The logarithmic equation is:
log₂128 = x
So the correct option is the third one
How to rewrite this as a logarithmic equation?
Here we have the expression.
2ˣ = 128
Now, if we apply the natural logarithm to both sides, we can get:
ln(2ˣ) = ln(128)
Because of the property of natural logarithms, we can write the left side as:
ln(2ˣ) = x*ln(2) = ln(128)
Now, if we isolate x, we get:
x = ln(128)/ln(2)
And remember that:
ln(k)/ln(n) = logₙ(k)
Then we can rewrite the logarithmic equation as:
x = log₂(128)
Which is the third option.
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1)give your answer in terms of π
2) give your answer using 3.14 for π
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
Volume of a cylinderA cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes
The volume of the composite cylinder is expressed as shown below;
V = πr²h
where
r is the radius
h is the height
According to the given diagram;
V = Vl - Vs
V = π(10)²*15 - π(5)²*15
V = 1500π - 375π
V = 1125π cubic inches
If the value of π is 3.14, hence;
V = 1125(3.14) cubic inches
V = 3532.5 cubic inches
The volume of the composite solid in terms of pi and using 3.14 as pi are 1125π cubic inches and 3532.5 cubic inches respectively
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Please help im not the brightest with math
Answer:
12 square in
Step-by-step explanation:
In the diagram, the diameter is 4 in. Radius is half the length of diameter, so the radius of the yellow circle is 2 in. Using the given formula, A = pi*r*r, we can calculate the approximate area of the circle.
A = pi*r*r = 3*2*2 = 12 square in
Answer:
12 in^2
Step-by-step explanation:
Since the formula to find the area of a circle is already up, we can use that to solve the question.
In the image, we can see that the diameter of the circle is 4inches. Since two radii equal one diameter, one radius is 2 inches.
--> The reason why we found the radius is because the 'r' in the formula means radius. We need the value of the radius to find the area of the circle.
Now, we can just replace r with 2.
--> A = 4[tex]\pi[/tex]
Since the question told us to replace [tex]\pi[/tex] with 3, we can do that.
--> A = 4 x 3
--> A = 12
We can conclude that the area of the circle is 12 in^2.
Someone help i cant answer this
Answer:
100%, 20%, 60%
Step-by-step explanation:
250/250 = 100/100 = 100%
50/250 = 1/5 = 20/100 = 20%
150/250 = 3/5 = 60/100 = 60%
A circle's diameter has endpoints at
(-4,-7) and (5,-2).
a) What is the length of the diameter?
b) What is the length of the radius?
Part (a)
We'll use the distance formula.
[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]
The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.
========================================================
Part (b)
We divide the diameter in half to get the radius.
Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.
Which is the graph of the equation y- 1 = (x − 3)?
Answer:
the graph is a linear function
root (2,0) vertical intercept (0,2)
Step-by-step explanation:
Is there any number in base 10 (positive or negative) that can be written in multiple
ways in base −4? Can you prove it? If yes, provide the number and the base −4
representations, and if no, show why.
The true statement is that no number in base 10 can be written in multiple ways in base 4
How to determine the true statement?The base of the numbers are given as:
Base 10 and base 4
Base 10 numbers are also referred to as decimal numbers, while base 4 numbers are quaternary numbers
There is only one equivalent of each number in each base.
This means that (for instance)
357 in base 10 is 11211 in base 4
The above number does not have any other representation in base 4 and it can not be written in another way.
This is the same for other numbers in base 10
Hence, the true statement is that no number in base 10 can be written in multiple ways in base 4
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What is the equation of the line that is parallel to the line y = -1/3x + 4 and passes through the point (6, 5)?
Answer:
[tex]y=-\frac{1}{3}x+7[/tex]
Step-by-step explanation:
Parallel lines have the same slope, so the slope of the line we need to find is -1/3.
Substituting into point-slope form and converting to slope-intercept form,
[tex]y-5=-\frac{1}{3}(x-6) \\ \\ y-5=-\frac{1}{3}x+2 \\ \\ y=-\frac{1}{3}x+7[/tex]
A three-digit number has one more ten than it has hundreds, and it also has one more than twice as many units as tens. The sum of the number and that number reversed is 31 less than 10 cubed. Find the reverse number.
15 pts
The reverse number of the three-digit number is 732
How to determine the reverse of the number?Let the three-digit number be xyz.
So, the reverse is zyx
This means that
Number = 100x + 10y + z
Reverse = 100z + 10y + x
From the question, we have the following parameters:
y = x + 1
z = 1 + 2y
The sum is represented as:
100x + 10y + z + 100z + 10y + x = 10^3 - 31
100x + 10y + z + 100z + 10y + x = 969
Evaluate the like terms
101x + 101z + 20y = 969
Substitute y = x + 1
101x + 101z + 20(x + 1) = 969
101x + 101z + 20x + 20 = 969
Evaluate the like terms
101x + 101z + 20x = 949
121x + 101z = 949
Substitute y = x + 1 in z = 1 + 2y
z = 1 + 2(x + 1)
This gives
z = 2x + 3
So, we have:
121x + 101z = 949
121x + 101* (2x + 3) = 949
This gives
121x + 202x + 303 = 949
Evaluate the sum
323x = 646
Divide by 323
x = 2
Substitute x = 2 in z = 2x + 3 and y = x + 1
z = 2*2 + 3 = 7
y = 2 + 1 = 3
So, we have
x = 2
y = 3
z = 7
Recall that
Reverse = 100z + 10y + x
This gives
Reverse = 100*7 + 10*3 + 2
Evaluate
Reverse = 732
Hence, the reverse number of the three-digit number is 732
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if csc(θ)=2 and tan (θ)<0, determine the exact value of cos(θ)
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
What is the exact value of a trigonometric function?
