=4.
The curve passes the vertical line test, so the relation IS A FUNCTION.
_____
The vertical line test asks whether any vertical line intersects the curve at more than one point. If so, the relation is NOT a function.
A ladder leans against a building. The foot of the ladder is 2 feet from the building and reaches to a point 7 feet high on the building. What is the measure of the angle formed by the ladder and the building? Enter your answer, rounded to the nearest degree, in the box. °
Answer:
74
Step-by-step explanation:
tan?=7/2
tan^-1(7/2)=?
?=74
Answer:
16°
Step-by-step explanation:
A ladder leans against a building . The foot of the ladder is 2 feet from the building and reaches to a point 7 feet high on the building . The measured angle formed by the ladder and building can be computed below.
The illustration forms a right angle triangle. Two sides are given and we are told to find an angle
Distance form the foot of the ladder to the building = 2 feet
The ladder reaches a point in the building which is the height of the building the ladder head started from = 7 feet
Using SOHCAHTOA principle
tan ∅ = opposite /adjacent
where
opposite = 2 ft
adjacent = 7 ft
∅ = angle formed by the ladder and the building
tan ∅ = 2/7
∅ = tan⁻¹ 2/7
∅ = 15.9453959
∅ ≈ 16°
A dress is on sale for d dollars. The regular price is 3 times as much.
Janine has enough money to buy 2 dresses at the regular price.
How many dresses can Janine buy at the sale price?
Answer:
6 dresses
Step-by-step explanation:
Given: sales price is $d
Regular price is 3 times of sales price
Janine has money to buy 2 dresses at regular price.
Now, finding the number of dresses Janine can buy at the sales price, if sale price is d
Regular price= [tex]3\times d= 3d[/tex]
Janine has total money= [tex]3d\times 2= 6d[/tex] (∵ regular price is 3d)
∴ Number of dresses bought by Janine= [tex]\frac{Total\ money}{sale\ price\ of\ one\ dress}[/tex]
⇒ Number of dresses bought by Janine= [tex]\frac{6d}{d} = 6\ dresses[/tex]
∴ Number of dresses bought by Janine is 6.
Prove that if the real-valued function f is strictly increasing, then f is oneto-one.
Answer:
See proof below
Step-by-step explanation:
Let x,y be arbitrary real numbers. We want to prove that if x≠y then f(x)≠f(y) (this is the definition of 1-1).
If x≠y, we can assume, without loss of generality that x<y using the trichotomy law of real numbers (without loss of generality means that the argument in this proof is the same if we assume y<x).
Because f is strictly increasing, x<y implies that f(x)<f(y). Therefore f(x)≠f(y) because of the trichotomy law, and hence f is one-to-one.
What are the equations of the asymptotes of the graph of the function f (x) = StartFraction 3 x squared minus 2 x minus 1 Over x squared + 3 x minus 10 EndFraction?
x = –5, x = 2 and y = 3
x = –2, x = 5 and y = 3
x = 3, y = –5, and y = 2
x = 3, y = –2, and y = 5
Answer:
As x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].
Therefore, x = -5, x = 2 and y = 3 is the right option.
Step-by-step explanation:
As the given function is
[tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex]
Determining Vertical Asymptote:
The line x = L is a vertical asymptote of the function if if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
Such as
[tex]x^{2} +3x -10 = 0[/tex]
[tex](x-2)(x-5)=0[/tex]
[tex]x=2[/tex] [tex]or[/tex] [tex]x=-5[/tex]
x=−5 , check:
[tex]\lim_{x \to -5^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]
Since, the limit is infinite, then x = -5 is a vertical asymptote.
x = 2, check:
[tex]\lim_{x \to 2^{+}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = -\infty[/tex]
Since the limit is infinite, then x = 2 is a vertical asymptote.
Determining Horizontal Asymptote:
Line y=L is a horizontal asymptote of the function y = f(x), if either
[tex]\lim_{x \to \infty^{}}{f(x)=L}[/tex] or [tex]\lim_{x \to -\infty^{}}{f(x)=L},[/tex] and L is finite.
Calculating the limits:
[tex]\lim_{x \to \infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]
[tex]\lim_{x \to -\infty^{}}({3x^{2}-2x-11 \over x^{2}+3x-10 }) = 3[/tex]
Thus, the horizontal asymptote is y=3.
