The fraction m/n that lies between 0 and 1 is equivalent to the real number m · n⁻¹, where m, n > 0 and m < n.
How can rational numbers between 0 and 1 be represented in terms of exponents?
By algebra, we know that fractions, a kind of rational numbers, are real numbers of the form m/n, where m and n are integers and n ≠ 0.
In addition, the operator "/" means division, an operator derived from the existence of multiplicative inverse and fundamental operation of multiplication in the real field.
Thus, the rational number m/n is equivalent to the number m · n⁻¹. If the rational number is between 0 and 1, then m, n > 0 and m < n.
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A surveyor found the angle of elevation from the ground to the top of the building at two locations 20 feet apart as shown below.
2 lines are drawn from the ground to the top of a building, forming 2 triangles with the ground. The angle of elevation of the first line is 48 degrees. The second line is 20 feet away from line 1. The angle of elevation of the second line is 33 degrees. c is the length of the first line and h is the height of the building. Angle A is the angle to the left of angle 48 degrees, and angle B is the angle at the convergence of the 2 lines with the top of the building.
Which measurements are correct? Round side lengths to the nearest hundredth. Check all that apply.
m∠A = 57°
m∠B = 15°
c ≈ 10.89 ft
h ≈ 8.09 ft
h ≈ 31.28 ft
Applying the sine ratio and law of sines, the correct measurements are:
B. m∠B = 15°
E. h ≈ 31.28 ft.
What is the Sine Ratio?Sine ratio that can be used to determine the side length of a right triangle is, sin ∅ = opposite side/hypotenuse.
Find c using the law of sines:
C = 33°
A = 180 - 48 = 132 [linear pair]
B = 180 - 33 - 132 = 15° [triangle sum theorem]
b = 20 ft
c = ?
Using the law of sines, b/sin B = c/sin C, we have:
20/sin 15 = c/sin 33
(c)(sin 15) = (20)(sin 33)
c = (20 × sin 33)/sin 15
c ≈ 42.09
Use the sine ratio to find h:
∅ = 48°
Hypotenuse = c = 42.09
Opposite = h = ?
sin 48 = h/42.09
h = (sin 48)(42.09)
h ≈ 31.28
The correct measurements are:
B. m∠B = 15°
E. h ≈ 31.28 ft
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Answer:
B. and E.
Step-by-step explanation:
the diagonal of the rectangle is 15 cm and one of its sides is 9 cm. find the area of the rectangle.
The area of the rectangle is 108 square centimeters.
Given Information
The following information has been given in the question,
Length of the diagonal of the rectangle, l = 15 cm
Length of one of the sides of the rectangle, a = 9 cm
Let the other side of the rectangle be b.
Finding the Other Side of the Rectangle
According to Pythagoras Theorem,
(hypotenuse)² = (base)² + (perpendicular)²
Applying this theorem in the right-angle triangle formed by the diagonal and 9cm side of the rectangle, we get,
l² = a² + b² [∵ The diagonal makes the hypotenuse]
(15)² = (9)² + b²
b² = (15)² - (9)²
b² = 225 - 81
b² = 144
b = √144
b = 12 cm
Calculating the Area of the Rectangle
Area of the rectangle, A = a × b
A = 9 × 12
A = 108 cm²
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Select the correct answer
The area of a triangle whose height is 1 more than 6 times its base is 13 square feet. If the base of the triangle is xfeet, which equation models
this situation?
A 6x²+x-12=0
B. 6x²+x -13=0
C 6x²+x-26=0
D. 36x² +6x-26= 0
Answer:
Step-by-step explanation:
The area for a triangle is
[tex]A=\frac{1}{2}bh[/tex]
Our base is given as x, the height is given as 1 more than 6 times the base which looks like this: 6x + 1. We know that the area is 13, so filling in everything:
[tex]13=\frac{1}{2} (6x+1)(x)[/tex]
We can get rid of the denominator of 2 by multiplying it on both sides to get:
[tex]26=(6x+1)(x)[/tex] and simplifying a bit:
[tex]26=6x^2+x[/tex]
Now we can move over the 26 and put the expression into standard quadratic form by setting it equal to 0:
[tex]6x^2+x-26=0[/tex] which is choice C
Can someone help me please
Answer:
y = x + 2
Step-by-step explanation:
You can find the slant asymptote using polynomial long division because the numerator is one degree higher than the denominator.
