Question 11
A card game is being played and the 5 of spades and 10 of clubs are drawn. In order to win the
hand, the next card must be higher than the highest card already on the table. Assuming the
game is played with a single deck, what is the chance that the next card drawn will win the
hand? (An ace has a value of 1.)
A.3%
B.12%
I
C.24%
D.25%
Answer:
24%
Step-by-step explanation:
trust me and get blessed
The probability of drawing a card that could win the hand and actually winning the hand is 12%.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
There are 50 cards left in the deck after the 5 of spades and 10 of clubs are drawn since there are 4 suits with 13 cards each, and 2 of those cards have already been drawn.
Out of the remaining 50 cards, there are 16 cards that could win the hand: the 9 remaining cards higher than the 10 of clubs in any suit, and the 6 remaining cards in the spade suit (since the 5 of spades is already on the table).
Therefore, the probability of drawing a card that could win the hand is 16/50, which simplifies to 8/25. This is approximately 0.32 or 32%.
However, we need to subtract the probability of drawing the 5 of clubs, 10 of spades, or any of the 8 remaining cards that would not win the hand.
The probability of drawing one of these cards is 10/50, which simplifies to 1/5 or 20%.
The probability of drawing a card that could win the hand and actually winning the hand is:
(16/50) x (1/5)
= 0.32 - 0.2
= 0.12 or 12%.
Thus,
The probability of drawing a card that could win the hand and actually winning the hand is 12%.
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Collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community. Arrange the maximum temperature of the 30 days in ascending order to summarize the data. Determine the mean, mode, median, and range. Use the maximum temperature data and draw for each section a frequency table with appropriate intervals in ANNEXTURE B Display or represent the data from the frequency table on a pie chart in ANNEXTURE B. First, calculate the size of the angles for the pie chart. Example: Intervals between 20-30 are 5. Therefore the proportion of the Segment: 11 [360° = 72° Show all your calculations. 11 Which data collection best describe the maximum and why?
Answer:
I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion * 360° = 0.6 * 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.
A box is 11 inches high, 18 inches long and 8 inches wide. What is the longest poster you could fit in the box? Explain why you can only fit one maximum length poster in the box but you can fit multiple 21 inch posters in the same box
Answer: the longest poster that could fit in the box is approximately 22.56 inches long.
Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:
diagonal^2 = 11^2 + 18^2 + 8^2
diagonal^2 = 121 + 324 + 64
diagonal^2 = 509
inclining = sqrt(509)
corner to corner ≈ 22.56 inches
the perimeter of a semicircle protractor is 14.8cm,find it's radius
The radius of the semicircle protractor is approximately 4.693 cm.
Given,Perimeter of a semicircle protractor = 14.8 cm.
To find:The radius of a semicircle protractor.Solution:We know that the perimeter of a semicircle protractor is the sum of the straight edge of a protractor and half of the circumference of the circle whose radius is the radius of the protractor.
Circumference of a circle = 2πrWhere, r is the radius of the circle.If the radius of the semicircle protractor is r, then Perimeter of a semicircle protractor = r + πr [∵ half of the circumference of a circle =\((1/2) × 2πr = πr]14.8 = r + πr14.8 = r(1 + π) r = 14.8 / (1 + π)r ≈ 4.693\) cm.
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The average pencil has 5,425 pencil shavings. How many pencils are found in 76,450 pencil shavings?
Answer:
14
Step-by-step explanation:
We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.
Prove that if parallel lines are crossed by a transversal, then the alternate interior angles are congruent. That is, use rigid transformations to map ∠CFG onto ∠BCF. Explain.
Alternate interior angles are congruent if parallel lines are crossed by a transversal.
What is congruent geometry?In congruent geometry, the shapes that are so identical. can be superimposed on themselves.
Here,
A figure has been shown below,
Where there is 2 parallel line intersected by a transversal line.
The measure of the alternate angle [besides interior and exterior angle], their measure are equal to corresponding angles as well as with alternate angles. As shown in the figure.
