Answer:
The problem statement suggests that the series of donations is arithmetic, as each student's donation increases by one as their number increases. Therefore, we can apply the formula for the sum of an arithmetic series to solve this problem.
In an arithmetic series, the sum S of n terms is given by:
S = n/2 * (a + l)
where:
- n is the number of terms (which represents the number of students in this case),
- a is the first term (in this case, the first student's number, which would be 1), and
- l is the last term (in this case, the last student's number, which we don't know yet).
Given that S = Rs. 13225, we have:
13225 = n/2 * (1 + l)
Since this is an arithmetic series starting from 1, the last term, l, is equal to n. Thus, we can substitute l with n:
13225 = n/2 * (1 + n)
Multiplying through by 2 to clear the fraction gives:
26450 = n * (1 + n)
Rearranging to a quadratic equation gives:
n^2 + n - 26450 = 0
This is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for n, we can use the quadratic formula, n = [-b ± sqrt(b^2 - 4ac)] / (2a). But since n cannot be negative in this context (as it represents the number of students), we will only consider the positive root.
Applying the quadratic formula, we find that the positive root is approximately 162.5. However, the number of students must be a whole number. Therefore, the number of students is 163, because the 163rd student did not donate fully as per their number, and that's why the total amount doesn't reach the full sum for 163 students.
So, there were 163 students who donated money to the fund.
Determine if the figure is a right triangle by substituting the side lengths into the Pythagorean formula.
Is ABC a right triangle? (0.73 cm) (0.7 cm) (0.24 cm)
Yes or no?
The figure ABC is not a right triangle
How to determine if the figure is a right triangleFrom the question, we have the following parameters that can be used in our computation:
Side lentghs = (0.73 cm) (0.7 cm) (0.24 cm)
Using the Pythagorean formula, we have
Square of longest sides = Sum of the squares of the other sides
using the above as a guide, we have the following:
0.73² = 0.7² + 0.24²
Evaluate
0.5329 = 0.5476
This equation is false
Hence, ABC is not a right triangle
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-
PART B: Use the digits 7 to 7 one time each to create five equations in which the value of x in all five equations is negative.
Show or explain your reasoning.
Below are five equations using the digits 7 to 7, each with a negative value for x:
How to explain the equationsEquation: 7 + x = 0
Explanation: If we subtract 7 from both sides, we get x = -7. Therefore, the value of x in this equation is negative.
Equation: x - 7 = -14
Explanation: If we add 7 to both sides, we get x = -7. Hence, the value of x in this equation is negative.
Equation: 7x - 14 = 0
Explanation: We can rearrange the equation as 7x = 14, and then divide both sides by 7, yielding x = 2. However, we are looking for a negative value of x. By negating the equation, we get -7x + 14 = 0. Solving for x gives x = -2, which is a negative value.
Equation: -7x + 14 = 0
Explanation: We can rearrange the equation as -7x = -14, and then divide both sides by -7. This yields x = 2, which is a positive value. However, we are looking for a negative value of x. By negating the equation, we get 7x - 14 = 0. Solving for x gives x = -2, which is a negative value.
Equation: -7 + x = -14
Explanation: If we subtract x from both sides, we get -7 = -14 - x. By rearranging the equation, we have -x = -7 - 14, which simplifies to -x = -21. Dividing both sides by -1 gives x = 21, but we need a negative value of x. Therefore, we can negate the equation, resulting in 7 - x = 14. Solving for x gives x = -7, which is a negative value.
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Question 13 (2 points)
If Mary bought 16 of the Brand X batteries, how many of them lasted more than 14 hours? (Please
show how you calculated this to get your answer) (2 points)
The number of brand X batteries that would last more than 14 hours is 12.
Interpreting the BoxplotBatteries with 14 hours battery life falls in the first quartile which is 25% of the distribution. Hence, 75% lasted more than 14 hours.
From the information we have established, If Mary bought 16 brand X batteries , then;
75% of the number of batteries would give us the answer :
75% of 16
0.75 × 16 = 12.
Therefore, 12 batteries would last more than 14 hours .
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7 over 19 as a percentage
Answer:
36.84%
Step-by-step explanation:
7 over 19 as a percentage?
We Take
(7 ÷ 19) x 100 ≈ 36.84%
So, the answer is 36.84%.
