What is the ones digit in the number 2 to the 2056 Power?Hint: start with smaller exponents to find the pattern
Answers
Follow the steps below to find the ones digit in the number:
[tex]\begin{gathered} 2^{2056} \\ \text{The base = 2} \\ \text{The power = 2056} \end{gathered}[/tex]step 1: Identify the unit digit in the base - the unit digit is 2.
step 2:
If the power or exponent is exactly divisible by 4
case 1: The unit digit of the number is 6 if the unit digit in the base is any of 2, 4, 6, 8.
case 2: The unit digit of the number is 1 if the unit digit in the base is 3, 7, 9.
In this case, the power 2056 is exactly divisible by 4 and the unit digit in the base is 2.
Therefore, the ones digit is 6
Related Questions
I need help with this question but no one is helping me! Can someone please help me
Answers
Answer:
Step-by-step explanation:
Number of yellow marbles =13
Number of teal marbles = 13
Two marbles are drawn randomly
Probability that both marbles are teal
Hence the probability that both marbles are teal is 0.026
HI there. I need some help with this question. I cannot figure out what the answer is.
Answers
From the question we were given the following:
Area of the square is 19 square units
Area of the circle is 30 square units
Area of intersection is 3 square units.
We are asked to find the area in square units of the entire coloured region.
So,
Are of Square = 19 square units
Are of Circle = 30 square units
Area of Intersection = 3 square units
Area of coloured region = Area of Square + Area of Circle - Area of Intersection
Therefore, Area of coloured region = 19 + 30 - 3
= 46 saqure units.
Ava can run 4/5 of a mile in 4/3 of an hour. How far can she run in 1 hour? *
Answers
Answer:
She can run 3/5 miles in 1 hour
Explanation:
Given that Ava can run 4/5 of a mile in 4/3 of an hour, we want to find how far she can run in 1 hour.
Let x represent the number of miles she can run in one hour.
The statement can be represented in the pair of equations:
[tex]\begin{gathered} \frac{4}{5}miles=\frac{4}{3}\text{hours} \\ \\ x\text{ hour }=1\text{hour} \end{gathered}[/tex]Using these equations, we have:
[tex]\begin{gathered} \frac{4}{5}=\frac{4}{3}x \\ \\ x=\frac{\frac{4}{5}}{\frac{4}{3}} \\ \\ x=\frac{4}{5}\times\frac{3}{4} \\ \\ =\frac{3}{5} \end{gathered}[/tex]That is, she can run 3/5 miles in 1 hour
Round to the answer to the nearest tenth.18. A 24-foot ladder leaning against a building forms an 18° angle with the side of the building,How far is the base of the ladder from the base of the building?
Answers
In order to solve this problem, first let's draw the corresponding image to the problem:
Then, to calculate the distance x, we can use the sine relation of the angle of 18°.
The sine relation is the length of the opposite side to the angle over the length of the hypotenuse.
So we have:
[tex]\begin{gathered} \sin (18\degree)=\frac{x}{24} \\ \text{0}.309=\frac{x}{24} \\ x=24\cdot0.309 \\ x=7.42 \end{gathered}[/tex]So the distance wanted is 7.42 ft.
Which expression below represents the average wages the company pays per employee each week?
Answers
According to the given data we have the following:
19 employees that earn $360
18 employees that earn $400
8 employyes that earn $480
5 employees that earn $600
The total employees would be=19+18+8+5=50
Therefore, to find the average we have to put at the numerator the amount of wages times of what correspond to each employee, and at the denominator the total of employees which are 50. Therefore, the expression that represents the average wages the company pays per employee each week would be 2.
If E is the midpoint of DF
with DE = 9x + 24 and
EF = 18x - 39, then find x
and DF.
Answers
Answer:
x=7, DF = 174
Step-by-step explanation:
18x-39=9x+24
9x=63
x=7
:]
In a triple batch of a spice mix, there are 6 teaspoons of garlic powder and 15
teaspoons of salt. Answer the following questions about the mix.
2. How much salt is used with 8 teaspoons of garlic powder
3. If there are 14 teaspoons of spice mix, how much salt is in it.
4. How much More salt is there than garlic powder if 6 teaspoons of garlic powder are use
Answers
The answers of the given questions are:
8 teaspoons of garlic powder are combined with 20 tablespoons of salt.10 teaspoons of salt are included in every 14 teaspoons of spice mixture.If 6 teaspoons of garlic powder are used, there are 15 teaspoons more salt than garlic powder.What exactly are ratio and proportion?A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as: 1: 3 (for every one boy, there are three girls).Given: There are 6 teaspoons of garlic powder and 15 teaspoons of salt in a triple batch of spice mix.