Thus, alternate interior angles are congruent if parallel lines are crossed by a transversal.
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please help
What is the distance to the earth’s horizon from point P?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
x =
mi
The measure of distance x, that is, the distance between a point P and the point of horizon, is equal to 284.372 miles.
How to find the distance to the earth horizon from a given point
In this problem we must determine the distance between a point P located about earth's circumference and the point of horizon, located on earth's circumference. Since the line between these two points is tangent to earth, then, distance x can be found by Pythagorean theorem:
x = √[(3959 mi + 10.2 mi)² - (3959 mi)²]
x = 284.372 mi
The distance x is equal to 284.372 miles.
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Julia has 9 one pound bags of sand each a different color. For a art project she will use 1/8 lb of each bag of sand to create sand art jar. How much sand will be in the jar?
a. 8/9, b. 1/72, c. 1 1/9, d. 1 1/8
2x = 7, 2Y = 5, then 2 x - y
The calculated value of the expression 2x - y for the given values of x and y is 9/2.
Evaluating the expression for x and yWe are given that 2x = 7 and 2y = 5, and we are asked to find the value of 2x - y.
This means that
x = 7/2 and y = 5/2
We can start by substituting the given values into the expression:
2x - y = 2(7/2) - (5/2)
Notice that since 2x = 7, then x = 7/2.
Similarly, since 2y = 5, then y = 5/2. Substituting these values into the expression, we get:
2x - y = 2(7/2) - (5/2) = 7 - 5/2 = 9/2
Therefore, the value of 2x - y is 9/2.
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To find the distance between (-2,-3) and (4,1), Peggy's teacher drew a diagram and marked blue lines to represent the legs of a right triangle. Peggy then used 42 and 62 to find the distance represented by the red segment. What distance did she find ?
A √114
B √52
C 2020
D 5252
E 25
By using the formula for the distance we will see that the correct option is B:
√52
What distance did she find?
We will use the general formula to find the distance between two points (a, b) and (c, d)
it is:
distance = √( (a - c)^2 + (b - d)^2)
Here we want to find the distance between the points (-2,-3) and (4,1), if we use the above formula we will get:
distance = √( (-2 - 4)^2 + (-3 - 1)^2) = √( 36 + 16)
distance = √52
The correct option is B.
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A colonoscopy is a screening test for colon cancer, recommended as a routine test for adults over age 50. A new study provides the best evidence yet that this test saves lives. The proportion of people with colon polyps expected to die from colon cancer is 0.01. A sample of 2602 people who had polyps removed during a colonoscopy were followed for 20 years, and 12 of them died from colon cancer. Does this provide evidence that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01?
What are the null and alternative hypotheses?
Answer:
Null hypothesis H0: p = 0.01
Alternative hypothesis Ha: p < 0.01
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
The null hypothesis is that the proportion of people with colon polyps expected to die from colon cancer remains 0.01 with or without colonoscopy.
H0: p = 0.01
The alternative hypothesis is that the proportion of people who die from colon cancer after having polyps removed in a colonoscopy is significantly less than the expected proportion (without a colonoscopy) of 0.01.
Ha: p < 0.01
If the image is rotated about the x-axis, which of the following images best represents the result?
A. Y
B. Z
C. X
D. W
The images best represents the result is image W.
We have, the image is rotated about the x-axis.
Now, rotating around x axis can give the other half of the image.
Also, rotating about x axis gives the mirror image of the figure.
So, the rotation leads to a circle.
and, In three dimensional we can say that Sphere.
Thus, the required image is W.
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The length of a gulf park is 2.5km long is represented on a map by a line 250mm long.What is the scale of the map.
The scale of the map is 1/10,000.
The formula used to find the formula to find the scale is
scale = length on the map / actual length
Given,
Actual length of the golf park = 2.5 km
length on map = 250 mm
Here, we need to convert both lengths into the same units
2.5 km = 2.5 x 1000 m/km x 1000 mm/m = 2,500,000 mm
we know that,
scale = length on the map / actual length
= 250 mm / 2,500,000 mm
= 1/10,000.