Determine the value of x in the figure below:
NO LINKS!
Answer:
x = 4
Step-by-step explanation:
Vertically opposite angles are equal.
5x + 3 = 2x + 15
Make x the subject:
Take 2x away from both sides.3x + 3 = 15
Take 3 away from both sides.3x = 12
Divide both sides by 3.x = 4
What is the compound interest earned on a four year investment at $3500 at 4.5% compounded monthly
The compound interest earned on a four year investment at $3500 at 4.5% compounded monthly is $724.46 (calculated by subtracting the initial investment amount of $3500 from the total amount of $4224.46).
Compound interest is the interest that is generated on the interest that has been accrued over a certain period of time.
The compound interest that is earned on a four year investment at $3500 at 4.5% compounded monthly can be calculated using the formula for compound interest, which is given as:
A = P(1 + r/n)^(nt)
Where:
A is the total amount of money after the investment period,P is the principal or initial amount of money invested,r is the annual interest rate,n is the number of times the interest is compounded in a year,
t is the total number of years the investment is held.Substituting the given values in the above formula,
we get:A = 3500(1 + 0.045/12)^(12*4)A
= 3500(1 + 0.00375)^(48)A
= 3500(1.00375)^(48)A
= 3500(1.2067)A
= $4,224.46
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Write two numbers that multiply to the value on top and add to the value on bottom.
-18
7
Answer:
9, -2
Step-by-step explanation:
You want two numbers with a product of -18 and a sum of 7.
FactorsThese are easiest if you list the factor pairs of the product. You want to choose them so their sum has the sign of the required sum.
-18 = (-1)(18) = (-2)(9) = (-3)(6)
Sums of these factor pairs are 17, 7, 3.
The pair of numbers you want is -2 and 9.
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Let f(x) be defined by the graph below.
Let g(x) = log(x+2) and h(x) = 2x/x+4
Select TWO x-values below that lie in the domain of all three functions
A) x = -4
B) x = -2
C) x = 0
D) x = -1
TWO x-values below that lie in the domain of all three functions are
C) x = 0
D) x = -1
How to find the domain valuesDomain values refer to the set of possible input values for a function or mathematical expression. In other words, the domain is the set of all possible x-values for which the function or expression is defined.
The equations is investigated as follows
h(x) = 2x / (x + 4) : would not have a domain of -4
log(x + 2 : would not have a domain of -2
The graph can have a domain of 0 and -1 hence this remains the correct option
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Find the probability that a randomly selected point within the square falls in the red-shaded square. 2 3 2 3 P = [?]
The probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.
To find the probability that a randomly selected point within the square falls in the red-shaded square, we need to compare the areas of the red square and the larger square.
The area of the larger square is given by the formula:
Area = side length x side length
In this case, the side length of the larger square is 3 units, so its area is:
Area of larger square = 3 x 3 = 9 square units
The area of the red square is given by the formula:
Area = side length x side length
In this case, the side length of the red square is 2 units, so its area is:
Area of red square = 2 x 2 = 4 square units
To find the probability, we divide the area of the red square by the area of the larger square:
Probability = Area of red square / Area of larger square
Probability = 4 / 9
Therefore, the probability that a randomly selected point within the square falls in the red-shaded square is approximately 0.4444, or 44.44%.
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If the measure smallest angle is a. 120° vb. 40° of for angles of a quadrilateral are in the ratio 1: 2: 4:5, then the d. 30° b. 60° c. 120° c. 45°
the correct option is b) 60°, as the smallest angle is 40°.
Step-by-step explanation:
Let's assume the angles of the quadrilateral are \(a\), \(2a\), \(4a\), and \(5a\), respectively.
According to the given information, the smallest angle is \(a\), which is either 120° or 40°.
a) If \(a = 120°\):
The four angles of the quadrilateral would be 120°, 240°, 480°, and 600°, respectively. However, angles in a quadrilateral cannot exceed 360°, so this option is not valid.
b) If \(a = 40°\):
The four angles of the quadrilateral would be 40°, 80°, 160°, and 200°, respectively. These angles are within the valid range for a quadrilateral.
Therefore, the correct option is b) 60°, as the smallest angle is 40°.
The table below shows (1) the population of Newark from 1840 to 2020 and (2) Newark's national population rank from 1840 to
2020.
Year
1840
1850
1860
1870
1880
1890
1900
1910
1920
1930
Population
17,290
38.864
71.941
105,059
135,508
181.830
246,070
347/MA
414.524
442.337
US Rank
123
19
11
13
15
17
16
14
15
18
Year
1940
1950
1960
1970
1980
1990
2000
2010
2020
Population
429,760
438.776
405.220
382417
329.240
275.291
272.665
277,140
310,350
US Rank
18
21
30
46
56
64
68
63
PART A: Find the percent increase in Newark's population from 2010 to 2020. Show or explain your reasoning
PART B: Find the decade in which Newark's population had the greatest percent increase. Show or explain your reasoning
PART C Find the 30-year period in which Newark's population had the greatest percent decmase. Show or explain your reasoning
PART D: Explain how it is possible that from 1920 to 1930, the Newark population increased from $14.524 to 442.337 yet Newark
fell from being the 15th largest city in the nation to the 18th largest city in the nation
The percent increase in Newark's population from 2010 to 2020 is 11.98%.
By comparing percent increases, the greatest percent increase occurred in the 1840s - 1850s decade with 124.83%.
What is the percent increase in Newark's population from 2010 to 2020?To get percent increase, we have to find difference between the population in 2020 and 2010, divide it by the population in 2010, and then multiply by 100.
Population in 2010: 277,140
Population in 2020: 310,350
Percent increase = ((310,350 - 277,140) / 277,140) * 100
Percent increase = (33,210 / 277,140) * 100
Percent increase = 11.983113228
Percent increase = 11.98%.
What decade did Newark's population have the greatest percent increase?To know decade with the greatest percent increase, we need to calculate percent increase for each decade and compare the values.
Percent increase for each decade goes as follows:
1840s to 1850s:
= ((38,864 - 17,290) / 17,290) * 100
≈ 124.83%
1850s to 1860s:
= ((71,941 - 38,864) / 38,864) * 100
≈ 85.08%
1860s to 1870s:
= ((105,059 - 71,941) / 71,941) * 100
≈ 45.87%
2010s to 2020s:
= ((310,350 - 277,140) / 277,140) * 100
≈ 11.97%
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enter the number that belongs in the green box
Answer:
Set your calculator to degree mode.
[tex] \frac{ \sin(29) }{6.78} = \frac{ \sin(x) }{4} [/tex]
[tex]6.78 \sin(x) = 4 \sin(29) [/tex]
[tex] \sin(x) = \frac{4 \sin(29) }{6.78} [/tex]
[tex]x = {sin}^{ - 1} ( \frac{4 \sin(29) }{6.78} ) = 16.62[/tex]
The number that belongs in the green box is 16.62.
A bag contains 3 blue marble, 7 green marbles, and 4 yellow marbles. Three marbles are picked from the bag at random without replacement. What is the probability that 2 green marbles and 1 blue marble are picked from the bag?
To find the probability of picking 2 green marbles and 1 blue marble from the bag, we need to determine the number of favorable outcomes (picking 2 green marbles and 1 blue marble) and the total number of possible outcomes.
Step 1: Determine the number of green marbles:
The given information states that there are 7 green marbles.
Step 2: Determine the number of blue marbles:
The given information states that there are 3 blue marbles.
Step 3: Determine the total number of marbles:
The given information states that there are 3 blue marbles + 7 green marbles + 4 yellow marbles = 14 marbles in total.
Step 4: Calculate the probability of picking 2 green marbles and 1 blue marble:
When picking without replacement, the probability of multiple events occurring is the product of their individual probabilities.
The probability of picking the first green marble is: 7 green marbles / 14 total marbles = 7/14.
After picking the first green marble, the total number of marbles remaining is 13 (since one green marble is already picked).
The probability of picking the second green marble from the remaining marbles is: 6 green marbles / 13 remaining marbles = 6/13.
After picking the second green marble, the total number of marbles remaining is 12 (since two green marbles are already picked).
The probability of picking the blue marble from the remaining marbles is: 3 blue marbles / 12 remaining marbles = 3/12.
To find the probability of all events occurring (picking 2 green marbles and 1 blue marble), we multiply their individual probabilities:
Probability of picking 2 green marbles and 1 blue marble = (7/14) * (6/13) * (3/12) = 126/2184 = 9/156.
Therefore, the probability of picking 2 green marbles and 1 blue marble without replacement is 9/156.
Please mark me as a
Brainliest
If the spinner is spun 1200 more times, about how many times would you expect to land on green? Round your answer to the nearest whole number.
The 156 times would expect to land on the green.
The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Given that the spinner is spun 1200 more times,
Probability of green:
P= 39/300
A number of attempts:
1200
Expected number of landing on green:
Expected frequency = probability × number of trials
1200 x 39/300 = 156 times
Hence, Answer is 156 times
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Help!!
a^n+3 -3a^n+2 -4a^n+1 -a^n by -a^n x²
[tex] \bold{a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n} \: \: by \: \: - a {}^{n} \: \: x {}^{2} }[/tex]
Step by step explanation :Case of multiplication of a Polynomial by a monomial. The rule says that, to multiply the monomial by each of the terms of the polynomial, taking into account the law of signs, separating the partial products with their own signs. That is, we apply the Distributive Law of multiplication.
Then, we will solve by Distributive law.
[tex]\bold{(a {}^{n + 3} - 3a {}^{n + 2} - 4a {}^{n + 1} - a {}^{n})( \: \: - a {}^{n} \: \: x {}^{2} ) }[/tex]
[tex] \sf{a {}^{n + 3}( - a {}^{n}x {}^{2}) - 3a {}^{n + 2}( - a {}^{n}x {}^{2}) - 4a {}^{n + 1} ( - a {}^{n} x {}^{2} ) - a {}^{n} ( - a {}^{n} x {}^{2}) }[/tex]
[tex] \sf{ - 1 \cdot 1a {}^{n + 3 + n}x {}^{2} + 3 \cdot1 a{}^{n + 2 + n}x {}^{2} + 4 \cdot1a {}^{n + 1 + n}x {}^{2} + 1 \cdot1a {}^{n + 2}x {}^{2} }[/tex]
[tex]\bold{ Answer}=\sf{- a {}^{2n + 3} x {}^{2} + 3a {}^{2n + 2}x {}^{2} + 4a {}^{2n + 2}x {}^{2} + a {}^{2n} x {}^{2}} [/tex]
Collect the data on consumption of electricity at your home and compute daily consumption of number of units. Using this data, compute the arithmetic mean.
To compute the arithmetic mean, you would need multiple data points of daily electricity consumption. For example: (30 + 35 + 25 + 40 + 30 + 35 + 40) kWh / 7 days = 33.57 kWh per day
To compute the daily consumption of electricity in units, you need two pieces of information: the total consumption of electricity and the time period over which it was measured. Let's assume you have the total consumption in kilowatt-hours (kWh) and the number of days the consumption was measured.
To calculate the daily consumption, divide the total consumption by the number of days. For example, if the total consumption is 300 kWh and it was measured over 10 days, the daily consumption would be 300 kWh / 10 days = 30 kWh per day.
To compute the arithmetic mean, you would need multiple data points of daily electricity consumption. Let's say you have collected data for a week, with daily consumption values of 30 kWh, 35 kWh, 25 kWh, 40 kWh, 30 kWh, 35 kWh, and 40 kWh. Add up all the daily consumption values and divide the sum by the number of days to calculate the mean.
For example: (30 + 35 + 25 + 40 + 30 + 35 + 40) kWh / 7 days = 33.57 kWh per day.
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What is the angle of p in the drawing below? Type in numerical answer only
Answer:
57° + 108° + p = 180°
165° + p = 180°
p = 15°
Find the least number which should be Subtracted from 56037 so that the difference is exactly divisible by 139.
Answer:
Answer will be 55898.
Step-by-step explanation:
Four people started a business by investing the following amounts: A: N30 000, B: N40 000, C: N60 000, D: N70 000. They agreed that A, as manager, should get one third of the profits, the rest being divided between all four in proportion to their investments. a Draw a pie chart showing the ratio of their investments. b Draw a pie chart to show how the profit was divided.
Answer: Ratio of their investments is 3:4:6:7. Ratio of profits is 13:4:6:7.
Step-by-step explanation:
a. we know that their investments are 30,000 , 40,000 , 60,000 , 70,000 respectively.
so the ratio o their investments is, A:B:C:D = 3:4:6:7
A: (360-120) x (30000/ 30000+40000+60000+70000) = 36
B: (360-120) x (40000/ 30000+40000+60000+70000) = 48
C: (360-120) x (60000/ 30000+40000+60000+70000) = 72
D: (360-120) x (70000/ 30000+40000+60000+70000) = 84
b. For dividing the profit, it is given that 1/3rd of the profit is reserved for the manager. So,
1/3 of360 = 120
A: 120 + (360-120) x (30000/ 30000+40000+60000+70000) = 156
B: (360-120) x (40000/ 30000+40000+60000+70000) = 48
C: (360-120) x (60000/ 30000+40000+60000+70000) = 72
D: (360-120) x (70000/ 30000+40000+60000+70000) = 84
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can you help me silve this please
Answer: Area of Cylinder = 753.982
Step-by-step explanation:
Given:
h = 7 cm
r = 8cm
Formula for cylinder:
A = (Perimeter of base) x height + 2 (Area of Base)
Breakdown:
Perimeter of base = 2[tex]\pi r[/tex]
Perimeter of base = 2 [tex]\pi[/tex] (8)
Perimeter of base = 50.2655
Area of Base = [tex]\pi r^{2}[/tex]
Area of Base = [tex]\pi 8^{2}[/tex]
Area of Base = 201.0619
Area of Cylinder = (Perimeter of base) x height + 2 (Area of Base)
Area of Cylinder = (50.2655)(7) +2(201.0619)
Area of Cylinder = 753.982
Using the standard normal table or a calculator, find the probability below assuming the distribution is a standard normal distribution. P(Z > −1.3)
The probability P(Z > -1.3) in a standard normal distribution is approximately 0.9032 or 90.32%.
We have,
To find the probability P(Z > -1.3) in a standard normal distribution, you can use a standard normal table or a calculator that provides cumulative probabilities.
Using a standard normal table:
The standard normal table provides the cumulative probabilities for values between 0 and the given z-score.
Since we want to find the probability of Z greater than -1.3, which is on the left side of the mean, we need to find the complementary probability of Z less than or equal to -1.3 and subtract it from 1.
Looking up -1.3 in the standard normal table, we find the cumulative probability to be 0.0968.
The probability P(Z > -1.3) is:
P(Z > -1.3) = 1 - P(Z ≤ -1.3)
P(Z > -1.3) = 1 - 0.0968
P(Z > -1.3) ≈ 0.9032
Using a calculator:
If you have a calculator that provides cumulative probabilities for the standard normal distribution, you can directly input the value -1.3 to find the probability.
Using the calculator, you would calculate:
P(Z > -1.3) ≈ 0.9032
Therefore,
The probability P(Z > -1.3) in a standard normal distribution is approximately 0.9032 or 90.32%.
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A rectangular room has length L and width W, where L and W are measured in feet.
a. Express the area in square feet algebraically.
b. If carpeting costs x dollars per square yard, express the cost of carpeting this room algebraically.
The area of rectangular room with length L and width W is LW/9 square yard.
Given that, a rectangular room has length L and width W, where L and W are measured in feet.
Here, L feet = L/3 yard and W feet = W/3 yard
a) Area = Length×Width
= L/3 × W/3
= LW/9 square yard.
b) Carpeting costs x dollars per square yard.
Total cost = x×LW/9
= LWx/9 dollars
Therefore, the area of rectangular room with length L and width W is LW/9 square yard.
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5 ten thousands 8 thousands 3 hundreds 7 tens 4 ones in standard
Step-by-step explanation:
Just : 5,8374
(q4) Which of the following integrals can be used to find the length of the curve described by the function
The arc length of a Curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx , the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.
The arc length of a curve is given by the formula:`L = int_a^b sqrt(1 + [f'(x)]^2) dx
where L is the length of the curve between x = a and x = b. In this formula, `f(x)` is the equation of the curve being considered and `f'(x)` is the derivative of `f(x)` with respect to x.
Using this formula, the following integrals can be used to find the length of the curve described by the function:`L = int_0^1 sqrt(1 + 4x^2) dx`This is because the function being described by this integral is the equation of a curve, and the integral finds the length of this curve between `x = 0` and `x = 1`.
To evaluate the integral, we can use trigonometric substitution. Let `x = (1/2) tan(theta)`. Then `dx/dtheta = (1/2) sec^2(theta)`, so `1 + 4x^2 = 1 + 2 tan^2(theta) = sec^2(theta)`.Substituting these expressions into the integral, we have:
`L = int_0^1 sqrt(1 + 4x^2) dx = int_0^(pi/4) sec(theta) (1/2) sec^2(theta) theta = (1/2) int_0^(pi/4) sec^3(theta) dtheta`
This integral can be evaluated using integration by parts, and the final answer will be in terms of trigonometric functions.
Therefore, the correct option is given by `L = int_0^1 sqrt(1 + 4x^2) dx`.
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there are 600 counters in a bag .
the counters are blue or red or yellow.
5/12 of the counters are blue.
194 of the counters are red
what precentage of the counters are yellow ?
step by step plsss
xoxoxoxoxo
Approximately 26 percentage of the counters are yellow.
To find the percentage of counters that are yellow, we first need to determine the total number of yellow counters.
Given that there are 600 counters in total, we know that the sum of the number of blue, red, and yellow counters should equal 600.
From the information provided, we know that 5/12 of the counters are blue. We can calculate the number of blue counters as follows:
Blue Counters = (5/12) * 600 = 250
We also know that 194 of the counters are red.
So, the total number of blue and red counters is:
Blue Counters + Red Counters = 250 + 194 = 444
To find the number of yellow counters, we subtract the sum of blue and red counters from the total number of counters:
Yellow Counters = Total Counters - (Blue Counters + Red Counters) = 600 - 444 = 156
Now, we can calculate the percentage of yellow counters by dividing the number of yellow counters by the total number of counters and multiplying by 100:
Percentage of Yellow Counters = (Yellow Counters / Total Counters) * 100 = (156 / 600) * 100 ≈ 26%
Therefore, approximately 26% of the counters are yellow.
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You are contracted to fabricate a gate with specifications shown below. You are using 1/4" x 3/4" flat bar. How many feet of flat bar is needed to complete the gate? Regardless of the remainder amount - round up to the nearest whole number
44
46
42
48
The number of feet of flat bar needed to complete the gate is 34 feet (rounded up to the nearest whole number).
To calculate the number of feet of flat bar needed to complete a gate with the given specifications of 1/4" x 3/4" flat bar, we can follow these steps:
Step 1: Convert the measurements to Feet To convert the measurements from inches to feet, we can divide them by 12. So, 1/4" = 0.02083 ft and 3/4" = 0.0625 ft.
Step 2: Calculate the length of each flat bar piece Needed For each flat bar piece, we need to add up the length of all the sides that will be made from the flat bar.
From the specifications given, we can see that there will be six pieces of flat bar needed:
four vertical pieces and two horizontal pieces. The length of each vertical piece will be the height of the gate plus an additional 2 inches at the top for the curve, and the length of each horizontal piece will be the width of the gate plus an additional 2 inches on either side for the curves.
So, the length of each piece can be calculated as follows:
Vertical pieces: (48 + 2 + 2) x 2 x 0.02083 ft = 2.083 ft Each Horizontal pieces: (120 + 2 + 2) x 2 x 0.0625 ft = 15.625 ft Each
Step 3: Add up the total length of flat bar Needed Finally, we can add up the total length of flat bar needed by multiplying the length of each piece by the number of pieces, which is 6 in this case:
Total length of flat bar needed = 2.083 ft x 4 + 15.625 ft x 2= 33.33 ft (rounded up to the nearest whole number)
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........................................
Answer:
a) x = 2 and x = 4
Step-by-step explanation:
A quadratic function is a mathematical function of the form f(x) = ax² + bx + c, where a, b, and c are constants and x represents the independent variable.
The solutions of a graphed quadratic function are the x-values of the points where the parabola crosses the x-axis.
These solutions are also known as the x-intercepts, roots, or zeros of the quadratic function.
From inspection of the given graph, the function crosses the x-axis at x = 2 and x = 4.
Therefore, the solutions of g(x) = -x² + 6x - 8 are:
x = 2 and x = 4Answer:
x=2 and x=4.
Step-by-step explanation:
The solution of g(x)=-x^2+6x-8 is the point where the graph of the function intersects the x-axis. This point is (4,0) and (2,0).
Therefore, the solution of g(x)=-x^2+6x-8 is x=4 and x=2.