So, x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function [tex]f(x)=\frac{3x^{2} -2x - 1}{x^{2}+3x-10 }[/tex].
Therefore, x = -5, x = 2 and y = 3 is the right option.
Keywords: asymptote, vertical asymptote, horizontal asymptote, equation
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I believe the answer is a.
The magazine Sports Illustrated asked a random sample of 750 Division I college athletes, "Do you believe performance-enhancing drugs are a problem in college sports?" Suppose that 30% of all Division I athletes think that these drugs are a problem. Let p^ be the sample proportion who say that these drugs are a problem.
Which of the following are the mean and standard deviation of the sampling distribution of the sample proportion p^?
a) Mean = 0.30, SD = 0.017
b) Mean = 0.30, SD = 0.55
c) Mean = 0.30, SD = 0.0003
d) Mean = 225, SD = 12.5
e) Mean = 225, SD = 157.5
Answer:
a) Mean = 0.30, SD = 0.017
Step-by-step explanation:
The mean and sampling distribution of the sample proportion can be found using the equations
Mean= p
[tex]SD=\sqrt{\frac{p*(1-p)}{n} }[/tex]
where
n is the sample size (750) p is the sample proportion of all Division I athletes think that these drugs are a problem (0.30 or 30%)Using these information:
Mean = 0.30
[tex]SD=\sqrt{\frac{0.30*0.70}{750} }[/tex] ≈ 0.017
Final answer:
The mean of the sampling distribution of the sample proportion is 0.30, and the standard deviation is found to be approximately 0.017. Therefore, the correct answer is Mean = 0.30, SD = 0.017.
Explanation:
To determine the mean and standard deviation of the sampling distribution of the sample proportion p, we use the formulas related to binomial distributions, since the survey outcome (believe that performance-enhancing drugs are a problem or not) follows a binomial distribution. The mean of the sampling distribution of the proportion is simply the population proportion, which is given as 0.30.
The standard deviation (SD) of the sampling distribution of p can be calculated using the formula SD = √[p(1-p)/n], where p is the population proportion and n is the sample size. In this case:
SD = √[0.30(1-0.30)/750] = √[0.21/750] = √[0.00028] ≈ 0.0167
Thus, the correct answer is a) Mean = 0.30, SD = 0.017
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles. Complete parts (a) through (c) below.
The sub-questions for this question are:
a) construct a binomial distribution using n=6 and p=0.34
b) graph the binomial distribution using a histogram and describe it's shape
c) what values of the random variable would you consider unusual? Explain your reasoning.
Answer:
a)
P(X=0) =0.0827
P(X=1) = 0.255
P(X=2) = 0.329
P(X=3) = 0.226
P(X=4) = 0.087
P(X=5) = 0.018
P(X=6) = 0.0015
b) graph D
c) x=5 and x=6
Step-by-step explanation:
a)
Formula for binomial distribution:
nCx(p^x)(q^(n-x))
Number of sample, n = 6
probability of success, p = 0.34
probability of failure, q = 1-p = 0.66
P(X=0) = 6C0(0.34^0)(0.66^6)
= 1*1*0.0827 = 0.0827
P(X=1) = 6C1(0.34^1)(0.66^5)
= 6*0.34*0.1252 = 0.255
P(X=2) = 6C2(0.34^2)(0.66^4)
= 15*0.1156*0.1897 = 0.329
P(X=3) = 6C3(0.34^3)(0.66^3)
= 20*0.0113 = 0.226
P(X=4) = 6C4(0.34^4)(0.66^2)
= 15*0.0058 = 0.087
P(X=5) = 6C5(0.34^5)(0.66^1)
= 6*0.003 = 0.018
P(X=6) = 6C6(0.34^6)(0.66^0)
= 1*0.0015 = 0.0015
b) the shape of the graph is the graph shape. Referring to the attachment, the correct graph is D
c) the unusual values would be x=6 and x=5, because those values are too small and lower than 0.05
Susie, Meg, and Jane drive together to visit their grandma. Audit drive for 65 miles,and Meg drives 2 times as far as Susie. Then Jane drives twice as far as Susie and Meg combined. How far did Jane drive
Answer:
Jane has drive 390 miles to visit Grandma.