Therefore, the scale of the map is 1/10,000.
i.e, one unit on the map is equal to 10,000 units of length in reality.
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A particle can move along only an x axis, where conservative forces act on it (Fig. 8−66 and the following table). The particle is released at x=5.00m with a kinetic energy of K=14.0J and a potential energy of U=0. If its motion is in the negative direction of the x axis, what are its (a) K and (b) U at x=2.00m and its(c) K and (d) U at x=0 ? If its motion is in the positive direction of the x axis, what are its (e) K and (f) U at x=11.0m, its (g) K and(h) U at x=12.0m, and its (i) K and ( j) U at x=13.0m? (k) Plot U(x) versus x for the range x=0 to x=13.0m.
Next, the particle is released from rest at x=0. What are (l) its kinetic energy at x=5.0m and (m) the maximum positive position x max it reaches? (n) What does the particle do after it reaches x = max ?
The remark in the problem is the statement that the forces can be associated with potential energies is explained as follows: the work from x=3.00m to x=2.00m is
W=F₂ Δx=(5.00N)(−1.00m)=−5.00J,
so the potential energy at x=2.00m is U₂=+5.00J.
(b Now, we should evident from the problem statement that Emax =14.0J, so the kinetic energy at x=2.00m is the kinetic energy at x=2.00m is
K₂=Emax−U₂=14.0−5.00=9.00J.
(c) the work from x=2.00m to x=0 is W=F₁Δx=(3.00N)(−2.00m)=−6.00J, so the potential energy at x=0 is
U₀=6.00J+U₂=(6.00+5.00)J=11.0J.
(d) Similar to reasoning presented in part (a) then gives
K₀=Emax−U₀=(14.0−11.0)J=3.00J.
(e) The work from x=8.00m to x=11.0m is
W=F₃Δx=(−4.00N)(3.00m)=−12.0J,
so the potential energy at x=11.0m is U₁₁=12.0J.
(f) The kinetic energy at x=11.0m is therefore
K₁₁=Emax−U₁₁=(14.0−12.0)J=2.00J.
(g) Now we have W=F₄Δx=(−1.00N)(1.00m)=−1.00J, so the potential energy at x=12.0m is
U₁₂=1.00J+U₁₁=(1.00+12.0)J=13.0J.
(h) Thus, the kinetic energy at x=12.0m is
K₁₂=Emax−U₁₂=(14.0−13.0)=1.00J.
(i) T There is no work done in the interval of x=12.0m to x=13.0m so the answers are the same as in part (g): U₁₂=13.0J.
.(j) In this also there is no work done in this interval so the answers are the same as in part (h): K₁₂=1.00J.
(k) Although the plot is not shown here, it would look like a “potential well” with piecewise-sloping sides: from x=0 to x=2 the graph of U is decreased from the line segment with 11 to 5, and from x=2 to x=3
it may be headed down to zero, where it stays until x=8, where it starts to increase to a value of 12 at which x=11, and in another positive-slope line segment it increased to the value of 13 at x=12.
For x>12 it is a value that does not change.
(l) The particle can be thought of as “falling” down the 0<x<3 slopes of the well, gaining kinetic energy as it does so, and certainly is able to reach x=5. Since U=0 at x=5, then its initial potential energy (11J) has completely converted to kinetic: now K=11.0J.
(m) This is not sufficient to climb up and out of the well on the large x side (x>8), but does allow it to reach a “height” of 11 at x=10.8m. As discussed in sections 8−5, this is a “turning point” of the motion.
(n) Next it “falls” back down and rises back up the small x slope until it comes back to its original position. Stating this more carefully, when it is stopped at x=10.8m it is accelerated to the left by the force F₃.
it gains enough speed as a result that it eventually is able to return to x=0, where it stops again.
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What is 6(4p - 2) + 2 (5p + 2)
Answer:
34p -8
Step-by-step explanation:
6 (4p- 2) + 2 (5p + 2)
24p - 12 + 2 (5p +2)
24p - 12 + 10p + 4
34p -8
find the surface area of the regular hexgonal prism.
