Part (a)
Note 999999=1000000-1. By Fermat's little theorem, since 100000=10⁶,
[tex]10^{6} \equiv 1 \pmod{7} \\ \\ \therefore 10^{6}-1 \equiv 0 \pmod{7}[/tex]
Part (b)
Note that
[tex]10^{12n}-1=(10^n)^{12}-1 \equiv 0 \pmod{13}[/tex]
Since
[tex]1 = 1001 - 1000[/tex]
and
[tex]-1 \equiv 1000 \pmod{1001}[/tex]
10³ is its own inverse modulo 1001, meaning that:
[tex]10^3 x \equiv 1 \pmod{1001} \implies x=10^3 \\ \implies 10^{12n}=(10^3 \cdot 10^3)^{2n} \equiv 1 \pmod{1001} \\ \\ \implies 10^{12n}-1 \equiv 0 \pmod{1001}[/tex]
Write the specified quantity as a function of the specified variable. It will help in each case to draw a picture. The height of a right circular cylinder equals its diameter. Write the volume of the cylinder as a function of its radius.
The volume of the cylinder as a function of its radius is V = 2πr^3
How to write the volume of the cylinder as a function of its radius?The given parameters are
Diameter = Height
This can be represented as
d = h
The radius of a cylinder is calculated as
r = d/2
This means that
d = 2r
Substitute d = 2r in d = h
h = 2r
The volume of a cylinder is
V = πr^2h
Substitute h = 2r in V = πr^2h
V = πr^2(2r)
Evaluate
V = 2πr^3
Hence, the volume of the cylinder as a function of its radius is V = 2πr^3
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a line passes through the points (9, 16) and (0, 5). what is it’s equation in slope intercept form
Answer:
y = x + 5
Step-by-step explanation:
Slope: m = (y2-y1)/(x2-x1)
m = (16 - 5)/(9 - 0) = 9/9 = 1
Using m = 1, y = 5, x = 0
then y = mx + b
5 = 1(0) + b
b = 5
so y = x + 5
Four cylindrical barrels each have a capacity of 100 L but have different diameters and heights. Determine the height of the barrel for each diameter. a) 40.0 cm b) 45.0 cm c) 50.0 cm d) 55.0 cm
Miguel made up an equation for his friend to solve. He told his friend that three times the square of a number is 265", What is the number to the nearest tenth
The number after rounding off to the nearest tenth will be 9.4
In this question, we have been given that Miguel made up an equation in which three times of square of a particular number equals 265. We have to set up the equation according to this.
Taking the number as 'x'. We get the equation according to the condition :
=> 3x² = 265
By solving this equation we get :
=> 3x² = 265 => x² = 88.3
=> x = 9.39
We get x = 9.39. By rounding off x to the nearest tens, we get x = 9.4
Hence, the number to the nearest tenth will be 9.4
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-2w+w+7w−2w+w+7w i need help please i dont know what to do 8th grade basic integers thanks.?
The expression is simplified to 6w
What are algebraic expressions?Algebraic expressions are expressions made up of terms, variables, factors, coefficients and constants.
They also consist of arithmetic operations such as addition, subtraction, multiplication, division, etc
Given the expression;
-2w+w+7w
Using the BODMAS rule, we have to add
-2w + 8w
6w
Thus, the expression is simplified to 6w
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An investigator wants to test for the presence of simple sugars in a sample. She adds reagent to her sample and also to a sample of distilled water. What reagent should she have added?.
The investigator can test the presence of simple sugars in the sample by using Benedict's solution.
What is Benedict's test ?Simple carbs are tested for using Benedict's Test. With free ketone or aldehyde functional groups, reducing sugars (monosaccharides and some disaccharides) are recognized by the Benedict's test.
What is Benedict's solution?Benedict's solution turns orange or brick red when heated in the presence of simple carbohydrates. The reducing characteristic of simple carbs is what triggers this response. The Benedict's solution changes color as a result of the reduction of copper (II) ions to copper (I) ions.
The produced red copper(I) oxide precipitates out of solution because it cannot be dissolved in water. This explains how the precipitate was created. The closer the final hue is approaching brick-red and the more precipitate is generated as the reducing sugar concentration rises. Copper oxide, a brick-red solid, can occasionally precipitate out of a solution and gather at the test tube's bottom.
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Which of these is a non-real complex number?
Find the measure of LBOD
m LBOD=
Classify LBOD
The measure of angle BOD is 65°
Calculating measure of anglesFrom the question, we are to determine the measure of angle BOD (m ∠ BOD)
The measure of angle BOD can be determine from the given protractor.
To determine the measure of angle BOD, we will read from line BO, in the counterclockwise direction, to line DO.
Reading in the counterclockwise direction, line BO is on 0°, and line DO is on midpoint of 60° and 70°.
The midpoint of 60° and 70° is 65°
Hence, the measure of angle BOD is 65°.
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order from greatest to least .7 .07 .072 7.2 7 .27
Order from greatest to least
0.7
0.07
0.072
7.2
7
0.27
Answer:
(largest) 7.2 , 7 , 0.7 , 0.27 , 0.072 , 0.07 (smallest)
help 32. (a) and (b)
Answer:
Below
Step-by-step explanation:
a) He answered 9 questions, lets say that he answered all 9 correctly
= 9x5 = 45 points (highest)
b) He answered 9 questions, lets say that he answered them all wrongly
0-(5x9)
0-45
-45
(14) Given L lI M || N, find the value of x.
Based on the corresponding angles theorem, the value of x is: 64°.
What is the Corresponding Angles Theorem?When two angles that are formed by a transversal and two parallel lines lie in relative position to each other on each of the parallel lines, they are called corresponding angles. According to the corresponding angles theorem, both angles are congruent to each other.
Angle x and 64 degrees are corresponding angles. They are therefore congruent to each other.
Thus, x = 64° [corresponding angles theorem]
In summary, based on the corresponding angles theorem, the value of x is: 64°.
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Please answer the 2 question in photo [ Brainliest + points ]
Answer:
3.) Obtuse &. 4.) Acute. ????
Step-by-step explanation:
Answer:
3. obtuse
4. acute
Step-by-step explanation:
Hope this helps
2. The sum of the interior angles in a quadrilateral is 360°. Determine the value of x in
the diagram on the right.
Answer:
267/5 ( or ) 53.2
Step-by-step explanation:
Note : -
□ means 90°
2x - 42 + 3x + 45 + 90 = 360
2x + 3x + 45 - 42 + 90 = 360
5x + 3 + 90 = 360
5x + 93 = 360
5x = 360 - 93
5x = 267
x = 267/5 ( in fraction )
( or )
x = 53.2° ( in decimal )
A square field has an area of 22,500 square feet. To the nearest foot, what is the diagonal across the field?
The length of the diagonal across the field is 212.132 feet.
What is a square?A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
Given that a square field has an area of 22,500 square feet. Now, the length of the side of the square field can be written as,
Area of the square field = (Length of square field)²
22,500 square feet = (Length of square field)²
Length of square field = √(22,500 sq. feet)
Length of square field = 150 feet
Now, the length of the diagonal of the field can be written as,
(Length of the diagonal)² = 2(Length of the side of square field)²
(Length of the diagonal)² = 2(150²)
(Length of the diagonal)² = 45,000 sq. feet
(Length of the diagonal) = 212.132 feet
Hence, the length of the diagonal across the field is 212.132 feet.
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Arnie decides to make 3 cups of dark orange paint and 3 cups of light orange paint. How many ounces of yellow paint does he need?