Let x be the teaspoons of salt.
Salt used with 8 teaspoons of garlic powder:
6/15 = 8/x
x = 20
Therefore, 20 teaspoons of salt is used with 8 teaspoons of garlic powder.
6 + 15 = 21 teaspoons of spice mix
Salt used in 14 teaspoons of spice mix:
21/15 = 14/x
x = 10 teaspoons of salt.
Therefore, if there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it.
If 6 teaspoons of garlic powder are used then,
21-6 = 15 teaspoons of more salt is used
Therefore, 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.
The answers of the given questions are:
20 teaspoons of salt is used with 8 teaspoons of garlic powder.If there are 14 teaspoons of spice mix, 10 teaspoons of salt is there in it. 15 teaspoons of more salt is there than garlic powder if 6 teaspoons of garlic powder are used.Learn more about ratio and proportion here:
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Tareq pays $22.10 for 2.6 pound of salmon. What is the price per pound of salmon?
Answers
Answer:
22.1$ = 2.6 pound
x = 1 pound
so when we criss cross
22.1$ X 1 pound = 2.6x pound
22.1 = 2.6x
22.1/2.6 2.6x/2.6
X=22.1/2.6
x=8.5
so it costs 8.5$ per pound
[tex] \sqrt{25} [/tex]what's the square root
Answers
[tex] \sqrt{25} [/tex] ()
what's the square root ?
√25 = 5
because 5*5= 25
[tex]\sqrt[]{5\cdot5}=\sqrt[]{5^2}=\text{ 5}[/tex]________________________
Answer
√25 = 5
To the nearest tenth of pound Does has need to buy?
Answers
Answer: She needs approximately 142.5 pounds
Explanation:
From the information given,
A pound of fertilizer covers 39 square feet of lawn.
If the lawn measures 5557.4 square feet, then
the number of pounds of fertilizer that she needs to buy = 5557.4/39 = 142.4975
Rounding to the nearest tenth,
She needs approximately 142.5 pounds
The half life of radium -226 is 1640 years. If a sample contains 200 mg, how many mg will remain after 4000 years?
Answers
Maya attended her town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt. Maya observed contestants' charming techniques and kept track of how many worms surfaced. The probability that a contestant tried tapping the ground is 0.22, the probability that a contestant charmed 5-10 worms is 0.71, and the probability that a contestant tried tapping the ground and charmed 5-10 worms is 0.16. What is the probability that a randomly chosen contestant tried tapping the ground or charmed 5-10 worms?
Answers
Using Venn probabilities, there is a 0.77 = 77% probability that a randomly chosen contestant tried tapping the ground or charmed 5-10 worms.
What is a Venn probability?In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given according to the following rule:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In the context of this problem, the events are given as follows:
Event A: Contestant tried tapping the ground.Event B: Contestant charmed 5-10 worms.From the text, the probabilities of the events are given as follows:
P(A) = 0.22, P(B) = 0.71, P(A and B) = 0.16.
Hence the or probability is given replacing the values as follows:
P(A or B) = P(A) + P(B) - P(A and B) = 0.22 + 0.71 - 0.16 = 0.77.
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if a student scored a 52 on his first test ,make a prediction for his score on the second test .Assume the regression equation is appropriate for the prediction. Round the answer to 2 decimal places.
Answers
Solution
We have the following info given:
x: 75,76, 91, 65,48,75,85,62,51,80,94,43
y: 69, 88, 101, 63, 59, 82, 86, 67, 56, 84, 105, 44
After apply OLS (Ordinary LEast Squares) we got the following regression line:
y= 1.0607x + 0.6442
We want to find the best prediction for a student who scored 52 in the first test so we have this:
y= 1.0607* 52 + 0.6442 = 55.80
Then the best prediction for this case is 55.80
4) The measure of one of two supplementary angles is 8 degrees more than three times the other. Find the measure of the larger of the two angles.
Answers
Supplementary angles add 180 degrees.
One of the two angles is 8 degrees more than 3 times the other.
If one of the angles is A and the other is B, then:
[tex]A=8+3B[/tex]As they are supplementary, they add 180 degrees:
[tex]A+B=180[/tex]We replace the information of the second equation in the first one and solve:
[tex]\begin{gathered} A=180-B \\ A=8+3B=180-B \\ 8+3B=180-B \\ 4B+B=180-8 \\ 5B=172 \\ B=\frac{172}{5} \\ B=34.4 \end{gathered}[/tex]Now we can solve for the other angle:
[tex]A=8+3B=8+3(34.4)=8+103.2=111.2[/tex]The measure of the angles is 34.4 degrees and 111.2 degrees.
Hey! what would the answer be, I am a little lost!
Answers
All of the triangles are an isosceles triangle, which means that they have two congruent side, and two congruent angles.
The first triangle has ∠B as 56°, AB ≅ BC.
The angle opposite to AB and BC are therefore, congruent, which means that
∠A + ∠B +∠C = 180°
∠A + 56° + ∠A= 180° (∠A and ∠C are congruent)
2∠A = 180° - 56°
2∠A = 124
∠A = 62°
The second triangle has ∠C equal to 62°. Since ∠A and ∠Care the angle opposite to the congruent side, they are also congruent which means ∠A = 62°.
The fourth triangle which has an exterior angle of ∠C equal to 118° forms a linear pair, and are thus supplementary
∠C = 62°, and both ∠C and ∠A are the corresponding angles to the congruent sides, it follows that they are also congruent.
∠A = 62°.
Conclusion
The following triangles have m∠A = 62°, first, second, and fourth triangle.
Find the coefficient of third term of (x + 2)³. A. 40 OB. 10 OC. 20 D. 80 Reset Selection A
Answers
Given:
The expression given is,
[tex]\left(x+2\right)^5[/tex]Required:
To find the coefficient of the third term.
Explanation:
Let us expand the expression to find the coefficient.
[tex]\begin{gathered} \left(x+2\right)^5 \\ =\frac{5!}{5!}x^52^0+\frac{5!}{4!}x^42^1+\frac{5!}{2!3!}x^32^2+\frac{5!}{3!2!}x^22^3+\frac{5!}{4!1!}x^12^4+\frac{5!}{5!0!}x^02^5 \\ =x^5+10x^4+40x^3+80x^2+80x+32 \end{gathered}[/tex]Hence, the coefficient of the third term is 40.
Final Answer:
The coefficient of the third term is 40.
Option A is correct.
Please show your but an short explanation, i inserted a picture of the question
Answers
With the given information we can make the following equation:
[tex]x+2x+3x=30[/tex][tex]6x=30[/tex][tex]x\text{ = 5}[/tex]Then David will have:
[tex]2\times5=10\text{ years}[/tex]Answer: 10 years.
A set of data has a mean of 9.6 and a standard deviation of 0.8. What number in the data set would have a z-score of -1.5?
Answers
A set of data has a mean of 9.6 and a standard deviation of 0.8. The number in the data set that would have a z-score of -1.5 is
x =8.4
This is further explained below.
What is the z-score?The number of normal deviations within which the value of a raw score is either above or below the average value of what is observed or measured is the number that is referred to as the standard score in the field of statistics.
Raw scores that are greater than the mean are assigned positive standard scores, and raw scores that are equal to or lower than the mean are assigned negative standard scores.
Generally, the parameters of the solutionare
[tex]\mu &=9.6 \quad \sigma=0.8 \quad z=-1.5 \\\\z &=\frac{x-\mu}{\sigma} \\\\-1.5 &=\frac{x-9.6}{0.8} \\[/tex]
Where
z=distribution
x=mean
[tex]\sigma[/tex]=standard deviation
u=population mean
Hence, solve for x
x =-1.2+9.6
x =8.4
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Starting at sea level, a submarine descended at a constant rate to a depth of −34 mile relative to sea level in 5 minutes.
What was the submarine's depth relative to sea level after the first minute?
Enter your answer as a fraction in simplest form.
Answers
Based on the fact that the submarine's depth was descended to at a constant rate, the submarine's depth relative to sea level with the passing of the first minute was -6⁴/₅ miles
How to find the submarine depth?The submarine descended at a constant rate to the current depth of -34 miles in 5 minutes. This means that the rate can be found by the formula:
= Current depth / Time
= -34 / 5
= -6.8 miles per minute
After the first minute, the depth is:
= -6.8 x 1
= -6.8 miles
This number in fractions is:
= -6 + 8/10
= -6 + 4 / 5
= -6⁴/₅ miles
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What is the probability of getting an even number on each one
Answers
Given:
Given that four far dice are thrown.
Required: Probability of getting an even number on each one.
Explanation:
The sample space is
[tex]S=\lbrace(x,y,z,w):\text{ x,y,z,w =1,2,3,4,5,6\textbraceright}[/tex]The number of elements in the sample space is
[tex]\begin{gathered} n(S)=6\times6\times6\times6 \\ =6^4 \end{gathered}[/tex]Let E be the event of getting even on each dice. Then
[tex]E=\lbrace(x,y,z,w);x,y,z,w=2,4,6\rbrace[/tex]The number of elements in E is
[tex]\begin{gathered} n(E)=3\times3\times3\times3 \\ =3^4 \end{gathered}[/tex]The probability of getting even on each dice is
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(S)} \\ =\frac{3^4}{6^4} \\ =\frac{3^4}{2^4\cdot3^4} \\ =\frac{1}{2^4} \\ =\frac{1}{16} \end{gathered}[/tex]The second option is correct.
Final Answer: The probability of getting even on each dice is 1/16.
Help Please!
A.
[tex] \frac{3}{4} [/tex]
B.
[tex] \frac{5}{4} [/tex]
C.
[tex] \frac{3}{5} [/tex]
D.
[tex] \frac{4}{5} [/tex]
Answers
Answer:
Step-by-step explanation:
Soh Cah Toa
S stand for sine, C stand for Cosine and the T stand for Tangent
'o' is the opposite, 'a' stand for adjacent (next to) and h stand for hypotenuse (the longest length of the triangle)
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
We care about angle A and we want sine. So we will use the first equation.
The opposite from A is 3 and the hypotenuse is 5.
[tex]sin(A)=\frac{3}{5}[/tex]
Find the midpoint of the segment with the following endpoints.
(4, 2) and (7, 6)
Answers
The midpoint of the segment with the following endpoints, (4, 2) and
(7, 6) is (5.5, 4).
How to determine the midpoint of a given segment?
The center point of a straight line can be located using the midpoint formula. We can use this midpoint formula to determine the coordinates of the supplied line's midpoint in order to discover its location on a graph. Assuming that the line's endpoints are (x₁, y₁) and (x₂, y₂), the midpoint (a, b) is determined using the following formula:
(a , b) ≡ (((x₁ + x₂)/2), ((y₁ + y₂)/2))
Let the line segment be AB having endpoints as A(4, 2) and B(7, 6);
also let the co-ordinates of midpoint be C = (a, b)
Using the given formula in the available literature,
(a, b) = ((4 + 7)/2, (2 + 6)/2)
Equating parts of the previous equation, we get,
a = (4 + 7)/2 = 11/2 = 5.5
b = (2 + 6)/2 = 4
Thus, the midpoint of the segment is (5.5, 4).
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Hey can someone please help me with this drag and drop? I’ll give brainliest :)
Answers
Lengths of similar triangles and similar polygons are proportional to each other so, answer to the question in image are-
a. ZY=20
b. X=20.8
c. 9miles
What are similar polygons?
similar polygons are the polygons in which all the corresponding angles are same. Hence, they have same shape. The ratio of sides in any two similar polygons are same. This concept of constant ratio of sides is useful in evaluating the length of sides.
a. A/a=B/b=C/c = D/d
WX/HI=ZY/JK
ZY=20
b. X=(2.4×39)/4.5
X= 20.8
c. If 5cm represents 2miles it implies 1cm represents
1cm=2/5
So, 22.5cm will represent
22.5cm=2/5×22.5
22.5cm=9miles
This means that 22.5cm track represents the distance of 9 miles on map
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Solve the inequality n minus three fifths is less than or equal to negative four sevenths for n.
n is greater than or equal to negative forty one over thirty five
n is less than or equal to negative one over thirty five
n is less than or equal to one over thirty five
n is greater than or equal to forty one over thirty five
Answers
The solution to the given inequality would be n ≤ 1/35 which is the correct answer would be an option (C).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
We have to determine the solution of the inequality n minus three-fifths is less than or equal to negative four sevenths for n.
As per the given condition, translate the phrase into an algebraic inequality as :
⇒ n - 3/5 ≤ - (4/7)
⇒ n ≤ 3/5 - (4/7)
⇒ n ≤ (21 - 20)/35
⇒ n ≤ 1/35
Therefore, the solution to the given inequality would be n ≤ 1/35.
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Given H(t)=10-2t^2 , find h^-1 (t), is h (t) one to one ? What does this imply about h^-1(t)
Answers
We have the function:
[tex]H(t)=10-5t^2[/tex]And we have to find the inverse function.
We can write this as:
[tex]H(H^{-1}(t))=t[/tex]We can solve this as:
[tex]\begin{gathered} H(H^{-1}(t))=10-2(H^{-1})^3=t \\ 10-2(H^{-1})^3=t \\ 2(H^{-1})^3=10-t \\ (H^{-1})^3=\frac{10-t}{2} \\ H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{} \end{gathered}[/tex]The inverse function is:
[tex]H^{-1}=\sqrt[3]{\frac{10-t}{2}}^{}[/tex]The domain of H is all the real numbers, as the domain of H^-1.
A marathon is 46,145 yards (about 26 miles) long. If Terrence has run 23,561 yards, estimate by rounding to thousands the number of yards he needs to run to complete the marathon.Terrence needs to run about ______ yards.
Answers
Given:
The length of the marathon is L= 46,145 yards.
The length covered by terrence is d = 23,561 yrads.
The objective is to find the remaining distance need to cover by terrence.
To calculate the remaining distance, we will use the relation,
[tex]x=L-d[/tex]On plugging the values in the above relation, we get,
[tex]\begin{gathered} x=46145-23561 \\ =22584\text{ yards} \\ \approx23000\text{ yards} \end{gathered}[/tex]Hence, Terrence needs to run about 23000 yards.
Find the slope of the line with the equation 8x + 2y=12 m = -8 Om= 8 m = -4 m = 2
Answers
Simplify the equation 8x + 2y = 12 to obtain the equation in y = mx + b.
[tex]\begin{gathered} 8x+2y=12 \\ 2y=-8x+12 \\ y=-\frac{8}{2}x+\frac{12}{2} \\ y=-4x+6 \end{gathered}[/tex]In equation y = mx + b, slope is m and y-intercept is b.
So on compare the equation y = -4x + 6 with standard equation the slope is m - -4.
Answer: m = -4.
Find solutions to the linear equation y=12x+24
Answers
Te solutions to the linear equation given as y = 12x + 24 are (0, 24), (1, 36) and (2, 48)
How to determine the solutions to the linear equation?From the question, the linear equation is given as
y = 12x + 24
To determine the solutions, we assume values for the variable x and then calculate the y values
Having said that, we have
y = 12x + 24
Set x = 0
So, we have
y = 12 x 0 + 24 = 24
Set x = 1
So, we have
y = 12 x 1 + 24 = 36
Set x = 2
So, we have
y = 12 x 2 + 24 = 48
So, the ordered pairs of the solutions are (0, 24), (1, 36) and (2, 48)
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Find the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300
Answers
the savings plan balance after 2 years with an APR of 7% and monthly payments of $.300 will be A = $209314.286 or A = $209314.3 .
The formula to calculate amount,
[tex]A= \frac{P[(1+\frac{APR}{100n})^{n*N}-1 ]}{(\frac{APR}{100n}) }[/tex]
where, we are given,
N = 2 years
APR = 7%
P = 300
n = 12
subsituting these values in the equation above we get,
[tex]A=\frac{300[1+\frac{7}{100*1} ]^{12*2} -1}{\frac{7}{100*12} }[/tex]
[tex]A=\frac{300*100*12}{7}} * [\frac{107}{100}^{24} -1][/tex]
[tex]A=\frac{ 360000}{7}[5.07-1][/tex]
[tex]A=\frac{360000}{7}[4.07][/tex]
A=51428.57 * 4.07
A = $209314.286
or
A = $209314.3
What is APR?
An annual percentage rate is a calculation that includes all fees and costs associated with borrowing in addition to the interest rate.
APR is a number provided for all mortgages, loans, and credit cards, and there is a precise formula the bank must use in order to calculate the number in accordance with the Financial Service Authority's guidelines. It is simple to compare the APR between various accounts. All of the additional fees and expenditures you must pay on top of the basic interest rate are factored into the APR calculation.
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Use the graph of the inequality to answer the question.Randy wants to make a mixture of raisins and nuts. Theraisins cost $3.00 a box, and the nuts cost $6.00 a tin. Canhe make a mixture consisting of 3 boxes of raisins and 1 tinof nuts if he wants to spend no more than $12.00?
Answers
The raisins cost $3.00 a box while the nuts cost $6.00 a tin.
The graph in the picture provide to us, in the shaded region, the relation between the number of boxes of raisins and the tins of nuts that can be buyed without spend more than $12.00.
We can check in the graph that the point representing a mixture consisting of 3 boxes of raisins and 1 tin of nuts is out of the shaded region.
Therefore, Randy can't make this mixture without spend no more than $12.00