Check the picture below.
so the hexagonal prism is really just a hexagon with six 8x27 rectangles, let's simply get the area of all and sum them up.
\(\textit{area of a regular polygon}\\\\ A=\cfrac{1}{2}ap ~~ \begin{cases} p=perimeter\\ a=apothem\\[-0.5em] \hrulefill\\ p=\stackrel{8\times 6}{48}\\ a=6.9 \end{cases}\implies A=\cfrac{1}{2}(6.9)(48)\implies A=165.6 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{six rectangles} }{(6)(8)(27)}~~ + ~~\stackrel{ \textit{hexgonal face} }{165.6}}\implies 1296+165.6\implies \text{\LARGE 1461.6}~in^2\)
Pls help math question 100 points NO SPAM
Step-by-step explanation:
U2 = 7
U1 = 35/2
r = 7 ÷ 35/2
r = 7 × 2/35
r = 14/35
r = 2/5
#7
Common ratio
t_3/t_214/5÷714/5×1/72/5#8
y=325d+8795As per slope intercept form 8795 is the y inetercept .
Here its
The fixed value for which the company charges excluding per car valueSolve: -5n + 6(5n - 5) = 38 + 8n
Consider the halfpipe with a diameter of 7 cm and a height of 20 cm.
Find its volume, rounding to 2 decimal places.
Answer: 384.85
Step-by-step explanation
Magic Realm, Inc., has developed a new fantasy board game. The company sold 15,000 games last year at a selling price of $20 per game. Fixed costs associated with the game total $182,000 per year, and variable costs are $6 per game. Production of the game is entrusted to a printing contractor. Variable costs consist mostly of payments to this contractor.
Required:
1) Prepare a contribution format income statement for the game last year and compute the degree of operating leverage.
2) Management is confident that the company can sell 18,000 games next year (an increase of 3,000 games, or 20%, over last year).
Compute:
a) The expected percentage increase in net operating income for next year.
b) The expected total dollar net operating income for next year.
The expected total dollar net operating Income for next year = $70,000
1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:
Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000
Variable expenses (15,000 × $6) = $90,000
Contribution margin = $210,000
Fixed expenses = $182,000Net operating income = $28,000
Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)
The expected percentage increase in net operating income for next year:
The expected sales in next year = 18,000
games selling price per game = $20
Therefore, Total sales revenue = 18,000 × $20 = $360,000
Variable expenses = 18,000 × $6 = $108,000
Fixed expenses = $182,000
Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses
= $360,000 – $108,000 – $182,000= $70,000
The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%
The expected total dollar net operating income for next year = $70,000
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a gallup poll utilizing a random sample of adults ages or older was conducted in april . the survey indicated a majority of americans () say driverless cars will be common in the next years (gallup,
A Gallup poll conducted in April found that 55% of Americans believe driverless cars will be common in the next 10 years, as presented in a histogram showing the percentage of responses in different time intervals.
A Gallup Poll was conducted in April that surveyed adults aged 18 or older to gauge their perceptions on when fully automated "driverless cars" will be commonly used in the United States.
The question asked was "how soon do you think driverless cars will be commonly used in the United States?" The survey indicated that 55% of Americans believe that driverless cars will be common in the next 10 years.
The results of the survey were presented in a histogram, showing the percentage of responses in different time intervals, which means it shows how many people responded within a certain time frame (e.g. within 5 years, within 10 years, etc.) when they think driverless cars will be commonly used.
This poll gives an insight into how people perceive the future of driverless cars and how soon they think it will become a common sight on the roads.
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The question is -
A Gallup Poll utilizing a random sample of adults ages or older was conducted in April. The survey indicated a majority of Americans () say driverless cars will be common in the next years (). The question asked was: Thinking about fully automated, "driverless cars," cars that use technology to drive and do not need a human driver, based on what you have heard or read, how soon do you think driverless cars will be commonly used in the [United States]? The figure below shows a summary of the results of the survey in a histogram indicating the percentage of the total responses in different time intervals.
What is the volume of the figure below? (Just put the number answer.)
Answer: 96ft³
Step-by-step explanation:
Answer:
96 ft³
Step-by-step explanation:
Volume = w × l × h
= 4 × 8 × 3
= 96 ft³
what fraction is 2500 of 3600
Answer:
25/36
Step-by-step explanation:
put 2500 over 3600 and remove the 0's to simplify it
which expression or expressions is equivalent to -24-12w
2) Ayanda wants to invest R200 000. The bank offers him 2 options for his
6 year investment.
Option 1: 12% Simple interest p.a.
Option 2: 9,5% Compound interest p.a.
4.2.1) Calculate the return on Ayanda's investment using Option 1.
●
●
4.2.2) Calculate the return on Ayanda's investment using Option 2.
4.2.3) Which option will render the most money?
Answer:
4.2.1) R140 000
4.2.2) R144 758.28
4.2.3) Option 2
Step-by-step explanation:
To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 12% = 0.12t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000 \cdot 0.12 \cdot 6\)
\(I=24000 \cdot 6\)
\(I=144000\)
Therefore, the return on Ayanda's investment using Option 1 is R144000.
\(\hrulefill\)
To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.
\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)
Given values:
P = R200 000r = 9.5% = 0.095t = 6 yearsSubstitute the given values into the formula and solve for I:
\(I=200000(1+0.095)^6-200000\)
\(I=200000(1.095)^6-200000\)
\(I=200000(1.72379142...)-200000\)
\(I=344758.28426...-200000\)
\(I=144758.28426...\)
\(I=144758.28\)
Therefore, the return on Ayanda's investment using Option 2 is R144758.28.
\(\hrulefill\)
Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.
A firm’s monthly cost for paying cleaners’ wages is $47 250. Under a new pay deal each cleaner earns $375 more each month. If the new pay deal goes through, the firm realises that it will need to reduce the number of cleaners by 3 if it is to cover its costs within the existing budget. What is the monthly salary of a cleaner before the pay rise?
Answer:
Answer attached in images below.
Question
From a point P on a level ground and directly west of a pole, the angle of elevation of the top of the pole is 45° and from point Q east of the pole, the angle of elevation of the top of the pole is 58°. If |PQ|= 10m, calculate, correct to 2 significant figures, the:
a) distance from P to the pole;
b) height of the pole.
a) The distance from point P to the pole is: 6.2 m
b) The height of the Pole is: 6.2 m
How to find the distance and height from angle of elevation?The triangle attached shows us the triangle formed as a result of the given word problem about angle of elevation and distance and height.
Now, we are given that:
The angle of elevation of the top of the pole = 45°
Angle of elevation of the top of the pole = 58°.
|PQ|= 10m
a) PR is distance from point P to the pole and using trigonometric ratios, gives us:
PR/sin 58 = 10/sin(180 - 58 - 45)
PR/sin 58 = 10/sin 77
PR = (10 * sin 58)/sin 77
PR = 8.7 m
b) P O can be calculated with trigonometric ratios as:
P O = PR * cos 45
P O = 8.7 * 0.7071
P O = 6.2 m
Now, the two sides of the isosceles triangle formed are equal and as such:
R O = P O
Thus, height of pole R O = 6.2 m
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Will mark Brainlest help plsssss
Answer:
45 is answer I guess cuz my teacher taught me just like that
Use the Distributive Property to simplify
1/7 x (56 - 1/4)
Leave your answer in simplest form in the form of a/b − c/d
If one of your numbers is a whole number, put a 1 in that denominator
well what i got was:
the exact form: 233/28
decimal form: 7.96428571...
mixed number form: 7 27/28
not sure if this is right at all but i hope it helps at least a little
hi
1/7 * (56 -1/4) = 56/7 - 1/28 = 224/28 - 1/28 = 223 /28
as 223 is prime, it's cannot be simplified. however it 7 +27/28
Help please i have no idea how to do this please help
Answer:
pretty sure its d
Step-by-step explanation: