Answer:
a) (8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S, b) (0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.
Step-by-step explanation:
Let be [tex]X[/tex] a point in the line between endpoints [tex]R[/tex] and [tex]S[/tex]. The ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is given by:
[tex]r = \frac{RX}{RS}[/tex]
Where:
[tex]RX = \sqrt{(x_{X}-x_{R})^{2}+(y_{X}-y_{R})^{2}}[/tex]
[tex]RS = \sqrt{(x_{S}-x_{R})^{2}+(y_{S}-y_{R})^{2}}[/tex]
Let be [tex]x_{R} = -4[/tex], [tex]y_{R} = 3[/tex], [tex]x_{S} = 16[/tex] and [tex]y_{S} = 18[/tex].
a) If we know that [tex]x_{X} = 8[/tex] and [tex]y_{X} = 12[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:
[tex]RX =\sqrt{[8-(-4)]^{2}+(12-3)^{2}}[/tex]
[tex]RX = 15[/tex]
[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]
[tex]RS = 25[/tex]
Then,
[tex]r = \frac{15}{25}[/tex]
[tex]r = \frac{3}{5}[/tex]
(8,12) is the point [tex]\frac{3}{5}[/tex] of the way from R to S.
b) If we know that [tex]x_{X} = 0[/tex] and [tex]y_{X} = 6[/tex], the ratio of the line segment [tex]RX[/tex] to the line segment [tex]RS[/tex] is:
[tex]RX =\sqrt{[0-(-4)]^{2}+(6-3)^{2}}[/tex]
[tex]RX = 5[/tex]
[tex]RS =\sqrt{[16-(-4)]^{2}+(18-3)^{2}}[/tex]
[tex]RS = 25[/tex]
Then,
[tex]r = \frac{5}{25}[/tex]
[tex]r = \frac{1}{5}[/tex]
(0, 6) is the point [tex]\frac{1}{5}[/tex] of the way from R to S.
A class of 33 students elected a class treasurer. There were 11 votes for Candidate A and 15 votes for Candidate B. The remaining students did not vote. Which expression gives the percent of voters who voted for Candidate A?
Answer:
[tex]\frac{11}{11+15}[/tex] * 100
Step-by-step explanation:
The voters would be 11+15 and since there were 11 votes for A, that is the equation you should use.
Use the following information to answer questions .
A purchasing unit for a state government has found that 60% of the winning bids for office- Cleaning contracts come from regular bidders, 30% from occasional bidders, and 10% from first- uime bidders. The services provided by successful bidders are rated satisfactory or unsatisfactory anter one year on the job. Experience indicates that 90% of the jobs done by regular bidders are satisfactory, as are 80% of the jobs done by occasional bidders and 60% of the jobs done by first- time bidders.
1. What is the probability a job will be done by a first-time bidder and be satisfactory?
a. 0.06
b. 0.09
c. 0.10
d. 0.60
2. What is the probability that a job will be satisfactory?
a. 0.54
b. 0.60
c. 0.84
d. 0.95
3. Given that a job is satisfactory, what is the probability that it was done by a regular bidder?
a. 0.5778
b. 0.6141
c. 0.6429
d. 0.9000
Answer:
1
The correct option is A
2
The correct option is C
3
The correct option is C
Step-by-step explanation:
From the question we are told that
The proportion of the winning bid from a regular bidder is [tex]P(R) = 0.60[/tex]
The proportion of the winning bid from a occasional bidders is [tex]P(O) = 0.30[/tex]
The proportion of the winning bid from a first- time bidders is [tex]P(F) = 0.10[/tex]
The proportion of satisfactory jobs done by a regular bidders is [tex]P(R|S) = 0.90[/tex]
The proportion of satisfactory jobs done by a occasional bidders is [tex]P(O|S) = 0.80[/tex]
The proportion of satisfactory jobs done by a first- time bidders is [tex]P(F|S) = 0.60[/tex]
Generally the probability that a job will be done by a first-time bidder and be satisfactory is mathematically represented as
[tex]P(F n S) = P(F) * P(S|F)[/tex]
=> [tex]P(F n S) = 0.10 * 0.60[/tex]
=> [tex]P(F n S) = 0.060[/tex]
Generally the probability that a job will be satisfactory is mathematically represented as
[tex]P(S) = 0.60 * 0.90 + 0.30 *0.80+ 0.10*0.60[/tex]
=> [tex]P(S) = 0.84 [/tex]
Generally given that a job is satisfactory, what is the probability that it was done by a regular bidder is mathematically evaluated as
[tex]P( S | R) = \frac{0.90* 0.60}{0.60}[/tex]
[tex]P( S | R) = 0.6429[/tex]
Alvin's mom loves to cook. For her birthday, Alvin surprises her with a new container for
her cooking spoons. The round container is divided into 5 equal sections. Alvin fills 4 sections
with wooden spoons.
What fraction of the container does Alvin fill with wooden spoons?
Answer:
4/5
Step-by-step explanation:
There Are 5 Sections, 5 Is The Denominator For Our Answer
He Fills 4 Sections, And That Means He Filled Four-Fifths Of The Container.
Hope This Helps!
Answer:
It's all about parts.
Step-by-step explanation:
Since the container has 5 sections we can look at it as ?/5. With every section that Alvin fills, we add 1 more to the fraction. So, if he fills 1 section, we have 1/5. If he fills 2 sections, we have 2/5, and so on. I hope this helps you.
Two numbers are in the ratio 9:7 if one number is 324, what is the other number?
Answer:
[tex]\boxed{\bold{\huge{\boxed{\sf x = 252}}}}[/tex]
Step-by-step explanation:
The ratio is 9 : 7
The first number is 324
Let's build the proportion for it.
9 : 7 = 324 : x [We've to find x]
Product of Extremes = Product of Means=> 9 * x = 324 * 7
=> 9x = 2268
Dividing both sides by 9
=> x = 252
So, The other number is 252.
I need to get slope intercept form
Terry is filling spherical water balloons with a faucet that puts out 100cm^3 of water per second. At that rate, it takes Terry 6 seconds to fill a balloon.
What is the radius of a filled balloon?
Round to the nearest centimeter.
Answer:
To the nearest centimeter
Radius= 5 cm
Step-by-step explanation:
Rate of filling balloon= 100cm³/s
Time to feel the balloon= 6 s
Volume of the filed balloon
= Rate*time
= 100*6
= 600 cm³
Volume of balloon= 4/3πr³
Volume of balloon=600cm³
600= 4/3πr³
(600*3)/4π= r³
1800/4π= r³
450/π= r³
143.239 = r³
5.232= r
To the nearest centimeter
Radius= 5 cm
Answer:
5
Step-by-step explanation:
Volume:
(100)(6) = 600
Radius:
[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex](r)^{3}[/tex] x [tex]\frac{/}{/\pi}[/tex]
[tex]\sqrt[3]{143.2}[/tex] = [tex]\sqrt[3]{r^{3} }[/tex]
= 5.2 = r
round it up = 5
SO: your answer is 5
Also I did it on khan
brainliest plz?
[(8-6 x 7]-3 can you guys tell me what's the answer?
Answer:
the answer is 11
the number of PI is 3.14 why do we use a special symbol for it
A bus first travels west for
38 kilometers. Then it turns south and
travels for 25 kilometers. Next it goes
east for 38 kilometers. Finally, it travels
north for an unknown number of
kilometers. At the end of the journey,
the bus is back at the original location.
How far did it travel northward?
A train is going on a journey. First it travels east for 50 kilometers. Then it turns north and travels for 22 kilometers. Next it goes west for 50 kilometers. Finally, it travels south for a certain number of kilometers. At the end of its journey it is back at its original location. How many kilometers did it travel in the southward direction?
Evaluate the numerical expression 3+21-180÷9. The value of the expression is?
Answer:
the answer is 4.
the steps are...
180÷9=20 then 3+21=24 the subtract 20 and 24 then you will get 4
Answer:
The answer is number 4
Step-by-step explanation:
4x9/108+21-3
The point (2,-4) is on the line given by which equation below?
2,-4)
A. y = -x + 3
B. y = x - 4
C. y=-2x
D. y = 2x
Answer:
C ) y = -2x
Step-by-step explanation:
(2, -4)
y = -2x
subsitute x for the value of x
y = -2(2)
-2 × 2 = -4
y = -4
so
the equation for the point (2, -4) is
y = -2x
three angles are adjacent to each other and form 140.the largest angle is twice the smaller angle and the angle which is middle size is 24 more than the smallest. find the angles
Answer:
Smallest: 29, Middle: 53, Largest: 58
Step-by-step explanation:
We can represent the angles in this problem using an equation.
We'll use x to represent the smallest angle, and work out other ways to represent the others.
As the largest angle is twice that of the smaller angle, we can represent the largest angle as 2x as 2x is two times x.
The middle angle is 24 more than the smallest, so we can represent that one as x + 24, since it is 24 more than the smallest.
Now we have our angles all represented with x:
Smallest angle = x
Middle = x+24
Largest = 2x
We know that they all add together to 140 so our equation is:
x+2x+(x+24) = 140
Now we can solve for x!
We can remove the brackets (addition does not change the terms) and combine the terms:
x+2x+x+24=140
4x+24=140
Next we move the 24 to the other side so we can solve for x:
4x + 24 - 24 = 140 - 24
4x = 116
Finally we divide both sides by 4:
x=29
The smallest angle is 29!
Now we can use our representations to find the other angles:
Middle angle = x+24, therefore it is 29+24 = 53
Largest angle = 2x therefore it is 2*29 = 58
58+53+29=140 so we have successfully worked out our angles!
Hope this helped!
. Elijah's workout at the gym consists of just the elliptical and treadmill. After burning 450
calories on the elliptical machine, Elijah switched to the treadmill. If he is burning 12.5 calories
per minute on the treadmill, find the total number of calories he will have burned during his
workout if he spends 30 minutes on the treadmill.
Answer:
375
Step-by-step explanation:
30*12.5 is equal to 15*25
15*25= 375
The total number of calories he will have burned during his workout if he spends 30 minutes on the treadmill will be 375 calories.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Elijah's workout at the gym consists of just the elliptical and treadmill. After burning 450 calories on the elliptical machine, Elijah switched to the treadmill.
The number of calories burnt will be calculated below,
30 x 12.5
15 x 25
15 x 25= 375 calories
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If the number 3 were added to the set {1,1,3,3,4,4,5}, which central tendency would change? A)Mean B)Mode C)Range D)Median
Answer:
Mode
Step-by-step explanation:
I took the test and got it correct!
I had $3.00. My mom gave me $10.00. My dad gave me $30.00. My aunt and uncle gave me $100.00. I had another $7.00. How much did I have?
After examining a child at his 2-year checkup, the boy's pediatrician said that the z-score for his height relative to other 2-year-olds in the country was 1.59. The pediatrician explains to the parents that the most extreme 5% of cases often require special treatment or attention. a) Does this child fall into that group? b) What do you need to assume about the heights of 2-year-olds to find your answer to part a? a) The child _______into this group because he is___________than_______ standard deviation from the mean.b) Choose al that apply. A. the distribution of heights is skewed B. the heights are independent C. the distribution of heights is symmetric D. the number of heights is very large E. the distribution of heights is unimodal
a)The child falls into the most extreme 5% group, we need to compare the z-score of 1.59 to the critical value for the 5th percentile.
b)The information to make assumptions about the skewness, symmetry, or the number of heights is not provided.
A z-score of 1.59 means that the child's height is 1.59 standard deviations above the mean height for 2-year-olds. To decide if the child falls into the most extreme 5% group, we need to find the critical value for the 5th percentile. The critical value corresponds to the z-score that separates the lowest 5% of the distribution from the rest.
b) To find the answer to part a we need to assume certain properties about the heights of 2-year-olds:
A. The distribution of heights is skewed - Skewness is not mentioned in the problem, so we cannot assume the distribution is skewed or not skewed based on the given information.
B. The heights are independent - The heights of 2-year-olds are independent in the sense that one child's height does not influence or depend on another child's height. This is a reasonable assumption in most cases.
C. The distribution of heights is symmetric - The given z-score doesn't tell us directly about the symmetry of the distribution, so we cannot assume the distribution is symmetric based on this information alone.
D. The number of heights is very large - The information about the size of the population is not provided, so we cannot assume that the number of heights is very large.
E. The distribution of heights is unimodal - We do not have information about the number of modes (peaks) in the height distribution. The z-score doesn't give us any insight into whether the distribution is unimodal or multimodal.
Thus, the result of the following questions will be:
a) The child falls into the most extreme 5% group, we need to compare the z-score of 1.59 to the critical value for the 5th percentile.
b)The information to make assumptions about the skewness, symmetry, or the number of heights is not provided.
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What is the volume of the figure? Enter the answer in the Box. In cubic centimeters
Answer:
264 cm³
Step-by-step explanation:
(5*5*8)+(*8*8*1)
200+64=
264 cm³
The volume of the figure 264 cubic centimeters.
What is rectangular prism?"It is a three-dimensional solid shape which has six faces that are rectangles."
Formula to calculate the volume of rectangular prism:V = l w h, where l is the length, w s the width and h is the height of the rectangular prism.
Given figure consists of two rectangular prisms.
For the smaller rectangular prism,
length(a) = 8 [tex]V_2= 8\times 5\times 5[/tex]cm, width(b) = 8 cm and height(h) = 1 cm
For the larger rectangular prism,
length(p) = 8 cm, width(q) = 5 cm and height(r) = 5 cm
Let [tex]V_1,V_2[/tex] represents the volume of the smaller and larger rectangular prisms respectively.
The volume of the smaller rectangular prism would be,
⇒ [tex]V_1=a\times b\times c[/tex]
⇒ [tex]V_1=8\times 8\times 1[/tex]
⇒ [tex]V_1=64[/tex] cu.cm.
The volume of the larger rectangular prism would be,
⇒ [tex]V_2=p\times q\times r[/tex]
⇒ [tex]V_2=8\times 5\times 5[/tex]
⇒ [tex]V_2 = 200[/tex] cu.cm.
The volume of the figure is:
= [tex]V_1+V_2[/tex]
= 64 + 200
= 264 cubic centimeters
The volume of the figure 264 cubic centimeters.
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Colton and his children went into a movie theater and he bought $48.50 worth of bags of popcorn and candies. Each bag of popcorn costs $5.50 and each candy costs $3.50. He bought a total of 11 bags of popcorn and candies altogether. Determine the number of bags of popcorn and the number of candies that Colton bought.
Answer:
5 bags of popcorn and 6 candies.
Step-by-step explanation:
(5 * $5.50) + ($3.5*6) = $48.5
Subtract.
Enter your answer, in simplest form, in the box.
-3 3/8 - 7/8
Answer:
The answer is
[tex] - \frac{17}{4} \: \: or \: \: - 4 \frac{1}{4} [/tex]Step-by-step explanation:
[tex] - 3 \frac{3}{8} - \frac{7}{8} [/tex]First of all convert the mixed number to an improper fraction
We have
[tex] - 3 \frac{3}{8} = \frac{27}{8} [/tex]So we have
[tex] - \frac{27}{8} - \frac{7}{8} [/tex]Since they have the same denominator we can subtract them directly
We have
[tex] - \frac{27}{8} - \frac{7}{8} = - \frac{34}{8} [/tex]Reduce the fraction with 2
We have the final answer as
[tex] - \frac{17}{4} \: \: or \: \: - 4 \frac{1}{4} [/tex]Hope this helps you
is the number 8.25 a rational number or an irrational number
Answer:
Rational
Step-by-step explanation:
An irrational number can't be written as a simple fraction. an irrational number will continue on forever without repeating. a rational number is any number that can be written by dividing two integers so basically any number that can be written as a fraction or decimal.
Answer:
Rational number.
Step-by-step explanation:
An irrational number is any real number that cannot be written as a simple fraction. Like square roots.
Mr.wilkins deposited $2,500 in a new account at his bank . •the bank pays 6.5% interest compounded annually on this account •mr.wilkins makes no additional deposits or withdrawals Which amount is closest to the balance of the account at the end of 2 years
Answer:
Step-by-step explanation:
$2,662.50
Order of operations A set of three scores consists of the values 6, 3, and 2. 1. Σ2X – 2 =______.a. 35.b. 33.c. 22.d. 6.2. Σ(2X)² =______.a. 248.b. 124.c. 61.d. 39.
Answer:
Step-by-step explanation:
Given the order of operations A set of three scores to consists of the values 6, 3, and 2, we are to evaluate the following
1) Σ2X – 2
= 2(6)+2(3)+2(2) – 2
= 12+6+4–2
= 22–2
= 20
2) Σ(2X)² = (2×6)²+(2×3)²+(2×2)²
Σ(2X)² = 12²+6²+4²
Σ(2X)² = 144+36+16
Σ(2X)² = 144+52
Σ(2X)² = 196
The results of the order of operations are: [tex]\sum 2x -2 = 16[/tex] and [tex]\sum (2x)^2 =196[/tex]
The scores are given as:
x = 6, 3 and 2
(a) The first set of operationThis is represented as:
[tex]\sum 2x -2[/tex]
So, we have:
[tex]\sum 2x -2 = 2 \times 6 - 2 + 2 \times 3 - 2 + 2 \times 2 - 2[/tex]
Evaluate the products
[tex]\sum 2x -2 = 12 - 2 + 6 - 2 + 4- 2[/tex]
[tex]\sum 2x -2 = 16[/tex]
(a) The second set of operationThis is represented as:
[tex]\sum (2x)^2[/tex]
So, we have:
[tex]\sum (2x)^2 =(2 \times 6)^2 + (2 \times 3)^2 + (2 \times 2)^2[/tex]
Evaluate the products
[tex]\sum (2x)^2 =12^2 + 6^2 + 4^2[/tex]
Evaluate the squares
[tex]\sum (2x)^2 =144 + 36 + 16[/tex]
[tex]\sum (2x)^2 =196[/tex]
Hence, the results of the order of operations are:
[tex]\sum 2x -2 = 16[/tex] and [tex]\sum (2x)^2 =196[/tex]
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What is the product of 3y
product of (3y^)(274)
3y^-4 × (2y^-4) = 6y^-8
= 6/1/y^8
= 6/y^8
.................................................
1) When x^1 multiply with x^2, 1 will add to 2 and become 3
= x^3
2) y^-1 = 1/y
3^-2 = 1/3^2 = 1/9
5^-2 = 1/5^2 = 1/25
- m(2m + m2); m =
-4
Answer:
-(-4)(2×-4+(-4×2).
4(-8+(-8)).
4(-16).
= -64.
Answer:-64
Step-by-step explanation:
-4(2×4+4×2)
-4(8+8)
-32-32=-64
GEOMETERYY!!!! PLEASE HELP HJ=5p JK=p KH=3
Answer:
P=5.4
Step-by-step explanation
H=5 times
K=3/5=0.6
K=0.6
P=0.6x3x3=1.8x3=5.4
P=5.4
Jamie has 105 pieces of candy leftover from Halloween. She would like to distribute them evenly to the 7 kids on her block. Write an equation to show how many pieces of candy each kid will receive. x = seven divided by one hundred five x = one hundred five divided by seven 7 + x = 105 x = 105 − 7
6(4.5x-12)=9
A. X= 0.6
B. x = 28
C. x= 3
D. x= 3.3
Answer:
Step-by-step explanation:
27x - 72 = 9
27x = 81
x = 3
answer is C
The Sports Brand Company is making a new shoe that has a wholesale price of $40, and it wishes to advertise a retail price of $89.99. What is the markup percentage? Give answer to nearest whole percent. (hint: change decimal to percent, % will not be typed)
Answer:
Markup Percentage = 125%
Step-by-step explanation:
The wholesale price is $40, the "selling price" is $89.99.
90-40=50 (Profit)
Now that we know the profit , we need to find the percentage.
To find this percentage we can use the formula: (M=Markup percent)
[tex]M=profit/cost*100%[/tex]
In this situation, we can insert PROFIT= 50, Cost=40
M=50/40*100
= 1.25*100
=125%
One side of a triangle is 8 feet longer than the second side. The third side is 4 feet longer than the second side. The perimeter of a triangle is 36 feet. Find the length of each side.
Answer:
The second side is 8.
The third side is 12.
The last side is 16.
Step-by-step explanation:
The third side is 12 because it is 8+4. Given these facts, it is 20 feet so far. And the last side of the triangle is 16, for it is 8+8. So, 16+20 is 36. Hope thsi helped.
Which properties of equality are used in the example shown on the left? Check all of the boxes that apply.
Answer:
Addition Property and substitution property