(a) The probability of the questions being history, literature, and science in that order is 5/18 x 6/17 x 7/16, which is 0.04.
(b) The probability of all three questions being literature questions is 6/18 x 5/17 x 4/16, which is 0.024.
(c) The probability of the first question being science, the second history, and the third science is 7/18 x 5/17 x 7/16, which is 0.05.
What is probability?In playing cards, it can be used to predict the likelihood of a certain outcome or to make decisions based on the probability of certain events occurring.
(a) The probability of the questions being history, literature, and science in that order is 5/18 x 6/17 x 7/16, which is 0.04.
(b) The probability of all three questions being literature questions is 6/18 x 5/17 x 4/16, which is 0.024.
(c) The probability of the first question being science, the second history, and the third science is 7/18 x 5/17 x 7/16, which is 0.05.
The probabilities of each of these scenarios can be calculated by multiplying the probabilities of drawing each of the three cards in the desired order.
For the first scenario, the probability of drawing a history question is 5/18, the probability of drawing a literature question is 6/17 (since there is one fewer card), and the probability of drawing a science question is 7/16 (since there are two fewer cards).
Multiplying these together gives us the probability of the questions being history, literature, and science in that order, which is 0.0771.
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A study was done to estimate the mean commute time for a population of employed adults. A random sample of
25 employed adults in a particular city was taken, and the 95% confidence interval for mean commute time was
calculated to be 34.42 ± 8.14 minutes. A councilman is advocating for road repairs and states that, in this city,
people with jobs commute an average of 45 minutes to work each day. Does the confidence interval justify the
councilman's statement?
No, because 45 minutes is greater than the upper bound of the confidence interval.
Yes, because 45 minutes is greater than the upper bound of the confidence interval.
No, because the mean commute time from the 25 sampled adults was 34.42 minutes.
O Yes, because there were almost certainly some people in the sample of 25 adults whose commute was greater
than 45 minutes.
The confidence interval does not justify the councilman's statement because 45 minutes is greater than the upper bound of the confidence interval.
What is a confidence interval?
A confidence interval is a statistical range that is used to estimate an unknown population parameter based on a sample from that population. It is a measure of the degree of uncertainty or precision associated with the estimated value of the parameter.
The confidence interval of 34.42 ± 8.14 minutes means that we are 95% confident that the true population mean commute time falls between 26.28 minutes (34.42 - 8.14) and 42.56 minutes (34.42 + 8.14). Since the councilman's statement of 45 minutes falls outside of this range, we cannot say that it is justified by the confidence interval.
Additionally, the fact that the mean commute time from the sample of 25 adults was 34.42 minutes does not necessarily mean that the true population mean commute time is also 34.42 minutes. It only provides an estimate, and the confidence interval takes into account the variability of the sample mean.
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Answer:
A. No, because 45 minutes is greater than the upper bound of the confidence interval.
Step-by-step explanation:
An airplane cruises at an altitude of 35,000 feet. It begins its descent at a rate of 1,200 feet per minute. Find a linear model
in the form h(t) = mt+b where h represents the altitude of the plane, in feet, after t minutes into its descent.
What scale factor was used to produce figure 1 from figure 2?
two triangles labeled figure 1 and figure 2, where figure 1 has legs that are 3 units long and figure 2 has legs that are 6 units long
one half
2
one sixth
6
Answer:
Since the legs of figure 2 are twice as long as those of figure 1, the scale factor to produce figure 1 from figure 2 would be 1/2. This means that every length in figure 1 is half the length of the corresponding length in figure 2.
Answer:
Option A. 1/2
Step-by-step explanation:
100 on the test!
Ellie and Jordan went to the store where packs of gum cost 85¢ each and candy bars cost 60¢ each. They spent $15.00 and brought 4 more packages of gum than candy bars. How many packages of gum did they buy?
Answer:
they bought 8 candy bars and 8 + 4 = 12 packs of gum.
Step-by-step explanation:
Let's use algebra to solve this problem:
Let x be the number of candy bars they bought.
Then, the number of packs of gum they bought is x + 4.
The total cost of the candy bars is 60x cents.
The total cost of the packs of gum is 85(x + 4) cents.
We know that they spent $15.00, which is 1500 cents, so we can write an equation:
60x + 85(x + 4) = 1500
Simplifying the equation, we get:
145x + 340 = 1500
145x = 1160
x = 8
Therefore, they bought 8 candy bars and 8 + 4 = 12 packs of gum
Answer: 22
Step-by-step explanation:
The number of the gum is 13 and the number of the candy will be 22.
