Answer:
His savings were of $4,200.
Step-by-step explanation:
Mr. Hughes gave 5/14 of his savings to his son, 2/3 of the remainder to his daughter, and the rest to his wife:
This means that the son and daughter amount is:
[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14})[/tex]
As [tex]\frac{9}{14}[/tex] is the remained that his son did not get. So
[tex]\frac{5}{14} + \frac{2}{3}(\frac{9}{14}) = \frac{15}{42} + \frac{18}{42} = \frac{33}{42}[/tex]
Fraction his wife got:
[tex]1 - \frac{33}{42} = \frac{42}{42} - \frac{33}{42} = \frac{9}{42}[/tex]
If his wife got $900, what were his savings?
Total savings are x, wife got [tex]\frac{9}{42}[/tex] of x. So
[tex]\frac{9x}{42} = 900[/tex]
[tex]9x = 900*42[/tex]
[tex]x = \frac{900*42}{9}[/tex]
[tex]x = 100*42[/tex]
[tex]x = 4200[/tex]
His savings were of $4,200.
The foot of a ladder is placed 7 meters from a wall. If the top of the ladder rests 9 meters up on the wall, how long is the ladder?
Answer:
8 meters
step-by-step explanation:
8 is in between 9 and 7
<4?
What is the solution of 3+
X-2
X-3
O x <3
O XS3
Ox>3
0 x23
Answer:
x < 3
Step-by-step explanation:
3 + x-2/x-3 ≤ 4, x ≠ 3
3 + x-2/x-3 -4 ≤ 0
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3, x ≠ 3
x < 3
x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
What is Inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality.
The given equation can be rewritten as 3 + (x-2) / (x-3) ≤ 4.
To solve for x, we need to multiply both sides by (x-3)
3(x-3) + (x-2) ≤ 4(x-3).
3 + x-2/x-3 -4 ≤ 0
Solve the above equation.
-1 + x-2/x-3 ≤ 0
-(x-3) + x-2/x-3 ≤ 0
1/x-3 ≤ 0
x-3 < 0
x < 3
Hence, x<3 is the solution of the equation 3 + (x-2) / (x-3) ≤ 4.
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Suppose we have a bag with 10 slips of paper in it. Eight slips have a 3 on them and the other two have a 5 on them.
(a) What is the expected value of the number shown when we draw a single slip of paper?
(b) What is the expected value of the number shown if we add one additional 3 to the bag?
(c) What is the expected value of the number shown if we add two additional 3's (instead of just one) to the bag?
The expected values for each experiment are:
A) 3.4
B) 3.36
C) 3.33
How to get the expected values?If we have an experiment with the outcomes:
{x₁, x₂, ..., xₙ}
Each one with the correspondent probability:
{p₁, p₂, ..., pₙ}
Then the expected value of that experiment will be:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
A) in this case we have 10 slips of paper, 8 of them with the number 3, and 2 of them with the number 5.
So the outcomes are:
{3, 5}
The probabilities are:
{8/10, 2/10}
Then the expected value is:
EV = 3*(8/10) + 5*(2/10) = 3.4
B) If we add another slip of paper with a number 3 on it, the new probabilities are:
{9/11, 2/11}
Then the new expected value is:
EV = 3*(9/11) + 5*(2/11) = 3.36
C) Finally, if we add 2 slips of paper with the number 3, now we will have a total of 12 slips of paper, then the new probabilities are:
{10/12, 2/12}
So the new expected value is:
EV = 3*(10/12) + 5*(2/12) = 3.33
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I NEED HELP FAST PLS
Answer:
234 feet cubed
Step-by-step explanation:
6 1/2 * 8 = 52
52 * 4 1/2 = 234
summarize how you can find the slope of a parallel line.
Summary of slope of parallel lines:
Parallel lines have equal slopes. The parallel lines are equally inclined with regard to the positive x-axis, and this is taken into account when calculating a line's slope.
If one line has a slope of m1, another line has a slope of m2, and both lines are parallel, then we get m1 = m2.
The coefficients for "x" and "y" in the equations that depict parallel lines are identical.