Another method:
Similarly, we can find the value of x by factorization method too.
g(x)=x^2+6x-8
let g(x)=0
0=x^2+6x-8
x^2-6x+8=0
doing middle-term factorization:
x^2-(4+2)x+8=0
x^2-4x-2x+8=0
x(x-4)-2(x-4)=0
(x-4)(x-2)=0
either
x=4
0r
x=2
Therefore x=4 and x=2.
Which statement below is not consistent with the distribution of sample means?
The statement that is inconsistent with the distribution of sample means is, "The distribution of sample means tends to pile up around the population standard deviation." Therefore the correct answer is option D.
The mean sample distribution does not "pile up" around the population standard deviation. The sample means are central tendency measurements that indicate the average values from various samples. The population standard deviation, on the other hand, measures the population's dispersion or variability. The spread of sample means can vary, but it does not explicitly "pile up" around the population standard deviation.
In summary, option (D) contradicts the distribution of sample means, since the distribution does not pile up around the population standard deviation. The other options (A, B, and C) appropriately represent the sample mean characteristics.
Learn more about distribution of sample means here:
brainly.com/question/30112112
The correct question is-
Which statement below is not consistent with the distribution of sample means?
A) The distribution of sample means tends to pile up around the population mean.
B) The distribution of sample means tends to be approximately normal.
C) The distribution of sample means depicts the means of all the random samples of a particular sample size.
D) The distribution of sample means tends to pile up around the population standard deviation.
The volume of the rectangular pyramid below is 468 units. Find the value of x.
Answer:
12
Step-by-step explanation:
Note that the area B of the rectangular base with length x and width 9 units is:
[tex]B=9x[/tex]
Then, the volume [tex]V=468[/tex] cubic units of the pyramid is related to its base area [tex]B=9x[/tex] and height [tex]h=13[/tex] as follows:
[tex]V=\frac{1}{3}Bh\\468=\frac{1}{3}\times 9x\times 13\\x=\frac{468\times3}{9\times 13}=12[/tex]
So, the value of x is 12.
Hello !
Answer:
[tex]\Large \boxed{\sf x=12}[/tex]
Step-by-step explanation:
The volume of a pyramid is given by [tex]\sf V_{pyramid}=\frac{1}{3}\times B\times h[/tex] where B is the area of the base and h is the height.
This is a rectangular pyramid. We have [tex]\sf B=l\times w[/tex] where l is the length and w is the witdth.
So [tex]\sf V_{pyramid}=\frac{1}{3}\times l \times w\times h[/tex]
Given :
l = xw = 9h = 13Let's substitute l, w and h with their values in the previous formula :
[tex]\sf V_{pyramid}=\frac{1}{3}\times x\times 9 \times 13\\\sf V_{pyramid}=3\times13\times x\\\sf V_{pyramid}=39x[/tex]
Moreover, we know that [tex]\sf V_{pyramid}=468\ units^3[/tex].
Therefore [tex]\sf 39x=468[/tex]
Let's solve for x :
Divide both sides by 39 :
[tex]\sf \frac{39x}{39} =\frac{468}{39} \\\boxed{\sf x=12}[/tex]
Have a nice day ;)
Show your work please help me please please help mee due Tuesday
Answer:
11.5 or 11 1/2 (eleven and a half)
Step-by-step explanation:
so we can add the whole numbers together
5 + 6 = 11
then we are left with the fractions
1/3 + 1/6
we need to make both sides equal so we multiply both the upper and lower part of 1/3 by 2
which gives us 2/6
then you simply add 2/6 and 1/6 together which is 3/6
3/6 can be simplified to 1/2 or 0.5
just add that back to the original 11 you added up and your final answer is
11.5 or 11 1/2 (eleven and a half)
Answer:
The answer is
[tex]11 \frac{3}{6} [/tex] or 11.5
or in simplest form
11½
Step-by-step explanation:
5⅓+6⅙
[tex] = \frac{16}{3} + \frac{37}{6} [/tex]
Taking LCM which is 6
[tex] \frac{ \frac{16}{3} + \frac{37}{6} }{6} [/tex]
[tex] \frac{2(16) + 1 \times 37}{6} [/tex]
[tex] \frac{32 + 37}{6} [/tex]
[tex] = \frac{69}{6} [/tex]
[tex] = 11 \frac{3}{6} [/tex]
11½ in simplest form or 11.5