Answer:
6.0 ounces
Step-by-step explanation:
An atom has a diameter of 2.00 Å and the nucleus of that atom has a diameter of 9.50×10−5 Å . Determine the fraction of the volume of the atom that is taken up by the nucleus. Assume the atom and the nucleus are a sphere.
fraction of the volume of the atom taken by nucleus = 1.07*10^-13
Space occupied by the sphere is the volume of sphere.
A straight line passing from side to side through the center of the body especially a circle or sphere is known as diameter.
Volume of sphere = 4/3πr³
Diameter of an Atom = 2.00Â
Diameter of an nucleus = 9.50×10⁻⁵Â
Radius of an Atom = 1.00Â
[tex]\frac{4}{3}\pi r^3=\frac{4}{3}\pi (4.75*10^(-5))^3\\[/tex]
Volume of an Atom = [tex]\frac{4}{3}\pi r^3= \frac{4}{3}\pi 1^3=\frac{4}{3}\pi[/tex]
Volume of nucleus = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi (4.75*10^-5)^3\\=\frac{4}{3} \pi 107.1718*10^-15[/tex]
fraction of the volume of the atom taken by nucleus =
4/3π 107.17*10^-15/ 4/3π =107.17*10^-15 = 1.07 *10^-13
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b) Find the values of y.
y² = 169
I wrote that it equals to 13 but it’s not right. Please help!!
If m ∠ E B C = 3 r + 10 ° and m ∠ A B E = 2 r − 20 ° , find m ∠ E B F .
The measure of ∠EBF is 56°.
Here, we are given that-
m ∠EBC = 3 r + 10 °
and m ∠ABE = 2 r − 20 °
Also we can observe that ∠EBC and ∠ABE are angles on a straight line and hence will be supplementary.
⇒ ∠EBC + ∠ABE = 180
⇒ 3r + 10 + 2r - 20 = 180
5r - 10 = 180
5r = 180 + 10
5r = 190
r = 190/5
r = 38
Thus, ∠ABE = 2(38) - 20
= 76 - 20
= 56
Now, from the figure, m ∠EBF = m ∠ABE
⇒ m ∠EBF = 56°
Thus, the measure of ∠EBF is 56°.
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Your question was incomplete. Check for the missing figure below.
Consider the system of equations 2x + 5y = 5 and -3x + 7y = 7. What number would you multiply to eliminate the y?
Answer:
(0, 1 )
Step-by-step explanation:
2x + 5y = 5 → (1)
- 3x + 7y = 7 → (2)
to eliminate y multiply (1) by 7 and (2) by - 5 , then add the result
14x + 35y = 35 → (3)
15x - 35y = - 35 → (4)
add (3) and (4) term by term to eliminate y
29x + 0 = 0
29x = 0 ⇒ x = 0
substitute x = 0 into (1) and solve for y
2(0) + 5y = 5y
0 + 5y = 5
5y = 5 ( divide both sides by 5 )
y = 1
solution is (0, 1 )
suppose M is the midpoint of FG. find each missing measure.
FM= 8a + 1, FG = 42, a =?
The value of a is 2.5
As FG is the line and M is the midpoint of the line
F ______________·_________________G
M
So by this, we have that
FG = FM + MG
Where FM = MG as M is the midpoint of the line.
Therefore FG = 2FM
As it is given that FM = 8a + 1 and FG = 42
Now putting the values we have
42 = 2( 8a + 1)
21 = 8a + 1
20 = 8a
a = 2.5
Therefore the value of a is 2.5.
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which expression shows the prime factorization of 40? 2 × 2 × 5 2 × 2 × 5 2 × 2 × 2 × 5 2 × 2 × 2 × 5 2 × 5 × 5 2 × 5 × 5 2 × 5 × 5 × 5
The expression 2×2×2×5 shows the prime factorization of 40.
Prime factorization:
The number 40 is equal to
2 x 2 x 2 x 5, or = 40
23 x 5. = 40
What does prime factorization serve as?In mental arithmetic, fractions, finding square roots, and computing the HCF and LCM of two smaller numbers, prime factorization is a highly helpful tool when working with whole numbers. A whole number higher than 1 whose only elements are 1 and itself is referred to as a prime number. A whole number that may be split evenly into another number is referred to as a factor.
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Answer:
2 × 2 × 2 × 5
Step-by-step explanation:
2 × 2 × 2 × 5 = 4 × 2 × 5 = 8 × 5 = 40
I help I need help please someone help me !!!!!
Answer:
answer for this question is alternative A (80, 60) & (95,85)
1.2.PS-12
Determine whether the given number belongs to each set.
Integers
72
72
Whole
Numbers
?
Vyriole
Numbers
Yes
?
integers
Yes
Rational
Numbers
?
Katorial
Numbers
No
Click to select your answer(s) and then click Check Answer.
All parts showing
Clear All
Answer: Yes it is rational number because it has a terminating decimal expansion
Step-by-step explanation:
Define Rational number:
rational number, in arithmetic, a number that can be represented as the quotient p/q of two integers such that q ≠ 0. In addition to all the fractions, the set of rational numbers includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator.
Yes it is rational number because it has a terminating decimal expansion.
7/2=3.5
Define Integer:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14.
all integers between -7 and 2 in increasing order are:
-6,-5,-4,-3,-2,-1,0 and 1.
since, it has to be in increasing order -6 will come first and 1 at the last.
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Find FH
FH = {Blank}
Answer:
FH = 24
Step-by-step explanation:
HG = 13
FH = 37 - 13
= 24
Answer:
The value of FH is 24.
Step-by-step explanation:
The equation will be,
→ FHG = FH + HG
Then the value of FH will be,
→ 37 = FH + 13
→ FH = 37 - 13
→ [ FH = 24 ]
Hence, the value of FH is 24.
Quadrilateral ABCD has the following angle measures:
m∠A = 105°, m∠B = ?°, m∠C = 34°, m∠D = 90°
What is m∠B?
pleeeeease help!!
Answer:
131°
Step-by-step explanation:
Sum of all angles of a quadrilateral = 360°
We can find the unknown angle ∠B, by subtracting the sum of the angles ∠A, ∠C, ∠D from 360°.
∠A + ∠B + ∠C + ∠D = 360
105 + ∠B + 34 + 90 = 360
∠B + 229 = 360
∠B = 360 - 229
∠B = 131°
Answer:
The measure of m<GHE is 49°, the correct option is B.
What is a Quadrilateral?
A quadrilateral is a polygon with four sides.
It is of various types,
Trapezoid, which have one pair of parallel sides,
Parallelogram, it has two pairs of parallel sides,
Rhombus, it has all sides equal,
Rectangle, opposite sides are parallel and equal, and,
Square, all sides are equal and opposite sides are parallel, and all angles have measure of 90 degree.
The quadrilateral ABCD is ≅ quadrilateral EFGH
When two figures are congruent then by CPCTC, corresponding parts of congruent figures are congruent.
The measure of the angle
B = m<BCD = 90°
m<BAD = 131°
As the quadrilaterals are congruent,
By CPCTC
∠F = ∠FGH = 90°
m ∠FEH = 131°
The measure of m<GHE has to be determined.
The sum of the measures of all angle so of a quadrilateral is 360 degree.
The ∠F + ∠FGH + ∠FEH + ∠GHE = 360
90 +90+ 131 +∠GHE = 360
∠GHE = 49°
Step-by-step explanation:
The figure below is not drawn to scale. What is the value of x?
1. Is x = 2, y = 6, z = 1 a solution to the system of equations? Explain.
1.5x + y-z = 8
x + 3y = 18
2y + z = 13
2. If y = 6, find the values of and z.
x
4x+y=z=15
x + 2y + z = 38
The solution to the system of equation is x = 6, y = 4, z = 5
The equation is
1.5x + y - z = 8
x + 3y = 18
2y + z = 13
From this we have,
y = 8 - 1.5x + z
x + 3y = 18
2y + z = 13
x + 3(8 - 1.5x + z) = 18
2(8 - 1.5x + z) + z = 13
Apply the Distributive Property
x + 24 - 4.5x + 3z = 18
16 - 3x + 2z + z = 13
Combine like terms
-3.5x + 24 +3z = 18
16 - 3x + 3z = 13
Rearrange variables to the left side of the equation
-3.5x + 3z = 18 - 24
-3x + 3z = 13 - 16
Subtract the two equation
-3.5x + 3z - (-3x + 3z ) = 18-24 - ( 13-16)
-3.5x + 3z + 3x -3z = 18 - 24 - 13 + 16
-3.5x + 3x = 18 - 24 - 13 + 16
x = 6
Substitute the value of x in one of the equation
-3×6 + 3z = 13 - 16
-18 + 3z = -3
3z = 15
z = 5
Now put the value of x and z
y = 8 - 1.5x + z
y = 8 - 1.5×6 + 5
= 8 -9 + 5
= 4
Therefore the solution to the system of equation is x= 6, y = 4 and z = 5
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Can someone please help mee (20 points + brainliest!!!)
Answer:
a. Price needs to decrease by 6 Bozats.
[tex]\sf b. \ \ \sf x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]
Explanation:
Equation: p = 200 - 6x
where:
p = price per kilogramx = number of kilogram of snig solda.
To sell an additional kilogram of snig that is (x + 1) kilogram of snig.
current price = 200 - 6(x + 1) = 200 - 6x - 6
b.
[tex]\rightarrow p = 200 - 6x[/tex]
[tex]\rightarrow - 6x = p-200[/tex]
[tex]\rightarrow x =\dfrac{ p-200 }{-6}[/tex]
[tex]\rightarrow x =-\dfrac{1}{6} p+\dfrac{100}{3}[/tex]
Aliza needs to run at a rate faster than 8.2 feet per second in order to exceed her fastest time in a race. After running for 15 minutes, her coach determines that she is running at an average rate of 5.8 miles per hour. He converts the average rate to feet per second as shown below:
He concludes that she is not running fast enough to exceed her fastest time.
Coach's errors are;
Wrong conversion when converting hour to seconds
There is wrong conclusion since Eliza was running fast enough at a speed of 34ft/s compared to 8.8ft/s
The speed required by eliza is 8.8 ft/s
Converting 5.8miles to feet per second
Taking the coach conversion
This shows that 5.8mi/hr is equivalent to 34.0ft/s in accordance with coach conversion rate.
The coach made the first error by taking 60s as 1hr instead of 3600s as 1hr
The mistake that Eliza is not running fast enough to exceed her fastest time. Eliza is running at pace as her speed at 34ft/s exceed 8.8ft/s.
Hence the second error was the wrong conclusion made by the coach.
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The label on a car's antifreeze container claims to protect the car between -40°C and 125°C. To covert Celsius temperature to Fahrenheit temperature, the formula is C = 5/9 (F - 32). Write a compound inequality to determine the Fahrenheit temperature range at which the antifreeze protects the car.
The compound inequality to determine the Fahrenheit temperature range is given by [tex]-40 < \frac{5}{9}(F-32) < 125[/tex] .
An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.
Inequality is represented by:
The notation x < y means that x is less than y.The notation x > y means that x is greater than y.The notation x ≤ y or x ⩽ y means that x is less than or equal to y The notation x ≥ y or x ⩾ y means that x is greater than or equal to yA compound inequality is of the form : a < x < b implies that the value of x lies between the values of a and b.
According to the question if temperature is denoted in Celsius the inequality can be written as : -40° < °C < 125°
Now we know that the relation between C and F can be written as
[tex]C=\frac{5}{9}(F-32)[/tex]
Therefore the required inequality will be of the form:
[tex]-40 < \frac{5}{9}(F-32) < 125[/tex]
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