What is linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Jane and Sophia went to the corner store where packages of gum cost 54¢ each and candy bars cost 88¢ each.
They spent $26.38 total and bought 35 items total.
Let x be the number of the gum and y be the number of the candy.
Then the equation will be
x + y = 35 ...1
0.54x + 0.88y = 26.38 ...2
By solving the equations 1 and 2, then we have
x = 13 and y = 22
Then the number of the gum is 13 and the number of the candy will be 22.
Find x using the Pythagorean Theorem.
The value of x for the given triangle is 14 according to the question.
EquationsIn triangle ABC, right-angled at B, let BM be the altitude from B to AC. Let CM be x.
Using the Pythagorean theorem in triangle ABC of the question:
[tex]AB^{2}[/tex] + [tex]BC^{2}[/tex] = [tex]AC^{2}[/tex]
Substituting AB = BM and BC = CM, we get:
[tex]BM^{2}[/tex] + [tex]CM^{2}[/tex] = [tex]AC^{2}[/tex]
Substituting the given values, we get:
[tex](2\sqrt{15}) ^{2}[/tex] +[tex]x^{2}[/tex] =[tex]16^{2}[/tex]
60 + [tex]x^{2}[/tex] = 256
[tex]x^{2}[/tex] = 196
x = 14
What is a perpendicular?A line or segment that forms a straight angle or 90-degree angle with the provided line is said to be perpendicular to it. It is also known as a "orthogonal" or "normal" line.
We must first choose a point on the supplied line in order to determine the perpendicular to it. Then, a line or segment that traverses that point and is perpendicular to the specified line can be created.
The fact that the slopes of perpendicular lines are the negative reciprocals of one another is used to accomplish this. The slope of any line perpendicular to the provided line will be -1/m if the slope of the given line is m.
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A poll of 1075 Americans showed that46.8 % of the respondents prefer to watch the news rather than read or listen to it. Use those results with a 0.10 significance level to test the claim that fewer than half of Americans prefer to watch the news rather than read or listen to it. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
By using the P-value method, we conclude that, fewer than half of Americans prefer to watch the news rather than read or listen to it.
What is p-value?
In statistics, the p-value is a probability value that measures the evidence against a null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the actual test statistic, assuming that the null hypothesis is true.
In this problem, we want to test the claim that fewer than half of Americans prefer to watch the news, based on a poll of 1075 Americans where 46.8% of the respondents said they prefer to watch the news.
Let p be the true proportion of Americans who prefer to watch the news. Then the null hypothesis is:
H0: p ≥ 0.5 (more than or equal to half of Americans prefer to watch the news)
The alternative hypothesis is:
Ha: p < 0.5 (fewer than half of Americans prefer to watch the news)
We will use the normal distribution as an approximation to the binomial distribution, since n = 1075 is large and the success-failure condition is satisfied. The expected number of respondents who prefer to watch the news is:
E = np = 1075 × 0.468 = 503.1
The standard deviation of the sampling distribution of p is:
σ = sqrt[(p(1-p))/n] = sqrt[(0.5×0.5)/1075] ≈ 0.015
We can now calculate the z-score for the sample proportion:
z = (x - E) / σ = (1075 × 0.468 - 503.1) / 0.015 ≈ -4.28
where x is the observed number of respondents who prefer to watch the news, which is 1075 × 0.468 ≈ 503.
The P-value for this test is the probability of getting a z-score less than or equal to -4.28 under the standard normal distribution. Using a standard normal table or calculator, we find that this probability is very close to 0. Therefore, the P-value is less than 0.10, the chosen significance level.
Since the P-value is less than the significance level, we reject the null hypothesis. We have sufficient evidence to conclude that fewer than half of Americans prefer to watch the news rather than read or listen to it.
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Write a quadratic function in standard form that models the table. X -5 -3 -1 13 y 0 12 12 16 12 0
Answer:
First, we need to find the quadratic function that models the given table. We know that a quadratic function has the form: y = ax^2 + bx + c where a, b, and c are constants to be determined. To find these constants, we need to use the values in the table. When x = -5, y = 0, we get: 0 = a(-5)^2 + b(-5) + c 0 = 25a - 5b + c When x = -3, y = 12, we get: 12 = a(-3)^2 + b(-3) + c 12 = 9a - 3b + c When x = -1, y = 12, we get: 12 = a(-1)^2 + b(-1) + c 12 = a - b
A vehicle purchased for $20,700 depreciates at a constant rate of 7%. Determine the approximate value of
the vehicle 15 years after purchase. Round to the nearest whole dollar.
1 pt
Answer:
Depreciation at a constant percent is exponential decay:V(t) = V0·(1-rate)tV(t) is the value at year t (we want t = 14 years)V0 is the starting value = $20,700rate is the depreciation rate expressed as a decimal = 0.05t = years = 14V(14) = $20700·(1 - 0.05)14Use your calculator to get the answer. Round your answer to the nearest cent, The units are $$.
Step-by-step explanation:
In the slope-intercept form y = m x + b, what does the m and the b stand for? a. m = slope, b = y-intercept c. m = variable, b = slope b. m = y-intercept, b = slope d. m = slope, b = variable Please select the best answer from the choices provided
Answer: Choice A
Step-by-step explanation:
M= slope
B= y-intercept
WILL GIVE TRUE 100 POINTS AND BRAINLYEST FOR THE CORRECT ANSWER
Answer:
y intercept = +4
slope = +2
domain = (-2,0)
range = (4,0)
Graph is increasing
x intercept = -2
Step-by-step explanation:
Line hits y axis at point 4
Slope is calculated by rise over run (2/1)
Domain is x,y listed
Range is y,x listed
Line is going up
Line hits x axis at -2
Dana had an equal number of red beads and yellow beads. After using 500 red beads to make necklaces, she had 3 times as many yellow beads as red beads. How many yellow beads does she have?
Answer:2000
Step-by-step explanation:
Dana has 1500 yellow beads when Dana had an equal number of red beads and yellow beads.
Dana had an equal number of red beads and yellow beads, so let's say she had x red beads and x yellow beads.
After using 500 red beads to make necklaces, she was left with x - 500 red beads.
Since she now had 3 times as many yellow beads as red beads, she had a total of 3 * (x - 500) = 3x - 1500 yellow beads.
We know that the total number of yellow beads is x, so we can set the two expressions equal to each other:
x = 3x - 1500
Solving for x, we get:
2x = 1500
x = 750
Therefore, Dana had x = 750 yellow beads.
Since she now has 3 times as many yellow beads as red beads, she has a total of 3 * 750 = 1500 yellow beads.
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Order the following from least to greatest: -1,0.25, 0.15,-0.10.
-1, -0.10, 0.15, 0.25
So, the answer is the way we do it
-1 , -0.1(or 0.10) , 0.15 , and 0.25
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You are the student council member responsible for planning a school dinner dance. You will
need to choose a caterer, hire a band, analyze costs, and choose flowers for decoration. You
need to keep the ticket price as low as possible and still cover the costs.
Part 1 Choosing a Band
Band A charges a flat fee of $500 to play for the evening.
Band B charges $350 plus $1.50 per student.
Part A: Write a system of equations to represent the cost of the two bands.
Part B: Graph the system of equations and find the number of students for which the cost of
the bands would be equal.
Part 2: Choosing a Caterer
A caterer charges a fixed amount for preparing a dinner plus a rate per student served. The
total cost is modeled by the equation:
Total cost = fixed amount + rate * number of students
You know that the total cost for 50 students will be $450 and the total cost for 150 students
will be $1050. Find the caterer's fixed cost and the rate per student served. Explain your
answer.
Part 3: Analyzing cost
Use the information from Items 1 and 2. Assume that 100 students come to the dinner dance.
Decide which band you should choose and what the total cost per ticket should be to cover
the expenses of the band and caterer. Then repeat your calculations for 200 students.
Explain your reasoning.
Part 4: Choosing Flowers
You can spend no more than $500 on flowers for the event. A bouquet of daisies cost $25
each and a bouquet of roses cost $35 each.
Part A: Write and graph an inequality that represents the number of each type of flower that you can buy.
Part B: Suppose you buy 15 bouquets of daisies. What is the maximum number of bouquets
of roses you can afford? Explain.
1) The cost of both bands would be equal for 100 students. 2) the fixed cost for the caterer is $150 and the rate per student served is $3. 3) Ticket Price = $4.75 4) you can afford a maximum of 3 bouquets of roses.
Let x be the total number of students in Part 1A.
Band A costs $500.
Band B costs $350 plus $1.50 times.
Part B: By graphing the equations, we can determine the location where the price of the two bands is equal.
$500 = $350 + $1.50x \s$150 = $1.50x \sx = 100
As a result, the price for both bands for 100 students would be the same.
Part 2: Let's solve for the fixed cost and rate per student served using the information provided:
50f + 50r = $450
150f + 150r = $1050
When we deduct the first equation from the second, we obtain:
100f + 100r = $600
F plus R equals $6 when we divide by 100.
The result of replacing the value of f in the first equation is:
50($6 - r) + 50r = $450
$300 - 50r + 50r = $450 \sr = $3
As a result, the caterer's fixed fee is $150, and the cost each student served is $3.
Part 3: For 100 pupils, Band A would cost $500, and Band B would cost $350 plus $1.50 (100) for a total of $500.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(100)).
Final price: $950
Total Cost / Number of Students x Ticket Price equals $9.50
Band A would cost $500 for 200 pupils, and Band B would cost $350 + $1.50 (200) = $650.
Hence, selecting Band A would be more economical. For the dinner dance, each ticket would cost:
Total Price = Band Fee + Caterer Fee
Expense in total is $500 plus ($150 + $3(200)).
Final price: $950
Total Cost / Number of Students x Ticket Price is $4.75
Let d be the total number of daisy bouquets and r be the total number of rose bouquets in part 4A.
[tex]25d + 35r \leq $500[/tex]
B. You would have spent $375 if you purchased 15 bouquets of daisies at a cost of 15 ($25).
When we deduct this from the overall budget, we get:
$500 - $375 = $125
The result of dividing by the price of one bunch of roses is: $125/$35 3.57.
Thus, you can buy no more than three rose bouquets.
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Find the measure of the indicated angle to the nearest degree
3. The ASHI Standard of Practice requires a home inspector to inspect
Safety glazing
Porches and railings
Children's play structures
Fences and gates around pools
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice. So, B is the right answer.
Explain ASHI?The American Society of Home Inspectors is known as ASHI. It is a non-profit company with its main office in Des Plaines, Illinois, and it was established in 1976.
ASHI's major objective is to advance professionalism in the home inspection industry by establishing and upholding high standards for its members. Home inspectors can get education, training, and certification from ASHI. Members are also obliged to abide by the organisation's Code of Ethics and Standards of Practice. The minimal requirements for a house inspection are outlined in the Standards of Practice, along with the inspector's obligations to the client.
A home inspector must examine porches and railings in accordance with the ASHI (American Society of Home Inspectors) Standard of Practice.
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Help need correct answer asap
Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on the ice. One skater follows
the path y = - 2x + 14, while the other skater follows the curve y = - 2x^2+ 14x.
Find all the points where they might collide if they
are not careful.
The two skaters might collide at the points (1, 12) and (7, 0).
What are the collide points?
To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.
Setting the two expressions for y equal to each other, we get:
-2x + 14 = -2x² + 14x
Simplifying this equation, we get:
2x² - 16x + 14 = 0
Dividing both sides by 2, we get:
x² - 8x + 7 = 0
This equation can be factored as:
(x - 1)(x - 7) = 0
Therefore, the possible values of x where the skaters might collide are x=1 and x=7.
To find the corresponding values of y, we can substitute each value of x into one of the original equations.
For x=1, we get:
y = -2(1) + 14 = 12
Therefore, one possible point of collision is (1, 12).
For x=7, we get:
y = -2(7)² + 14(7) = 0
Therefore, another possible point of collision is (7, 0).
Therefore, To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations simultaneously.
Setting the two expressions for y equal to each other, we get:
-2x + 14 = -2x² + 14x
Simplifying this equation, we get:
2x² - 16x + 14 = 0
Dividing both sides by 2, we get:
x² - 8x + 7 = 0
This equation can be factored as:
(x - 1)(x - 7) = 0
Therefore, the possible values of x where the skaters might collide are x=1 and x=7.
To find the corresponding values of y, we can substitute each value of x into one of the original equations.
For x=1, we get:
y = -2(1) + 14 = 12
Therefore, one possible point of collision is (1, 12).
For x=7, we get:
y = -2(7)² + 14(7) = 0
Therefore, another possible point of collision is (7, 0).
Therefore, the two skaters might collide at the points (1, 12) and (7, 0).
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what is the missing polynomial?
The missing polynomial is 40 - 4x - 12x²
How to find the missing polynomialThe missing polynomial is solved by comparing the polynomials as done below
? - (20 - 4x - 5x²) = 20 - 7x²
? = 20 - 7x² + (20 - 4x - 5x²)
comparing the terms
constant terms: 20 + 20 = 40
x terms : -4x
x² terms : -7x² - 5x² = -12x²
This can be combined as 40 - 4x - 12x²
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While riding "The Screamer" (an unreliable ferris wheel with a radius of 100 feet) you start getting nervous about how
high in the air you are...you estimate you're about 95 feet high in the air... how much could The Screamer have rotated
(round to the nearest whole degree). There are 2 answers
The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.
What is circumference?Circumference is the distance around the edge of a closed curve or a circle. It is the length of the boundary of a circular object or shape. In other words, it is the total length of the circular shape.
According to question:We can use trigonometry to determine the rotation's angle. The rider's height above the ground is equal to the ferris wheel's radius plus the distance travelled around its circle. Let's call the angle of rotation we're trying to find θ.
The distance traveled along the circumference of the wheel can be calculated as follows:
distance = θ/360 * 2πr
where r is the radius of the wheel. Substituting the given values, we get:
95 = 100 + θ/360 * 2π(100)
Simplifying the equation:
θ/360 = (95-100)/(2π(100))
θ/360 = -0.007957747
θ = -2.8661 degrees or 357.1339 degrees
So there are two possible answers: The Screamer could have rotated either about -2.87 degrees or 357.13 degrees from its starting position.
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False False Exercise 4 The steps to draw a pentagonal prism are listed below. Identify the missing step. response - correct Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Step 1: Draw identical pentagonal bases. Step 2: 1 Step 3: Change any hidden lines to dashed lines.
You could shade in the faces of the prism or add labels to identify different parts of the drawing.
What is Pentagonal ?
"Pentagonal" is an adjective that describes something that has five sides or angles. In geometry, a pentagon is a two-dimensional shape with five straight sides and five angles.
To draw a pentagonal prism, you'll need to follow these steps:
Draw identical pentagonal bases: Start by drawing two identical pentagons. Make sure they have the same size and shape. You can use a ruler and a protractor to help you draw the lines.
Draw five vertical lines: Connect each vertex of one pentagon to its corresponding vertex on the other pentagon using straight lines. These lines should be perpendicular to the base and have the same length. You should end up with five evenly spaced vertical lines.
Change any hidden lines to dashed lines: Identify any lines that won't be visible in the final drawing and change them to dashed lines. This will help to make the drawing easier to read and understand.
Add any additional details: Once you've completed the basic shape of the pentagonal prism, you can add any additional details or shading to make the drawing more realistic or interesting.
Therefore, You could shade in the faces of the prism or add labels to identify different parts of the drawing.
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It costs $3.50 for 25 fl. oz. of detergent. Which graph models a relationship with the same unit rate? 10 POINTS
The 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
What are arithmetic operations?Arithmetic operations is a concept that concerns the study of mathematical operations like addition, subtraction, division, and multiplication.
The determination on the type which is a better buy can be estimated by finding the cost of each detergent in the two cases.
To determine which is a better buy, we need to compare the cost per fl. oz. of detergent for both options.
For the first option, the cost is $3.99 for 25 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $3.99 / 25 fl. oz. ≈ $0.16/fl. oz.
For the second option, the cost is $6.99 for 90 fl. oz., so the cost per fl. oz. is:
Cost per fl. oz. = $6.99 / 90 fl. oz. ≈ $0.08/fl. oz.
Since the cost per fl. oz. is lower for the second option, it is a better buy. Therefore, the 90 fl. oz. option is a better buy compared to the 25 fl. oz. option.
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The complete question is:
It cost $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
Monday: 4 miles
Tuesday: 4 miles
Wednesday: 5 miles
Thursday: 5 miles
Friday: 7 miles
Saturday: 7 miles
Sunday: 7 miles
Joel is training for a marathon. He records the number of miles that he ran each day for a week. In two weeks he plans on increasing the distance he runs on Monday and Tuesday by 1 mile, and the distance he runs on Friday, Saturday and Sunday by 2 miles. How will this affect the RANGE of his data set?
Responses
A The range will increase by 2 miles.The range will increase by 2 miles.
B The range will not change.The range will not change.
C The range will increase by 4 miles.The range will increase by 4 miles.
D The range will increase by 1 mile.The range will increase by 1 mile.