(x^2+x+4)/(x-1)
I'm not sure how to show long division but you should get:
x+2 with remainder 6
Then your slant asymptote is y = x + 2
You can graph it on Desmos to verify
When an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by:_______
When an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence
Precedence is known to be a kind of rule that tells the order in which a specific operations need to be carry out in an arithmetic expression.
The precedence of an operator specifies how tightly it binds two arithmetic expressions together.
In the arithmetic expression 4 + 5 * 3 , the answer is 19 and not 27 because the multiplication (*) operator has a higher precedence than the addition (+) operator.
Operator associativity is nothing but how operators of the same precedence are evaluated in an arithmetic expression. It can be either from left to right or right to left.
Therefore, when an arithmetic expression contains two or more different operators, such as * and , the order in which the operations is done is determined by: Operator precedence
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Quick please!!
What’s the distance between the following points?
Answer:
answer is 6^2 × 6^2 = squate root 72
distance equals 8.485
Answer:
6[tex]\sqrt{2}[/tex] ≈ 8.49 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = ( 8, - 9 )
d = [tex]\sqrt{(8-2)^2+(-9-(-3))^2}[/tex]
= [tex]\sqrt{6^2+(-9+3)^2}[/tex]
= [tex]\sqrt{36+(-6)^2}[/tex]
= [tex]\sqrt{36+36}[/tex]
= [tex]\sqrt{72}[/tex]
= [tex]\sqrt{36(2)}[/tex]
= [tex]\sqrt{36}[/tex] × [tex]\sqrt{2}[/tex]
= 6[tex]\sqrt{2}[/tex] units ← exact length
≈ 8.49 units ( to 2 dec. places )
Which graph represents y= cos(2x - π) +5?
The graph that represents y= cos(2x - π) +5 is illustrated below.
What is a graph?It should be noted that a graph simply means a series of connections among variables given.
In this case the graph that represents y= cos(2x - π) +5 is illustrated below.
The graph is attached.
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What is it the same of?
Answer:
C. [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex]
Step-by-step explanation:
When you convert a fraction division into multiplication, you convert the divisor into its reciprocal. The reciprocal of [tex]\frac{2}{7}[/tex] is [tex]\frac{7}{2}[/tex]. So you get your answer [tex]\frac{1}{4}[/tex]× [tex]\frac{7}{2}[/tex].
Here is Dan's recipe for breakfast.200ml of milk,50g of oats,30g of barley,40g of raisins.If he uses 100g of oats,how many grans of barley does he need
Answer:60g
Step-by-step explanation:
Hope this the answer
To find the quotient of 3 divided by one-sixtto find the quotient three-fourths divided by one-eighth,h, multiply 3 by
The quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively
How to find the quotientFrom the given equation, we have to find
= 3/4 ÷ 1/8
First , we take the denominator of the second fraction to be the numerator, we have
=
[tex] \frac{3}{4} \times \frac{8}{1} [/tex]
Multiply through
=
[tex] \frac{24}{4} [/tex]
=
[tex]6[/tex]
To find the quotient of 3 by 1/6
=
[tex]3 \times \frac{1}{6} [/tex]
=
[tex] \frac{3}{6} [/tex]
=
[tex] \frac{1}{2} [/tex]
Thus, the quotient of 3 by 1/ 6 and that of 3/4 by 1/ 8 is 1/2 and 4 respectively
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Im very confused about my precourse work for AP environmental science.
The conversion method given on the paper is something I am not used to and I cant seem to find any information about anything like this. I only need help with #3 and #4.
The computation shows that the values are 64000 acres and 563 metric tons.
How to compute the values?1. A 100 square mile area of national forest is how many acres?
1 mile square = 640 acres
100 square miles = 100 × 640 = 64000 acres.
2. Fifty eight thousand kilograms of solid waste is equivalent to how many metric tons?
1 metric ton = 103kg
58000 kg = 58000/103 = 563 metric tons
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1. Find the pattern in this sequence. Then write
the next three terms in the sequence.
5,2,1,...
Answer:
-1,-3,-4 it is just subtracting the same amount.