Step-by-step explanation:
Given:
Number of miles Susie drive = 65 miles
Meg drives 2 times as far as Susie.
It means Number of miles Meg drive is equal to twice the number of miles driven my Susie.
Framing equation we get;
Number of miles Meg drive = 2 × Number of miles Susie drive = [tex]65 \times 2=130\ miles[/tex]
Also Given:
Jane drives twice as far as Susie and Meg combined.
Number of Miles Driven by Jane is equal to twice the sum of Number of miles Susie drive and Number of miles Meg drive.
Framing equation we get;
Number of miles Meg drive = 2 × (Number of miles Susie drive + Number of miles Meg drive) = [tex]2\times (65+130) = 2\times 195 = 390\ miles[/tex]
Hence Jane has drive 390 miles to visit Grandma.
For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.
Answer: Samantha's Recipe:
Ratio of lemonade = 2 1/2 : 6
Caden's Recipe:
Ratio of lemonade = 15 : 32
Step-by-step explanation:
Samantha's Recipe
3 1/2 parts cranapple juice
2 1/2 parts lemonade
Caden's Recipe
4 1/4 parts cranapple juice
3 3/4 parts lemonade
For each recipe, write a ratio that compares the number of parts of lemonade to the total number of parts.
Solution:
For Samantha's Recipe:
Total number of parts = cranapple juice parts + lemonade parts = 3.5 + 2.5 = 6.0
Ratio of lemonade to total number of parts = (2.5)/(6.0) = 2 1/2 : 6
For Caden's Recipe:
Total number of parts = cranapple juice parts + lemonade parts =(17/4)+(15/4) = (32/4) = 8
Therefore, Ratio of lemonade to total number of parts = (15/4) / (8) =(15)/(32) = 15:32
Nigel is planning his training schedule for a marathon over a 4-day period. He is uncertain how many miles he will run on two days. One expression for the total miles he will run is 12+y+17+z. Use the Commutative Property to write an equivalent expression.
Answer:
[tex]12+17+y+z[/tex] or [tex]29+y+z[/tex].
Step-by-step explanation:
We have been given that Nigel is planning his training schedule for a marathon over a 4-day period. He is uncertain how many miles he will run on two days. One expression for the total miles he will run is [tex]12+y+17+z[/tex].
The Commutative Property of Addition states that we can add numbers in any order. For example a and b be two numbers.
According to Commutative Property of Addition [tex]a+b=b+a[/tex].
Similarly, we can write an equivalent expression to our given expression as:
[tex]12+17+y+z[/tex]
We can simplify our expression as:
[tex]29+y+z[/tex].
Therefore, our required expression would be [tex]12+17+y+z[/tex] or [tex]29+y+z[/tex].
A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?A. 32
B. 37
C. 40
D. 43
E. 50
Answer:
Option D.
Step-by-step explanation:
It is given that a set of 15 different integers has a median of 25 and a range of 25.
Total number of integers is 15 which is an odd number.
[tex](\frac{n+1}{2}) th=(\frac{15+1}{2}) th=8th[/tex]
8th integers is median. It means 8th integers is 25.
7 different integers before 25 are 18, 19, 20, 21, 22, 23, 24.
It means the greatest possible minimum value is 18.
Range = Maximum - Minimum
25 = Maximum - 18
Add 18 on both sides.
25 +18 = Maximum
43 = Maximum
The greatest possible integer in the set is 43.
Therefore, the correct option is D.
Answer:
D. 43
Step-by-step explanation:
We have been given that a set of 15 different integers has a median of 25 and a range of 25.
Since each data point is different, so we can represent our data points as:
[tex]N_1,N_2,N_3,N_4,N_5,N_6,N_7,N_8, N_9,N_{10},N_{11},N_{12},N_{13},N_{14}, N_{15}[/tex]
Since there are 15 data points, this means that median will be 8th data point.
We have been given that median is 25, so [tex]n_8=25[/tex].
Since each data point is different, so 7 data points less than 25 would be:
18, 19, 20, 21, 22, 23, 24.
We know that range is the difference between upper value and lower value.
[tex]\text{Range}=\text{Upper value}-\text{Lower value}[/tex]
[tex]\text{Range}+\text{Lower value}=\text{Upper value}[/tex]
Upon substituting our given values, we will get:
[tex]25+18=\text{Upper value}[/tex]
[tex]43=\text{Upper value}[/tex]
Therefore, the greatest possible integer in this set could be 43 and option D is the correct choice.
Andre sometimes mows on the weekend to make extra money. Two weeks ago, he mowed a neighbor's lawn for 1/2 hour and earned $10. Last week, he mowed his uncles lawn for 3/2 hours and earned $30. This week, he mowed the lawn of a community center for 2 hours and earned $30. Which job paid better than others?
Answer:
Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.
Step-by-step explanation:
Given:
Andre mowed a neighbor's lawn for 1/2 hour and earned $10.
For 1/2 hour = $10
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{10}{\frac{1}{2}} = \frac{10\times2}{1} = \$20[/tex]
Hence Andre hourly rate to mowed neighbor's lawn is $20.
Also Given:
Andre mowed a Uncle's lawn for 3/2 hour and earned $30.
For 3/2 hour = $30
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{30}{\frac{3}{2}} = \frac{30\times2}{3} = \$20[/tex]
Hence Andre hourly rate to mowed Uncle's lawn is $20.
Also Given:
Andre mowed Community center's lawn for 2 hour and earned $30.
For 2 hour = $30
So for 1 hour = Money earned in 1 hour.
By using Unitary method we get;
Money earned in 1 hour = [tex]\frac{30}{2}=\$15[/tex]
Hence Andre hourly rate to mowed Community Center's lawn is $15.
Now Since we can see that when he mowed neighbor and uncle's lawn he was paid at rate of $20 and when he mowed Community Center's lawn he got paid at rate of $15.
Hence Andre got better paid when he mowed for neighbor's and uncle's lawn which is $20/hr than Community center's lawn which is $15/hr.
Miguel spends $35 a day for 4 days. He earns $21 a day for 5 days. Does Miguel end up with more or less money than he started with? By how much?
a. Miguel ends up with $35 more than he started with.
b. Miguel ends up with $35 less than he started with.
c. Miguel ends up with $91 more than he started with.
d. Miguel ends up with $91 less than he started with.
Answer:
b. Miguel ends up with $35 less than he started with
Step-by-step explanation:
He spends $35 × 4 = $140.
He earns $21 × 5 = $105.
His net increase is $105 -140 = -$35.
Miguel ends up with $35 less than he started with.
Graph the system of inequalities presented here then use your graph to answer the following questions:
y > 5x + 5
y is greater than negative 1 over 2 times x plus 1
Part A: Graph both equations and use 2 different colors to shade. Use a 3rd color to show the solution area. Describe the graph of the system, including shading and the types of lines graphed (dotted or solid lines). Provide a description of the solution area.
Part B: Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically.
Please help. I'm so sick today that I can't think and just need to finish my homework
Answer:
Part A) The graph in the attached figure (see the explanation)
Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)
Step-by-step explanation:
Part 1) Graph the system of inequalities
we have
[tex]y> 5x+5[/tex] ----> inequality A
The solution of the inequality A is the shaded area above the dashed line [tex]y=5x+5[/tex]
The slope pf the dashed line A is positive m=5
The y-intercept of the dashed line A is (0,5)
The x-intercept of the dashed line A is (-1,0)
[tex]y>-\frac{1}{2}x+1[/tex] ----> inequality B
The solution of the inequality B is the shaded area above the dashed line [tex]y=-\frac{1}{2}x+1[/tex]
The slope pf the dashed line B is negative m=-1/2
The y-intercept of the dashed line B is (0,1)
The x-intercept of the dashed line B is (2,0)
The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B
using a graphing tool
see the attached figure
Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
substitute the value of x and the value of y in each inequality
For x=-2, y=5
Verify inequality A
[tex]5>5(-2)+5[/tex]
[tex]5>-5[/tex] ---> is true
so
The ordered pair satisfy inequality A
Verify inequality B
[tex]5>-\frac{1}{2}(-2)+1[/tex]
[tex]5>2[/tex] ---> is true
so
The ordered pair satisfy inequality B
therefore
The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)
Find the slope of the line
A) 4
B) 1
C) -1
D) -4
Answer:
(-1,3), (0,-1)
(-1-3)/(0+1)= -4/1= -4
the answer is d
Answer:
D) -4Step-by-step explanation:
[tex]\bold{METHOD\ 1:}\\\\\text{look at the picture}\ \#1\\\\\text{The fomula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{Form the graph wi hate points:}\\\\(-1, 3)\ \text{and}\ (0, -1).\\\\\text{Substitute:}\\\\m=\dfrac{-1-3}{0-(-1)}=\dfrac{-4}{1}=-4[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{look at the picture}\ \#2\\\\slope=\dfrac{rise}{run}\\\\rise=-4\\run=1\\\\slope=\dfrac{-4}{1}=-4[/tex]
As Jupiter revolves around the sun, it travels at a speed of approximately 8 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Jupiter travel in 5 minutes? Do not round your answers
Answer:
The answer to your question is
a) [tex]\frac{480 mi}{min}[/tex]
b) distance = 2400 mi
Step-by-step explanation:
a) 8 mi/s convert to mi/min
[tex]\frac{8 mi}{s} x \frac{60 s}{1 min} = \frac{8 x 60 mi }{min} = \frac{480 mi}{min}[/tex]
b) [tex]speed = \frac{distance}{time}[/tex]
distance = speed x time
distance = [tex]\frac{480 mi}{min} x 5 min[/tex]
distance = 2400 mi
will give brainliest for the CORRECT answer and 80 points please answer quickly
the weights (in ounces) of 14 different apples are shown below.
4.3 6.1 4.5 5.2 6.8 4.3 6.1 5.6 4.7 5.2 4.3 5.6 6.0 4.0
the measure of center is found to be 4.3 oz. which measure of center is used?
a:midrange
b:mean
c;median
d:mode
Answer: Median
Step-by-step explanation:
In a plane, points P and Q are 20 inches apart. If point R is randomly chosen from all the points in the plane that are 20 inches from P, what is the probability that R is closer to P than it is to Q?
Answer:
[tex]P = \frac{2}{3}[/tex]
Step-by-step explanation:
All the points in the plane that are 20 inches from P constituing a circle with center in P and with radius 20 inch
We need find the angle in this circle by which the point R is closer to P than it is to Q. The limit situation occurs when the distances from P to R and from R to Q are equals and have the value 20 inches. In this situation the points P, R y Q form a equilater triangle with angles of value 60°.
Thus, the point R is closer to P than it is to Q in 240° of the circle, except 60° above of the line PQ and 60° below the line PQ.
Then the probability is
[tex]P= \frac{240}{360} = \frac{2}{3}[/tex]
If five times the smaller of two numbers is subtracted from twice the larger the result is 16 if the larger is increased by three times the smaller the result is 63 by the numbers
Answer:
Smaller Number = 10
Larger Number = 33
Step-by-step explanation:
Let the smaller number be "x" and the larger number be "y"
5 TIMES smaller is SUBTRACTED from TWICE larger, the result is 16, we can write:
2y - 5x = 16
and
Larger increased by 3 TIMES SMALLER, result is 63, so we can write:
y + 3x = 63
We can write this in terms of x, as:
y = 63 - 3x
Now we put this in equation 1 and solve for x first:
2y - 5x = 16
[tex]2(63 - 3x) - 5x = 16\\126-6x-5x=16\\11x=110\\x=10[/tex]
Now,
y = 63 - 3x
y = 63 - 3(10)
y = 63 - 30
y = 33
Smaller Number = 10
Larger Number = 33
What is the average rate of change of the function
f(x)=480(0.3)x from x = 1 to x = 5?
The rate of change of the function is -35.7
Step-by-step explanation:
The rate of change of a function [tex]f(x)[/tex] between two points [tex]x_1[/tex] and [tex]x_2[/tex] is given by the ratio between the increment of the function itself and the increment of the x-variable:
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
The function of this problem is
[tex]f(x)=480 (0.3)^x[/tex]
For [tex]x_1=1[/tex], the value of the function is
[tex]f(1)=480(0.3)^1=144[/tex]
For [tex]x_2=5[/tex], the value of the function is
[tex]f(5)=480(0.3)^5=1.2[/tex]
Therefore, the rate of change of the function is
[tex]m=\frac{f(5)-f(1)}{5-1}=\frac{1.2-144}{5-1}=-35.7[/tex]
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John is planning to go to graduate school in a program that will take three years. John wants to have available $10,000 available each year for his school and living expenses.