Answer:
the answer is d
Step-by-step explanation:
before the increase the range is three with the lowest number being four and the highest 7
where as after the increase the lowest value is 5 and the highest nine giving us a range of four
four minis three is one therefore the range increases by one mile
Answer: D: The range will increase by 1 mile.
Step-by-step explanation:
The current range is solved by doing the highest number minus the lowest number, so 7-4. The current range would therefore be 3.
The miles on Monday and Tuesday have been increased by 1 mile, from 4 miles to 5 miles.
The miles on Friday, Saturday and Sunday have been increased by 2 miles, from 7 miles to 9 miles.
You subtract the new values: 9 miles - 5 miles = 4 miles
And subtract your new values from your old range: 4 miles - 3 miles = 1 mile
The range would therefore increase by 1 mile.
10b + 12 = 62
what is b?
Step-by-step explanation:
10b = 62 - 12
10b = 50
b = 50/10
b = 5
Answer:
5
Step-by-step explanation:
When trying to find the value of an unknown variable, it is important to take into factors on how to reverse an effect being done to the variable, which is how we can isolate b and figure out the value.
- Addition reverses subtraction
- Multiplication reverses division
We have a simple equation, [tex]10b+12=62[/tex] , and we need to work around the variable b in order to isolate it. By doing this, we are able to find the true value of b.
We can subtract 12 on each side to get the term away from the constant.
[tex]10b+12=62[/tex]
- 12 -12
[tex]10b=50[/tex]
Then, to isolate the variable from the coefficient, which is 10, we can divide it to negate the multiplication factor on the term.
[tex]\frac{10b}{10} = \frac{50}{10}[/tex]
b=5
Therefore, the variable b=5.
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Find where f(x) = g(x), when f(x) = √40x and g(x)=√x + 3.
Therefore, f(x) = g(x) when function x is approximately 0.235 or 33.765.
Quadratic equations?A quadratic equation is a polynomial equation of the second degree, which means that the highest power of the variable in the equation is 2. A general quadratic equation can be written in the form:
[tex]ax^2 + bx + c = 0[/tex]
Where 'a', 'b', and 'c' are constants, and 'x' is the variable. The value of 'x' that satisfies the equation is called the root or solution of the equation.
To find where f(x) = g(x), we need to solve the equation:
[tex]\sqrt40x = \sqrt{x} + 3[/tex]
Squaring both sides, we get:
[tex]40x = (x + 3)^2[/tex]
Expanding the right-hand side, we get:
40x = x² + 6x + 9
Bringing all terms to one side, we get:
[tex]x^2- 34x - 9 = 0[/tex]
We can solve this quadratic equation using the quadratic formula:
[tex]x = (-b± \sqrt{(b^2 - 4ac))}/2a[/tex]
where a = 1, b = -34, and c = -9.
Plugging in these values, we get:
x = (34 ± √ (34² + 419)) / 2
x = (34 ± √1165) / 2
x ≈ 0.235 or x ≈ 33.765
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The weight of 1000 children's an average of 50 kilograms and the standard deviation is 5 kilograms how many children weigh between 40 kilograms and 55 kilograms
There are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
What is Standard deviation ?
Standard deviation is a measure of the spread or dispersion of a set of data from its mean. It is calculated as the square root of the variance.
To solve this problem, we can use the properties of a normal distribution, assuming that the weights of the children follow a normal distribution.
We know that the mean weight of 1000 children is 50 kilograms and the standard deviation is 5 kilograms. This means that the weights of the children are distributed around the mean with a spread of 5 kilograms.
We want to find the number of children who weigh between 40 kilograms and 55 kilograms. To do this, we can standardize the values using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We can use the following formula to standardize the values:
z = (x - μ) ÷ σ
where z is the standard score, x is the raw score, μ is the mean, and σ is the standard deviation.
For x = 40 kilograms:
z = (40 - 50) ÷ 5 = -2
For x = 55 kilograms:
z = (55 - 50) ÷ 5 = 1
Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 1. This area represents the proportion of children who weigh between 40 kilograms and 55 kilograms.
Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 1 is approximately 0.8186.
Therefore, the number of children who weigh between 40 kilograms and 55 kilograms is:
0.8186 * 1000 = 818.6 children
Since we can't have a fraction of a child, we round this number to the nearest whole number, which is 819 children.
Therefore, there are approximately 819 children who weigh between 40 kilograms and 55 kilograms.
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the official world record for the men's marathon is 2 hours and 3 minutes 59 seconds set by Haile Gebrselassie of Ethiopia. This berlin, marathon, held in September 2008, was 42.195 kilometers long. Write Gebrselassie's average speed for this marathon in meters per second. round your answer to the nearest tenth
Step-by-step explanation:
2 hrs = 7200 seconds
3 min 59 = 239 s
total seconds = 7439 s
42.195 km = 42159 m
42159 m / 7439s = 5.7 m/s
PLEASE ANSWR ASAP BOTH QUESTIONS WITH WORK WILL MARK BRAINLIST
The answer of 2nd question Quadrilateral JUMP in a circle is = Supplementary
What do you mean by Supplementary angle?
Supplementary angles are two angles whose measures add up to 180 degrees. In other words, if angle A and angle B are supplementary, then A + B = 180 degrees.
Supplementary angles are important in geometry and trigonometry, and they can be used to solve various problems involving angles and their measures. For example, if you know that two angles are supplementary and you know the measure of one of them, you can find the measure of the other by subtracting the measure of the known angle from 180 degrees.
According to question
Quadrilateral JUMP in a circle so opposite angle J and M is supplementary
∴ The sum of opposite angle of a circle Quadrilateral is supplementary
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Factor x2y – 3xy – 40y.
A cereal comes in three different package sizes.
8 = $12
12 = $16
16 = $20
What is the ratio of the cost of an 8-ounce box to a 16-ounce box of
cereal?
1:2
3:5
5:3
2:1
Answer: To find the ratio of the cost of an 8-ounce box to a 16-ounce box of cereal, we can divide the cost of an 8-ounce box by the cost of a 16-ounce box:
8 oz: $12
16 oz: $20
The ratio of the cost of an 8-ounce box to a 16-ounce box of cereal is:
12/20 = 3/5
So the answer is 3:5.
Step-by-step explanation:
Here are three similar cuboids, A, B and C.
A has length 6 cm, width 2 cm
and height 5 cm
B has length 12 cm
C has length x cm
b) Volume of A x 343/8 = Volume of C
Work out the value of x in cm.
Your final line must be, x = ...cm
The required value of x is approximately [tex]x = 257.25[/tex] cm.
How to find the volume of cuboid?The volume of cuboid A can be found by multiplying its length, width, and height:
[tex]$V_A = 6\text{ cm} \times 2\text{ cm} \times 5\text{ cm} = 60\text{ cm}^3$[/tex]
To find the volume of cuboid C, we can use the given information that the volume of A multiplied by 343/8 is equal to the volume of C:
[tex]$V_C = V_A \times \frac{343}{8} = 60\text{ cm}^3 \times \frac{343}{8} =2572.5[/tex]
Now, we can use the formula for the volume of a cuboid to find the length of C:
[tex]$V_C = \text{length} \times \text{width} \times \text{height}$[/tex]
[tex]$2572.5}\text{ cm}^3 = x\text{ cm} \times 2\text{ cm} \times 5\text{ cm}$[/tex]
[tex]{2572.5}\text{ cm}^3 = 10x\text{ cm}^3$[/tex]
[tex]x = 257.25[/tex]
Therefore, the value of x is approximately [tex]x = 257.25[/tex] cm.
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The rectangle below represents a table top that Lakita wants to cover with tiles. Each tile has an area of 7 square inches. To find the maximum number of tiles that will fit the table top, Lakita wants to use the inequality 7x < y. What is the value of y? What is the maximum number of tiles she can use?
The total space that the tiles will cover is 7x, where x is the number of tiles, and each tile has an area of 7 square inches. the maximum number of tiles that Lakita can use is [tex]20[/tex] .
What are the parameters for maximum number?Since each tile has an area of 7 square inches, the total area that the tiles will cover is 7x, where x is the number of tiles.
Lakita wants to find the maximum number of tiles she can use, so she needs to find the largest integer value of x that satisfies the inequality 7x < y, where y is the total area of the table-top.
To find the value of y, we need to find the area of the rectangle. The rectangle is 10 inches wide and 14 inches long, so its area is:
A = length × width [tex]= 10 \times 14 = 140[/tex] square inches
Therefore, [tex], y = 140[/tex] square inches.
To find the maximum number of tiles, we can divide the total area of the table-top by the area of each tile:
[tex]x = y/7 = 140/7 = 20[/tex]
Therefore, the maximum number of tiles that Lakita can use is [tex]20[/tex] .
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