Step-by-step explanation:
Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10{,}00010,00010, comma, 000 cm^3
3
cubed. The base of the box is 252525 cm by 101010 cm.
The height of the rectangular cereal box is 40 cm.
How to find height of a rectangular prism?Volume of a rectangular prism = lwh
where
l = lengthw = widthh = heightTherefore,
10000 = 25 × 10 × h
10000 = 250h
h = 10000 / 250
h = 40 cm
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When solving an equation, Anne's first step is shown below. Which property justifies
Anne's first step?
The justification used is multiplicative property of equality because both sides are multiplied by the same value
Solving linear equationsGiven the expression below
-1/3(4x^2 - 3) - 3 = 5x^2 - 2
We are to determine the justification by Anne to get the step 2 as shown
(4x^2 - 3) - 3 = -3(5x^2 - 2)
Expand
(4x^2 - 3) - 3 = -15x^2 + 6
Hence the justification used is multiplicative property of equality because both sides are multiplied by the same value
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Player A throws the ball 25 yards to Player B. After catching the ball, Player B immediately turns 90 degrees to his left
and runs with the ball for 30 yards. At the end of the play, how far away is the ball from where it started? Round your
answer to the nearest whole number.
Answer:
39
Step-by-step explanation:
HELP PLEASE IM REALLY STUCK
A plane can cover 9904 km in 8 hours how mucb distance will it cover in 1 hour?
In one hour the plane will cover a distance of 1238 km.
What is a linear equation?
A linear equation has one or two variables. No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.
solving this we will get the valve of Y is x is given.
calculation:-
today distance = 9904 km.
total time is taken = 8 hours.
∴total distance covered in one hour = 9904/8
= 1238 km.
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Nina thought of a number. she added 24 , tripled the result, subtracted 18 , multiplied the result by 2 and got 120 . what was nina's number?
Answer:
Step-by-step explanation:
If we subtract 3 from the unknown number, we get just as much as if we subtracted 7 from the unknown number and we multiplied the result by 2
(Refer to the attached image)
Answer:
D. 10
Step-by-step explanation:
To find the distance between two points, use the distance formula:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points}[/tex]
Define the two points:
[tex]\textsf{Let }(x_1,y_1)=(4,-3)[/tex]
[tex]\textsf{Let }(x_2,y_2)=(-4,3)[/tex]
Substitute the two defined points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-4-4)^2+(3-(-3))^2}[/tex]
[tex]\implies d=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\implies d=\sqrt{(-8)^2+6^2}[/tex]
[tex]\implies d=\sqrt{64+36}[/tex]
[tex]\implies d=\sqrt{100}[/tex]
[tex]\implies d=\sqrt{10^2}[/tex]
[tex]\implies d=10[/tex]
Therefore, the distance between the two given points is 10 units.
Formula given by
[tex]\boxed{\sf Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{(-4-4)^2+(3+3)^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{8^2+6^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=\sqrt{10^2}[/tex]
[tex]\\ \tt{:}\longrightarrow D=10units[/tex]
Option D
WILL MAKE BRAINLIEST!! Solve for x.
[tex]3x + 2 = 47 \\ 3x = 47 - 2 \\ 3x = 45 \\ x = \frac{45}{3} = 15[/tex]
Convenience sampling Multiple Choice is the same as simple random sampling. ensures that samples are representative of the population. is an unbiased sampling method. collects sample information from groups that are easy to obtain.
Option (d) is correct. Convenience sampling collects sample information from easy-to-collect groups.
Given convenient sampling.
Convenience sampling is defined as a method adopted by researchers in which they collect market research data from a pre-existing group of respondents. This is the most commonly used sampling technique because it is extremely fast, simple and economical. In many cases, members are easily accessible to be part of the template. It is non-probability sampling and therefore different from random sampling. Since the samples are taken for convenience, the samples are not always representative of the population and therefore have bias. In this case, people were sampled simply because they were convenient.
Thus, convenience sampling collects sample information from easy-to-collect groups.
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Write as a decimal the number that is exactly halfway between 1 100 and 1 10
Answer:
605
Step-by-step explanation:
We are starting at 110 and not zero, so I need to find have the distance between 110 and 110 and add that to 110.
110 + 1/2(1100 - 110) Subtract what is in the parentheses
110 + 1/2(990) Find 1/2 of 990
110 + 495
604
majorly behind, anyone know the answer?
HELP HURRY pls
Draw the image of AABC under a dilation whose center is P and scale
factor is 3
Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.
How to generated a resulting triangle by transformation rules
In this question we must apply a kind of rigid transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:
P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)] (1)
Where:
O(x, y) - Point of referencek - Dilation factorP(x, y) - Original pointP'(x, y) - Resulting pointLet assume that the point P is the origin of a rectangular system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).
Then, the vertices of the resulting triangle A'B'C' are, respectively:
A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]
A'(x, y) = (- 3, 6)
B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]
B'(x, y) = (- 3, - 3)
C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]
C'(x, y) = (6, 0)
Finally, we draw the resulting triangle with the help of a graphing tool.
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Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by where the measurements are in meters. What is the width of the cooling tower at the base of the structure
The width of the cooling tower is 36 meters.
What is a cooling tower?A cooling tower is a vent that is built for the purpose of releasing waste heat back to the atmosphere.
Now we can model the system using; x²/324 - (y² - 90)²/1600. Thus, the width can be obtained from;
2 × ✓324
= 2 × 18
= 36 meters
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Missing parts;
Cooling towers are used to remove or expel heat from a process. A cooling tower's walls are modeled by x squared over 324 minus quantity y minus 90 end quantity squared over 1600 equals 1 comma where the measurements are in meters. What is the width of the cooling tower at the base of the structure? Round your answer to the nearest whole number.
36 meters
48 meters
80 meters
89 meters
Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight
The probability will be:
Case 1 matches with 5/48.
Case 2 matches with 1/12.
Case 3 matches with 1/4.
Case 4 matches with 1/8.
Case 5 matches with 5/16.
How to illustrate the probability?We have a total sample space of six-sided die and an eight sided die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)
Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are: (3,5),(3,7),(5,3),(5,5),(5,7)
And the total number of outcomes are: 48.
The required probability is 5/48.
Case 2: The probability that the second number is twice the first number are:
(1,2),(2,4),(3,6),(4,8)
And the total number of outcomes are 48.
So, the required probability is 1/12.
Case 3: The probability of a number whose sum is a multiple of 4 are:
(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).
And the total number of outcomes are: 48.
The required probability is 12/48 = 1/4
Case 4: The probability that the sum of two numbers is greater than 11.
(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)
And a total number of outcomes are 48.
So, the required probability is 6/48 = 1/8.
Case 5: The probability that the second number rolled is less than the first number are:
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)
And the total number of outcomes are: 48.
The required probability is 15/48 = 5/16.
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In standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to?
in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3
What is standard form?Standard form is simply a value with an exponential powerl
Given the values;
It is important to note that any number to the power of O is equivalent to 1
So, we have
10^ 0 = 1
4( 10^-3) = 37
5(10^3) = 5000
Now, let's substitute the values
(10°) + 4 (10-3) + 5 (10³)
It is equivalent to
⇒1 + 4 × 10^-3 + 5 × 10^3
⇒1 + 37 + 5000
Add the values
= 5038
Let's convert it to standard form, we have
= 5. 04 × 10 ^3
Thus, in standard form, 7 (10°) + 4 (10-3) + 5 (10³) is equal to 5. 04 × 10 ^3
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Find the area of the figure.
Answer:
60 ft^2
Step-by-step explanation:
increase $32 in the ratio 2:5
decrease 54 litter in the ratio 5:1
Answer:
Step-by-step explanation:
32 = 2 : 5
32/7 = 4
2 x 4 : 4 x 5
8 : 20
The probability is .80 that a standard normal random variable is between -z and +z. The value of z is approximately:________
The z value for the probability in the standard normal table is 1.29.
In this question,
Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean. A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution.
The value of probability is 0.80
A standard normal random variable is between -z and +z, So
P(-z < 0 < z) = 0.80
⇒ 2P(0 < z) = 0.80
⇒ P(0 < z) = [tex]\frac{0.80}{2}[/tex]
⇒ P(0 < z) = 0.40
From the standard normal table, z value for the probability 0.40 is
⇒ z = 1.29
Thus P(0 < 1.29) = 0.40
Hence we can conclude that the z value for the probability in the standard normal table is 1.29.
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