Ax + by + c2 = 0 is the line that is parallel to ax + by + c1 = 0. Observation reveals that the x and y coefficients in both equations are equivalent.
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Drag each question to the correct location on the table.
Classify the questions as statistical or not statistical.
Each of the questions should be correctly classified as statistical or not statistical as follows:
Not statistical question: "How many hours did I jog yesterday?"Not statistical question: "How many students in my class can swim?"Not statistical question: "How many students in my class watch television?"Statistical question: "How many hours a day do the students in my class watch television?"Statistical question: "How many TV shows did each student in my class watch yesterday?"Statistical question: "How many days a week did each student in my class go swimming in the last month?"What is a statistical question?In Mathematics, a statistical question can be defined as a type of question in which the resulting answer is in the form of an average, percentage, or a range such as "How many TV shows did each student in my class watch yesterday?"
What is a non-statistical question?A non-statistical question simply refers to a question that is not non-statistical and it can be defined as a type of question which has an exact or fixed answer such as "How many students in my class can swim?"
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how many 5-digit even numbers can be formed with the digits 1,2,3,4,5, and 6 if repetition is allowed?
Given:
The given digits are 1,2,3,4,5, and 6.
To find:
The number of 5-digit even numbers that can be formed by using the given digits (if repetition is allowed).
Solution:
To form an even number, we need multiples of 2 at ones place.
In the given digits 2,4,6 are even number. So, the possible ways for the ones place is 3.
We have six given digits and repetition is allowed. So, the number of possible ways for each of the remaining four places is 6.
Total number of ways to form a 5 digit even number is:
[tex]Total=6\times 6\times 6\times 6\times 3[/tex]
[tex]Total=3888[/tex]
Therefore, total 3888 five-digit even numbers can be formed by using the given digits if repetition is allowed.
During the last class period of the semester, each student in a graduate computer science class with 10 students is required to give a brief report on his or her class project. The professor randomly selects the order in which the reports are to be given. Two students have been working on similar projects and would like to give their reports consecutively. What is the probability that this will happen
Answer:
Probability = 1/5
Step-by-step explanation:
Total ways of arrangement for 10 students = 10 !
Ways to arrange 2 students consecutively & other 8 students = 9 ! x 2
( As 9! to arrange 9 units, as 2 considered together ; & 2 for arranging 2 consecutive students - respectively )
So, Probability = Favourable outcomes / Total outcomes
= ( 2 x 9! ) / 10! = ( 2 x 9 x 8 x ..... 2 x 1 ) / 10 x 9 x ....... 2 x 1)
= 2 / 10 = 1/5
6. Name the polygon. Write whether it is regular
or not regular
Answer:
this shape is a pentagon. this is a regular shape because all the sides are even and all the angles on the inside are also even.
Step-by-step explanation:
pls mark brainliest!
Will someone please help me with finding the median
Answer:
remember this rhyme
Step-by-step explanation:
hey diddle diddle,
the median in the middle
you add and divide for the mean
the mode is the one you see the most
and the range is the differences between.
for median put them in order and then it's the one in the middle
so what you have to do is you have to get all the numbers put them in least to greatest order and slowly you're going to mark one off on the side and then on the other side Mark went off and keep on doing that until you get into the middle and then that should be your median
In 2012, the population of Cincinnati, Ohio, was 296,550 with a population density of approximately 3800 people per square mile. What is the approximate land area of Cincinnati in square miles to the nearest whole number?
Answer:
≈ 78mi^2
Step-by-step explanation:
To find approximate land area:
296,550/3,800 = 78.039
Round to nearest whole number:
Area = 78
A light bulb consumes 5400 watt-hours in 3 days and 18 hours. How many watt-hours does it consume per day?
We are given:
Time period: 3 days and 18 hours
Energy consumed in given time period: 5400 watt-hours
Converting time to hours:
We know that one day is 24 hours
So, 3 days = 72 hours
Time period = 3 days + 18 hours
Time period = 72 hours + 18 hours
Time period = 90 hours
Converting to days
Time period = 3.75 days
Watt-hour consumption in a day:
Consumption = 5400 watt-hours / 3.75 days
Consumption = 1440 watt-hours/day
Correct Answer= Brainliest
Answer:
49
Step-by-step explanation:
Convert the dot plot into numbers
40, 40, 40, 45, 45, 50, 55, 55, 60, 60
Add all together
40+40+40+45+45+50+55+55+60+60 =490
Divide by amount of numbers there are
Amount of numbers = 10 --> 490/10 = 49
Mean = 49
Peter and his four brothers combined all of their money to buy a video game. If 30% of the total money is Peter's, and $6.00 of the total money is Peter's, how much do all five brothers have combined?
A.
$26.00
B.
$20.00
C.
$14.00
D.
$1.80
find the value of x thanks! :D brainliest will be awarded!
Answer:
19
Step-by-step explanation:
point y is 90
x is 3x - 5
w is 2x
so
3x - 5 + 2x = 90
5x - 5 = 90
5x = 95
x = 19
Why is the discriminant a useful tool to use when solving quadratic equations?
Abigail goes to a restaurant and the subtotal on the bill was x dollars. A tax of
6% is applied to the bill. Abigail decides to leave a tip of 22% on the entire bill
(including the tax). Write an expression in terms of x that represents the total
amount that Abigail paid.
Answer:
Step-by-step explanation:
Total after tax:
x(1+0.06)
x(1+0.06)
x(1.06)
x(1.06)
1.06x
1.06x
{Total after tip:}
Total after tip:
1.06x(1+0.22)
1.06x(1+0.22)
1.06x(1.22)
1.06x(1.22)
1.2932x
1.2932x
Two brothers are allowed to spend a maximum of 5.90 money as pocket money.the elder brother spent 2.97 money. How much was left for the younger brother?
Given the relation x = y 2 − 1, identify the x- and y- axis intercepts.
The effectiveness of two types of textbook is compared. A class of 30 students is randomly divided into two groups. One group uses digital textbooks and the other group uses paper textbooks. A summary of their test scores at the end of the session is given below. Digital Textbook: Paper Textbook: Construct a 90% confidence interval for the difference in scores between the two groups assuming underlying normal distributions with equal variance. Find the lower bound of the confidence interval (round off to first decimal place).
Answer:
- 18.377
Step-by-step explanation:
n1 = 17 ; xbar1 = 78.4 ; s1² = 90.3
n2 = 13 ; x2bar = 92 ; s2² = 107.8
Confidence interval :
(x1 - x2) ± Tcritical * sqrt[(sp²/n1 + sp²/n2)]
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
df = n - 1
Sp² = (16*90.3 + 12*107.8) / 28
Sp² = 97.8
Tcritical, 90%, df = n1 + n2 - 2 = 28 (1 - tail)
Tcritical = 1.313
(78.4-92)±1.313*sqrt[(sp²/n1 + sp²/n2)]
Margin of Error = Tcritical * sqrt[(sp²/n1 + sp²/n2)] Margin of Error = (1.313 * √(97.8/17 + 97.8/13)) = 4.7771473
Lower boundary :
(78.4-92) - 4.7771473
-13.6 - 4.7771473
= −18.3771473
= - 18.377
can you help me for this math?
Answer:
3
Step-by-step explanation:
27-6=7q
21/7=q
3=q
hope it helps
27 = 7q + 6
=> 27 - 6 = 7q
=> 21 = 7q
=> 21/7 = q
=> 3 = q
So, q = 3.
An experienced census official feels that she can accurately estimate the number of inhabitants of a city block by simply noting the size of the block and the types of buildings (single family homes, apartments, businesses, etc.) that are found on the block. This procedure, if accurate, would be much quicker and cheaper than visiting each residence and taking a survey of its inhabitants. The data below are estimates of block populations provided by the official for 10 blocks in a large city, and the actual numbers of inhabitants for the same 10 blocks. Inhabitants of City Blocks Estimate 193 86 81 87 223 226 151 126 120 76 Actual 163 140 150 179 204 128 73 89 136 145 Step 1 of 2: Find the value of the test statistic for testing whether there is a linear relationship between the actual number of inhabitants and the estimated number. Round your answer to two decimal places, if necessary.
Answer:
035
Step-by-step explanation:
193
86
81
87
223
226
151
126
120
76
Y:
163
140
150
179
204
128
73
89
136
145
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
Draw a diagram of x + 2, and a separate diagram of 3x, when x is 2.
The graph of the equation x + 2 would be a straight line that starts at the point (-2, 0) and goes up 2 units on the y-axis. So, the line would pass through the point (0,2) and would be parallel to the x-axis.
The graph of the equation 3x when x is 2 would be a straight line that starts at the point (0,0) and goes up 6 units on the y-axis for each 1 unit on the x-axis. So, the line would pass through the point (2,6) and would have a slope of 3.
What is diagram in mathematics?In mathematics, a diagram is a visual representation of mathematical concepts or ideas. Diagrams can take many forms, such as graphs, charts, illustrations, and figures, and can be used to help explain or understand mathematical concepts.
For example, a graph is a type of diagram that is used to represent the relationship between two variables. It is commonly used in algebra and calculus to show the relationship between an independent variable (x-axis) and a dependent variable (y-axis).
A chart is a type of diagram that is used to organize and present data. It is commonly used in statistics to show the distribution of data or to compare different sets of data.
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29. For all values of X,
x^2+2x+4 = (x + 2)^2 + a(x+2) + b,
where a and b are constants. What is the value
of a?
(A) -2
(b) - 1
(c) 0
(d) 1
Dilate the line shown by a scale factor of 1/4 with the center as (-3,9). Graph the dilated line
On solving the provided question we can say that - the coordinates from the graphs will be P' = (0.0); Q' = (1,0); R' = (1,1); S' = (0,1)
what are coordinates?A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is r
A fixed point serves as the dilation's center.
Dk is used to represent dilation, where k is the scale factor.
Dk (x, y) = for a dilation centered on the origin (kx, ky)
Let's assume that you have a PQRS rectangle where
P = (0,0)
Q = (4,0)
R = (4,4)
S = (0,4)
You must multiply each coordinate by 1/4 to achieve the dilation of this PQRS to P'Q'R'S' with a scale factor of 1.
P' = (0.0)
Q' = (1,0)
R' = (1,1)
S' = (0,1)
You may plot both of these rectangles to see that they are the same size and are centered on the origin, but they have different shapes.
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Can somebody help me please
Answer:
[tex] \frac{34.25}{6.5} [/tex]
Which of the following would not be an example of a compound event?
(1) having a coin land on heads three consecutive times
(2) pulling a king out of a deck of cards
(3) missing two free throws in a row
(4) answering four true/false questions correctly by guessing
The only option that is not a compound event is; (2) pulling a king out of a deck of cards
How to identify a compound event?Compound probability is defined as a mathematical term that relates to the likeliness of two independent events occurring.
Thus, a simple event has only one outcome while a compound event involves the probability of more than one outcome
1) For a coin to land on heads three consecutive times means that there can only be three possible independent outcome and so this is a compound event.
2) Pulling a king out of a deck of cards is a simple event and not compound because it has only one outcome.
3) This is a compound event because we are dealing with two independent probabilities.
4) This is a compound event because we are dealing with two independent events which are true or false answers.
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Y
P
Q
S
R
Part A
Rectangle PQRS is rotated 90° counterclockwise about the origin to create rectangle PQR'S' (not shown). What are the coordinates of point R?
0 (-7,6)
O (7,6)
• (-6,7)
O (6,7)
Part B
Answer:
The coordinates of point R are (7,6), second option
Step-by-step explanation:
Coordinates of point R:
The coordinates of point R are , so (6,-7).
90° counterclockwise rule:
The rule for a rotation of 90º counterclockwise is given by:
(x,y) -> (-y,x)
What are the coordinates of point R?
(6,-7) -> (-(-7),6) = (7,6).
The coordinates of point R are (7,6), second option
I need help finding the median :)
Answer:
15
Step-by-step explanation:
find the test statictis
Answer:
5
Step-by-step explanation: