There are a total of 20 * 6 = 120 numerals when you form a numeral between 300 and 899, inclusive, using only the digits 1, 4, 5, 6, 8, and 9
What is meant by Permutation and Combination?Two mathematical ideas, permutation and combination, are used to specify the many ways in which items from a set can be chosen, often without replacement, to produce subsets.Combination is the selection , while permutations is the arrangement.For instance, if we have a group of three letters (A, B, C) inclusive, they may be combined to form the combinations ABC, ACB, BAC, BCA, CAB, and CBA. However, the result of these three letters combined would be ABC, AB, AC, BC, BA, CA, CB, and C. Probability, statistics, and computer science are just a few of the disciplines that benefit from permutation and combination.
How to solve?
We can choose 3 of the 6 digits in a total of 6C3 = 20 ways. Once we have chosen the 3 digits, we can arrange them in a total of 3! = 6 ways. Therefore, there are a total of 20 * 6 = 120 numerals.
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What is the X intercept of X 3y =- 3?.
The x-intercept is ( 3,0) and The y-intercept is ( 0, -1)
Why does x-intercept matter?
The points where a line crosses an axis are known as the x-intercept and the y-intercept, respectively.
-x + 3y = -3 is a linear equation in standard form:.
X-intercept: value of x when y = 0
Substitute 0 for y and solve for x.
-x + 3 * 0 = -3
-x = -3
x = 3
The x-intercept is (3,0)
Y-intercept: value of y when x = 0
Substitute 0 for x and solve for y.
0 + 3y = -3
3y = -3
y = -1
The y-intercept is ( 0,-1)
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The complete question is -
What is the X intercept of -x + 3y = -3?.
write the following expression in simplest form. the expression quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
The simplified form of the expression is, negative five sixths times x plus eight.
What is word problem?
A math word problem is a mathematical question that is stated as one sentence or more and asks students to use their arithmetic skills in a "real-life" situation. Therefore, in order for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are used to.
Given that: quantity negative two thirds times x minus 6 end quantity minus quantity negative 14 plus one sixth times x end quantity
It can be write in mathematical form as,
[tex](-\frac{2}{3}x-6) - (-14+\frac{1}{6}x)[/tex]
Simplifying the parenthesis,
[tex]= -\frac{2}{3}x-6+14-\frac{1}{6}x\\ = 8 - \frac{15}{18}x\\ = 8 - \frac{5}{6}x\\= -\frac{5}{6}x+8[/tex]
Hence, the simplified form of the expression is, negative five sixths times x plus eight
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Point DD is located at (2,1)(2,1) on the coordinate plane. Point DD is reflected over the yy-axis to create point D'D ′ . Point D'D ′ is then reflected over the xx-axis to create point D''D ′′ . What ordered pair describes the location of D''?D ′′ ?
Answer: (-2,-1)
Step-by-step explanation: First, plot the point. Then you go to the left 4 times. Then you plot your new point. Then go down 2 times. Plot your final point.
unoccupied seats on flights cause airlines to lose revenue. suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. to accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. the sample mean is 11.2 seats and the sample standard deviation is 4.3 seats. note: if you are using a student's t-distribution, you may assume that the underlying population is normally distributed. (in general, you must first prove that assumption, though.)
The confidence interval for the mean is (10.7485, 11.6515)
Given Data:
n = 225
×= 11.2
s = 4.1
Note that, Population standard deviation([tex]\alpha[/tex]) is unknown. So we use t distribution.
Our aim is to construct a 90% confidence interval.
c = 0.90
[tex]\alpha[/tex] = 1- c = 1- 0.90 = 0.10
[tex]\alpha[/tex]/2 = 0.10/2 = 0.05
Also, d.f = n - 1 = 225 - 1 = 224
t[tex]\alpha[/tex]/2.d.f- = t[tex]\alpha[/tex]/2.n-1 = t0.05,224 = 1.652
( use t table or t calculator to find this value..)
The margin of error is given by
E = t[tex]\alpha[/tex]/2,d.f. * (s / [tex]\sqrt{n}[/tex])
= 1.652 * (4.1/ √225)
= 0.4515
Now , confidence interval for mean(\mu) is given by:
(× - E ) < μ< x + E)
(11.2 - 0.4515) < μ < (11.2 + 0.4515)
10.7485 < μ< 11.6515
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MAJOR HELP !!!!! in a butcher shop, each slab of beef weighs6^7 pounds. if there are 6^3 containers filled with beef, how much does all the beef weigh ? Keep your answer in a^b form.
The weight of each beef will be 6⁴
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
From the information, in a butcher shop, each slab of beef weighs 6^7 pounds and there are 6^3 containers filled with beef, the weight of each beef will be:
= Total pounds / Container
= 6^7 / 6^3.
= 6^(7 - 3).
= 6^4
The weight is 6⁴.
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Choose a set of transformations that you can use to show that 1 is congruent to 8 HELP!
The transformations is rotate 180° and translate down.
Transformations:
Transformations can be non-rigid (when the preimage's size or shape is unaltered) or stiff (where the size is changed but the shape remains the same). These are the fundamental guidelines that this concept abides by. It is a straightforward approach to alter 2D forms. Planar transformations and spaces can be distinguished from one another using the dimensions of the operand sets. Their characteristics can also be used to classify them.The image of a shape will resemble the pre-image when its size is increased or decreased. The dimensions of the comparable figures are proportionately equal.
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What is the magnitude of 3 4j?.
The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a² + b²). In this case, a is 3 and b is 4, and the square root of (3² + 4²) is 5.
The magnitude of a complex number is the length of a line from the origin to the point on the complex plane that represents the number. The magnitude of 3 4j can be calculated using the Pythagorean theorem.
Using the theorem, the magnitude of 3 4j is 5. This is because 3 and 4 are the lengths of the sides of a right triangle and 5 is the length of the hypotenuse. The equation to calculate the magnitude of 3 4j is the square root of 3 squared plus 4 squared. This is written as the square root of (3² + 4²) = 5.
The magnitude of 3 4j is 5. This is because the magnitude of any complex number in the form a + bi is the square root of (a^2 + b^2). In this case, a is 3 and b is 4, and the square root of (3^2 + 4^2) is 5. This means that the magnitude of 3 4j is 5.
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Solve the equation please!!!!!
Answer:
x = 4 ; y = 12
Step-by-step explanation:
y = 3x
5x - 3x = 8
2x = 8
2/2 x = 8/2
x = 4
y = 3(4)
y = 12
solve for the unknown, t
3e^9t = 100
Solving for the unknown variable t in the natural exponent expression 3e^9t = 100 gave
t = 0.3896175How to solve for tThe given expression is given in natural exponent and is solved as follows
3e^9t = 100
dividing through by 3
3e^9t / 3 = 100 / 3
e^9t = 100/3
take natural logarithm of both sides
In e^9t = In (100/3)
9t = In (100/3)
divide through by 9
9t / 9 = 3.5065578 / 9
t = 0.3896175
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bethany and joseph are preparing budgets for a new product as well as finalizing plans for the full-scale marketing and manufacturing of the new utilibot. they are in the phase of the new-product development process.
The answer for the given statement is commercialization. Bethany and Joseph are in the commercialization phase of the new-product development process, since they are preparing budgets for a new product as well as finalizing plans for the full-scale marketing and manufacturing of the new UtiliBot.
What is Commercialization?Commercialization is the process of carrying new products or services to the market. Commercialization needs a correctly-developed three-tiered product roll-out and marketing strategy, which includes the ideation phase, the business process, and the stakeholder stage. The launch or commercialization of a new product is contemplated the final stage of new product development (NPD). Commercialization consists of stages such as production, distribution, marketing, sales, and customer support.
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cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers. how far is cori from where she started?
The required distance of Cori from where he started is 35km.
What is meant by distance?Distance is a quantitative or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimation based on other criteria in physics or everyday usage. Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is also used metaphorically to mean a measurement of the amount of difference between two similar objects or a degree of separation. The concept of a metric space is used to codify most such conceptions of distance, both physical and metaphorical.
Given,
Cori races her friend heading south for 9 kilometers, east for 20 kilometers, then south for 6 more kilometers.
The distance of Cori from starting point=9+20+6
=15+20
=35
Hence, the required distance of Cori from where he started is 35km.
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Exercise statement: the life spans of car batteries are normally distributed, with a mean of 44 months and a standard deviation of 5 months. A car battery is selected at random. Find the probability that the life span of the battery is less than 36 months. What is the shortest life expectancy a car battery can have and still be in the top 5% of life expectancies
The shorted life expectancy to be in top 5% is 52.225
Given that.
Mean = 44
Standard Deviation = 5
a)
Z =36 – 44/5
Z =-8/5
Z =-1.6
P(z<-1.6)=normsdist(-1.6)=0.0548
b)
P(Z > 2) = 0.05
P(Z <=) = 1 -0.05 = 0.95
z=normsinv(0.95)=1.645
shorted life expentancy to be in top 5%=
= 44+1.645*5
Shorted life expentancy to be in top 5% = 52.225
For Minitab use:
Choose Calc > Probability Distributions > Normal.
Select Inverse cumulative probability.
In Mean, enter 44.
In Standard deviation, enter 5.
In Input column, enter Probability=0.95
Hence, The shorted life expectancy to be in top 5% is 52.225.
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What are the 5 rules of congruence?.
Two shapes of the same size and shape are congruent. There are five conditions or rules for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS joint properties.
Triangle Congruence:
The congruence of two or more triangles depends on the measurements of their sides and angles. The three sides of a triangle determine its size, and its three angles determine its shape.
Two triangles are considered congruent if their pairs of corresponding sides and corresponding angles are equal.
SSS (side-side-side) :
According to this criterion, two triangles are congruent if his three sides of one triangle are equal to the corresponding sides of the other triangle.
ASA ( Angle-Side-Angle ) :
According to the ASA criterion, two triangles are congruent if any two angles and the inner side of one triangle between them are equal to the corresponding angles and inner sides of the other triangle.
SAS (Side Angle Side)
According to this criterion, two triangles are congruent if two sides and included angles of one triangle are equal to the corresponding sides and included angles of the other corresponding triangle.
AAS ( Angle - Angle Side) :
According to the AAS standard, two triangles are congruent if any two angles and the excluded side of one triangle are equal to the corresponding angles and the excluded side of the other triangle
RHS (Right Angle Two-sided)
According to this criterion, two triangles are congruent if the hypotenuse and side of one right triangle are equal to the hypotenuse and corresponding side of another right triangle.
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Minimize the objective function p = 45x 48y for the given constraints.
Answer:
1640y
Step-by-step explanation:
the reason is y is known as variables constant is number 48y is a monomial that is why it is 26840y
A freeway has a capacity of 4000 vph. The normal flow rate on the freeway is 3000 vph. An incident blocks the freeway for 5 min. After 5 min, the freeway is opened to full traffic flow. Approximately how long does it take to dissipate the queue that resulted from the blockage? (4pts)
It will take 20 minutes to dissipate the queue that resulted from blockage if
the freeway has the capacity of 4000 vph.
Mean service rate(M) = 4000vph
Mean arrival rate(λ) = 3000vph
Block time duration of queue (r) = 5min
Time taken to dissipate the queue = t
t = (M * r)/(M-λ)
Substitute the given values
t = (4000*5)/(4000-3000)
t = 20000/1000
t = 20minutes.
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Please help me this is geometry
Answer: The last option, [tex]8\sqrt{2}[/tex]
Step-by-step explanation:
When looking at this triangle, there are two things we can note about it right away. First, it's a right triangle so we can use the Pythagorean theorem. Second, the two legs of the triangle are congruent (as shown by the dash lines) so both of them are equal to 8.
Using the Pythagorean theorem we will solve.
a² + b² = c²
(8)² + (8)² = c²
64 + 64 = c²
128 = c²
c = [tex]\sqrt{128}[/tex]
c = [tex]\sqrt{64*2}[/tex]
c = [tex]8\sqrt{2}[/tex]
(a) find the critical numbers of (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, and (d) use a graphing utility to confirm your results.
The critical numbers of the function x³ - 6x² + 15 is 0 and 4
The given function is x³ - 6x² + 15
To find the critical value first we need to find the derivative, then set the derivative f'(x) to zero
The derivative of x³ - 6x² + 15 is
3x³⁻¹ - 2(6)x²⁻¹ = 0
3x² - 12x = 0
3x(x - 4) = 0
3x = 0
x = 0
x - 4 = 0
x = 4
so, x = 0 or 4
Therefore, the critical numbers of the function x³ - 6x² + 15 is 0 and 4
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Can you prove triangles congruent by SAS?.
The triangle ABC and XZY are proved to be congruent by SAS.
Explain the concept of congruence.Congruence of triangles: Two triangles are supposed to be harmonious assuming each of the three comparing sides are equivalent and every one of the three relating angle are equivalent in measure. These triangles can be slides, pivoted, flipped and went to be seemed to be indistinguishable.
By the rule of SAS which means, Two sides are equal thhen the angle between the two sides is also equal (SAS: side, angle, side)
Here in he given triangle,BC=YZ
AC=XZ
∠ACB=∠XZY
By SAS ΔABC≅ΔXYZ
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How many Nadhs are needed for the reduction of one oxygen molecule?.
To reduce 1 molecule of oxygen 4 electron are required, which means 4 Nadhs are needed for the reduction of one oxygen molecule
NADH donates one electron to become NADH⁺ + e⁻
So, the number of Nadhs are needed for the reduction of one oxygen molecule is same as the number of electrons needed for the reduction of one oxygen molecule
Water has 2 hydrogen and each hydrogen needs only one electron. Hence, four electrons along with four hydrogen atoms are required to reduce one molecule of oxygen to two molecules of water.
Therefore, To reduce 1 molecule of oxygen 4 electron are required, which means 4 Nadhs are needed for the reduction of one oxygen molecule.
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MEASUREMENT
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7°. If Paula is 5. 5 feet tall,
approximately how wide is the river, to the nearest foot?
Answer:
45
Step-by-step explanation:
Based on the given conditions, formulate: [tex]5.5\div\text{tan}7^o[/tex]
Calculate the approximate value: [tex]\frac{5.5}{0.122785}[/tex]
Calculate: [tex]44.793745[/tex]
Find the closest integer: 45
Answer: 45
gardeners on the west coast of the united states are investigating the difference in survival rates of two flowering plants in drought climates. plant a has a survival rate of 0.67 and plant b has a survival rate of 0.48. the standard error of the difference in proportions is 0.097. which of the following is the margin of error for a 99% confidence interval?
The 99% confidence interval would be given (0.04;0.46).
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
pA represent the real population proportion A
^pA = 0.67 represent the estimated proportion A
pB represent the real population proportion B
^pB = 0.48 represent the estimated proportion B
z represent the critical value for the margin of error
The population proportion have the following distribution
p ~ N(p,√p(1-p)/n
The confidence interval for the difference of two proportions would be given by this formula
(^pA - ^pB) ± zα/2 √^pA(1-^pA)/nA + ^pB(1-^pB)/nB
For the 99% confidence interval the value of α = 1-0.99 = 0.01 and α/2 = 0.005 , with that value we can find the quantile required for the interval in the normal standard distribution.
zα/2 = 2.576
The standard error is given by:
= 0.084
And replacing into the confidence interval formula we got:
(0.67-0.42) - 2.576(0.084) = 0.04
(0.67-0.42) + 2.576(0.084) = 0.46
And the 99% confidence interval would be given (0.04;0.46).
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The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.
The creation of anxiety to decrease maladaptive behavior occurs in Aversion therapy; the induction of relaxation to increase an adaptive behavior occurs in Systematic desensitization.
Given,
In the question:
The question is based on fill in the blanks:
The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.
Let's Know:
Maladaptive Behaviour:
Maladaptive behaviors are things that you do that may shield you from changing in accordance with circumstances. Frequently found in those with social nervousness issue (SAD), maladaptive behaviors are utilized to attempt and lessen tension and dread at the time. You may accidentally build up these propensities to adapt in social and execution circumstances since it feels like they are helping you deal with your anxiety.
Now, According to the question:
The creation of anxiety to decrease maladaptive behavior occurs in _____ therapy; the induction of relaxation to increase an adaptive behavior occurs in _____.
Hence, In the first fill up :
The answer is Aversion.
In the second fill up:
The answer is Systematic desensitization.
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A population of insects increases at a rate of 290+8t+0.6t2 insects per day.
Find the insect population after 5 days, assuming that there are 70 insects at t=0. Round your answer to the nearest whole number.
The insect population after five days is 1645 in population of insects increases at a rate of 290+8t+0.6t2 insects per day.
A total of 290+8t+0.6t2 insects are added to the insect population per day. If there are P insects in the population,
then dP/dt = 290 + 8 + 0.6
since there are P insects at t=0, then
[tex]\int\limits^5_0[/tex][tex]{dP = (290 + 8 + 0.6) (290+8t+0.6t2)dt}[/tex] [after 5 days]
P(5) -V(0) = 290(5)+ 4t2 + t3/5)
P= 290t + 4t2 + t3/5) (5)
Insects: 2+ (5) 3/5 - 200 (0) + 5 (0) - 2+ (0) 3/5 P(5) - 70
= 1450 + 100 + 25-0 P(5)
= 70 + 1575 P(5) = 1645.
In the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations, calculus, also known as infinitesimal calculus or "the calculus of infinitesimals," is the study of continuous change in mathematics.
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In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to.
Answer:
The equality sign should be present in the null hypothesis during hypothesis testing. In a two-tailed hypothesis test, the rejection region's area in each tail is equal to [tex]\alpha[/tex]. If you choose an alpha of 0.01 then beta will equal 0.99
What is the slope of a line perpendicular to the line whose equation is 10x-12y=-24.
The slope of a line perpendicular to the line whose equation is 10x - 12y = -24 is 5/6
Given equation,
10x - 12y = -24
This line's parallel has the same slope as this line. Solve for y to alter the equation in order to calculate the slope.
y = mx + b
Where m is the slope and b is the y-intercept.
From the given equation,
10x - 12y = -24
-12y = -10x - 24
y = -10x/-12 + 24/12
y = 5x/6 + 2
Therefore, m = 5/6
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the local restaurant reported losses of $275 each day for three days. what was the loss for the three days?
Answer:
loss of $825
Step-by-step explanation:
$275 x 3 =$825
Answer: 825
Step-by-step explanation:
Just times 275 by 3 and you have the answer.
rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt.
D > B=E > F > A > C
The ranking is like, D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)
Given,
Forces;
D > B=E > F > A > C
We have to rank these forces (a through f) on the basis of the magnitude of the torque they apply to the wrench, measured about an axis centered on the bolt
Magnitude of torque;
The ratio of the force's and the lever arm's magnitudes yields the torque's magnitude. Force has a dimensional formula of [M1L1T2], whereas a lever arm has [L]. Consequently, [M1L2T]2 is the dimensional formula for torque.
Here,
The ranking is;
D (next to the end of the wrench, B=E (middle of the wrench), F next to the top of the wrench, A (top of the wrench), C (bottom of the wrench)
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fail 59 45 67 after running an independence test, can it be concluded that pass/fail rates are dependent on school?
The correct option is B
No, it cannot be concluded that pass/fail rates are dependent on school because the p-value = 0.9373.
What is meant by an alternative hypothesis?In statistical hypothesis testing, the alternative hypothesis is one of the suggested propositions in the hypothesis test. In general, the purpose of a hypothesis test is to demonstrate that, under the given conditions, there is sufficient evidence to support the believability of an alternate hypothesis rather than the test's exclusive statement (null hypothesis). Because it is based on a review of the literature and previous studies, it is usually congruent with the research hypothesis.
Null hypothesis : H₀ : pass/fail rates are independent on school
Alternative Hypothesis : H₁: pass/fail rates are dependent on school
Test Statistic is,
x²stat=∑(O-E)²/E
Here O is the observed frequency and E is the Expected frequency.
E=(Row total× Column total)/Grand total
O E O-E (O-E)² (O-E)² /E
40 41.4184 -1.4184 2.-118 0.0486
33 32.6327 0.3673 0.1349 0.0041
50 48.9490 1.0510 1.1046 0.0226
59 57.5816 1.4184 2.0118 0.0349
45 45.3673 -0.3673 0.1349 0.0030
67 68.0510 -1.0510 1.1046 0.0162
Total=0.1294
Degrees of freedom=(Number of rows-1)×(Number of columns-1)
=(2-1)×(3-1)
=2
p-value=P(x²>x²stat)=P(x²>0.1294)
For 3 degrees of freedom,
P(x²>0.1294)=0.9373
Level of significance α=0.10
As p-value is 0.9373>α:0.10
Fail to reject the null hypothesis.
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one cubic foot will hold 7.5 gallons of water. a rectangle-shaped tank is 10 feet by 8 feet by 8 feet. how many gallons of water will this tank hold?
The rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
Cubic foot holds 7.5 gallons of water
We need to find the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet.
Vol = L*W*H
10 x 8 x 8
640 cubic feet
1 cubic feet hold 7.5 gallons of water
640 cubic feet hold 7.5 x 640 = 4800
Therefore, the amount of gallons of water can a rectangle-shaped tank is 10 feet by 8 feet by 8 feet is 4800 gallons of water.
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What is the unit digit in 3 65 times6 59 times7 71 ))?.
4 is the unit digit in product .
What do Units digits mean?
The digit that goes in the place of one in a number is known as the units digit. It is the number's last digit on the right, for example.For instance, the units digit for 243 is 3 and for 39 it is 9.The Unit Place Digit refers to the digit placed in the one's position of the particular number.Unit digit in 3⁴ = 1
Unit digit in( 3⁴)¹⁶ = 1
Unit digit in 3⁶⁵ = Unit digit in( 3⁴)¹⁶ = 1 * 3 = 3
Unit digit in 6⁵⁹ = 6
Unit digit in 7⁴ = 1
Unit digit in (7⁴)¹⁷ = 1
Unit digit in 7⁷¹ = Unit digit in (7⁴)¹⁷ * 7³ = 1 * 3 = 3
Required digit= Unit digit in ( 3 * 6 * 3 ) = 4
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The complete question is -
What is the unit digit in the product (3⁶⁵ * 6⁵⁹ * 7⁷¹ ) = ?