If he earns 6% on his investments, how much must be deposited at the start of his studies for him to withdraw $10,000 a year for three years?
a) $10,000
b) $29,100
c) $30,000
d) $18,390
Answer:
d) $18,390
Step-by-step explanation:
Let X be the amount of money he deposited on the first year of his study.
The question says that he earns 6% on his investment without specifying the investment return time. However, normally it's annually, so let's assume his earning is 6% per annum.
Given that he did not make any withdrawal until the end of the first year, in 2nd year, he'll get the earning of his investment minus 10,000 to pay for his first year study
2nd year Y = X(1.06 ) - 10000
The same goes with 3rd year
3rd year Z = Y(1.06) - 10000
In worst case scenario, let's assume all of the money is used up at the end of third year
Z = 0
Y(1.06) - 10000 = 0
Substitute the first year into the equation:
Y(1.06) - 10000 = 0
(X(1.06)-10000)1.06 -10000 = 0
(1.06^2)X -1.06(10000) - 10000 = 0
X = (10000+10600)/1.06^2 = 18333.92
So the minimum deposit he needs to make to survive for the whole 3 years is $18333.92.
From the answer selection, the nearest value is d) $18,390
Melanie bought 4 large gifts and 2 small gifts. Mary bought 1 large gift and 20 small gifts. Each small gift costs $10. They both spent the same amount of money. What's the price of one large gift?
Answer:the price of one large gift is $60
Step-by-step explanation:
Let x represent the cost of one large gift.
Melanie bought 4 large gifts and 2 small gifts. Since each small gift costs $10, it means that the total amount that Melanie spent is
4x + 2×10 = 4x + 20
Mary bought 1 large gift and 20 small gifts. It means that the total amount that Mary spent is
x + 20×10 = x + 200
They both spent the same amount of money. This means that
4x + 20 = x + 200
4x - x = 200 - 20
3x = 180
x = 60
To find the price of one large gift, we compare the total amount spent by Melanie and Mary. By setting up an equation and solving for the price of one large gift, we find that it is $60.
Explanation:To find the price of one large gift, we need to calculate the total amount spent on gifts by both Melanie and Mary and divide it by the total number of large gifts they bought. Melanie bought 4 large gifts and 2 small gifts, while Mary bought 1 large gift and 20 small gifts. Let's assume the price of one large gift is x.
The total amount spent by Melanie can be calculated as (4x + 2*10), since each small gift costs $10. The total amount spent by Mary can be calculated as (x + 20*10). Since both of them spent the same amount of money, we can set up the equation: 4x + 2*10 = x + 20*10.
Simplifying the equation, we get 4x + 20 = x + 200. Subtracting x from both sides, we get 3x + 20 = 200. Subtracting 20 from both sides, we get 3x = 180. Dividing both sides by 3, we find that x = 60. Therefore, the price of one large gift is $60.
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The amount of money earned on a job is directly proportional to the number of hours worked. If 70.00 is earned in 5 hours, how much money is earned in 22 hours of work?
Answer:$308.44
Step-by-step explanation:
$70.00/5= $14.02 an hour
14.02*22 = $308.44
Amount of money earned in 22 hour is 308
Given that;Amount of money earned in 5 hour = 70
Find:Amount of money earned in 22 hour
Computation:Amount of money earned in 22 hour = 22[70/5]
Amount of money earned in 22 hour = 22[14]
Amount of money earned in 22 hour = 308
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Simplify the polynomial
Answer:
[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to simplify the Polynomial.}[/tex]
[tex]\large\underline{\textsf{What is a Polynomial?}}[/tex]
[tex]\textsf{A Polynomial is an \underline{expression} that is made up of 1 or more terms.}[/tex]
[tex]\textsf{Terms can be a single whole number, variables, or a combination.}[/tex]
[tex]\large\underline{\textsf{How to Simplify a Polynomial?}}[/tex]
[tex]\textsf{There are a few ways to simplify a Polynomial. Let's identify them.}[/tex]
[tex]\textsf{A way to simplify a polynomial is by using the Distributive Property.}[/tex]
[tex]\textsf{Another way is to combine like terms.}[/tex]
[tex]\textsf{For this problem, we will have to do both!}[/tex]
[tex]\large\underline{\textsf{What is the Distributive Property?}}[/tex]
[tex]\textsf{Distributive Property is a property that allows us to distribute a number left to a set}[/tex]
[tex]\textsf{of parentheses inside the values of the parentheses.}[/tex]
[tex]\underline{\textsf{How the Distributive Property works;}}[/tex]
[tex]\textsf{Example;} \tt -2(x+y)[/tex]
[tex]\textsf{-2 would multiply with x and y.}[/tex]
[tex]\mathtt{ -2(x+y)=\boxed{-2x-2y}}[/tex]
[tex]\large\underline{\textsf{What is Combining Like Terms?}}[/tex]
[tex]\textsf{Combining Like Terms is a simple way to simplify an expression by adding/subtracting}[/tex]
[tex]\textsf{like terms. This helps to make the expression much simpler.}[/tex]
[tex]\textsf{Now, we should know how to simplify the given polynomial.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Begin by using the Distributive Property on the left side of the Polynomial.}[/tex]
[tex]\textsf{Afterwards, Combine Like Terms.}[/tex]
[tex]\large\underline{\textsf{Simplifying;}}[/tex]
[tex]\tt -(5j^{2}+2j-7)-(3j+2)[/tex]
[tex]\textsf{The negative sign on the left side of the parentheses is the same as -1. Turn terms}[/tex]
[tex]\textsf{into their opposite value.}[/tex]
[tex]\tt -(5j^{2}+2j-7) \rightarrow (-1 \times 5j^{2})+(-1\times2j)-(-1\times-7)[/tex]
[tex]\tt -(3j+2) \rightarrow (-1 \times3j) + (-1 \times 2)[/tex]
[tex]\underline{\textsf{After Simplifying;}}[/tex]
[tex]\tt -5j^{2}-2j+7-3j-2[/tex]
[tex]\underline{\textsf{Combine All Like Terms;}}[/tex]
[tex]\tt -5j^{2}\boxed{-2j}+7\boxed{-3j}-2[/tex]
[tex]\tt -5j^{2}-5j\boxed{+7}\boxed{-2}[/tex]
[tex]\large\tt\boxed{D. \ \tt -5j^{2}-5j+5}[/tex]
5. Reggie picked 3 3/4 quarts of blueberries and 4 1/4 quarts of raspberries at a fruit farm. How many total quarts of berries did he pick? Show your work or explain your reasoning.
Answer:
Reggie picked total 8 quarts of berries.
Step-by-step explanation:
Given:
Amount of Blueberries picked by Reggie = [tex]3\frac{3}{4} [/tex] quarts
[tex]3\frac{3}{4}[/tex] can be Rewritten as [tex]\frac{15}{4}[/tex]
Amount of Blueberries picked by Reggie = [tex]\frac{15}{4}[/tex] quarts
Amount of Raspberries picked by Reggie = [tex]4\frac{1}{4} [/tex] quarts
[tex]4\frac{1}{4}[/tex] can be Rewritten as [tex]\frac{17}{4}[/tex]
Amount of Raspberries picked by Reggie = [tex]\frac{17}{4}[/tex] quarts
We need to find Total quarts of berries he picked from fruit farm.
So we can say Total quarts of berries he picked from fruit farm is equal to sum of Amount of Blueberries and Amount of Raspberries.
Framing in equation form we get;
Total Quarts of Berries = [tex]\frac{15}{4}+\frac{17}{4} = \frac{15+17}{4}=\frac{32}{4} = 8\ quarts[/tex]
Hence Reggie picked Total 8 quarts of berries.
A girl is flying two kites at the same time. She has 380 ft of line out to one kite and420 ft to the other. She approximates the angle between the two lines to be 30◦.Approximate the distance between the two kites.
The distance between the two kites is approximately 380 ft.
Explanation:To find the distance between the two kites, we can use the law of cosines. Let's call the distance between the two kites as 'd'. We can use the equation:
d^2 = 380^2 + 420^2 - 2 * 380 * 420 * cos(30)
By plugging in the values, we get:
d^2 = 144400
Taking the square root of both sides, we find:
d = 380 ft
So, the distance between the two kites is approximately 380 ft.
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