In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:
cos θ = - √[1 - (1 / csc θ)²]
If we know that csc θ = 2, then the exact of the cosine function is:
cos θ = -√[1 - (1 / 2)²]
cos θ = -√(3 / 4)
cos θ = -√3 / 2
By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.
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Paulo wants to buy new carpet for his bedroom. The floor is in the shape of a rectangle. Its length is 16 feet and its width is 11 feet. The carpet he wants costs $9 per square foot. How much will the carpet cost for the floor?
Answer:
11x9=99 16x9=144=243 144+99
The cost of the carpet required for the given rectangular floor is $1584.
A rectangle is a quadrilateral with equal pairs of sides.
Given that:
The shape of the floor is a rectangle.
The length of the floor is 16 feet.
The width of the floor is 11 feet.
So,
The area of the floor = length × breadth
= 16 × 11
= 176 sq feet
The area of the floor is 176 sq feet.
The cost of the carpet for a 1 sq foot floor = $9
The cost of the carpet for a 176 sq feet floor = $9 × 176
= $1584
Thus, the cost of the carpet for a 176 sq feet floor is $1584.
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On average, mary has noticed that 18 trains pass by her house daily (24 hours) on the nearby train tracks. what is the probability that exactly 1 train will pass her house in a 3 hour time period?
The probability that exactly 1 train will pass Mary's house is 0.00889.
According to the given question.
On average, 18 trains pass by Mary's house daily i.e. in 24 hours.
As, we know that "Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event".
Therefore,
The probability that exactly one train will pass Mary's house in a 3 hour period
= [tex]\frac{^{18C_{1} } }{^{24} C_{3} }[/tex]
[tex]= \frac{\frac{18!}{1!\times17!} }{\frac{24!}{3!\times 21!} }[/tex]
[tex]= \frac{18}{\frac{24\times23\times22}{3\times2\times1} }[/tex]
[tex]=\frac{18}{8\times23\times\ 11}[/tex]
= 18/2024
= 0.00889
Hence, the probability that exactly 1 train will pass Mary's house is 0.00889.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
○ [tex]x = -7[/tex]
Step-by-step explanation:
Given the equation:
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex],
to solve for [tex]x[/tex], we have to rearrange the equation to make [tex]x[/tex] its subject.
[tex]10(x + 10) - 4 = 11 - 5(2x + 11)[/tex]
⇒ [tex]10x + 100 - 4 = 11 - 10x -55[/tex] [expand brackets]
⇒ [tex]10x + 96 = -44 - 10x[/tex]
⇒ [tex]10x + 10x + 96 = -44[/tex] [add [tex]10x[/tex] to both sides]
⇒ [tex]20x + 96 = -44[/tex]
⇒ [tex]20x = -44 - 96[/tex] [subtract 96 from both sides]
⇒ [tex]20x = -140[/tex]
⇒ [tex]x = \frac{-140}{20}[/tex] [divide both sides by 20]
⇒ [tex]x = \bf-7[/tex]
Answer:
B) x = -7
Step-by-step explanation:
Given equation: [tex]10(x+10)-4=11-5(2x+11)[/tex]
Step 1: Distribute [tex]10[/tex] and [tex]-5[/tex] through the parentheses.
[tex]\implies 10(x)+10(10)-4=11-5(2x)-5(11)[/tex]
[tex]\implies 10x+100-4=11-10x-55[/tex]
Step 2: Simplify (combine like terms).
[tex]\implies 10x+100-4=11-10x-55[/tex]
[tex]\implies 10x+96=-44-10x[/tex]
Step 3: Add [tex]10x[/tex] to both sides.
[tex]\implies 10x+10x+96=-44-10x+10x[/tex]
[tex]\implies 20x+96=-44[/tex]
Step 4: Subtract [tex]96[/tex] from both sides.
[tex]\implies 20x+96-96=-44-96[/tex]
[tex]\implies 20x=-140[/tex]
Step 5: Divide both sides by [tex]20[/tex] to isolate [tex]x[/tex].
[tex]\implies \dfrac{20x}{20}=\dfrac{-140}{20}[/tex]
[tex]\implies \boxed{x=-7}[/tex]
Convert the cartesian coordinate (-6,-1) to polar coordinates, 0 ≤ θ < 2 π , r > 0 0≤θ<2π, r>0
The polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
In this question,
We have been given the cartesian coordinate (-6, -1)
We need to convert given cartesian coordinate to polar coordinates.
We know that the polar coordinates is of the form (r, θ)
where, r is the magnitude with r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
and θ is the angle associated with the coordinates which is given by θ = [tex]tan^{-1}(\frac{y}{x} )[/tex]
The magnitude of the given polar coordinate is,
⇒ r = [tex]\sqrt{x^{2}+ y^{2} }[/tex]
⇒ r = [tex]\sqrt{(-6)^{2}+ (-1)^{2} }[/tex]
⇒ r = [tex]\sqrt{36+ 1}[/tex]
⇒ r = [tex]\sqrt{37}[/tex]
⇒ r = 6.08
And the angle associated with the coordinate is,
⇒ θ = [tex]tan^{-1}(\frac{-1}{-6} )[/tex]
⇒ θ = [tex]tan^{-1}(0.167 )[/tex]
⇒ θ = 9.48°
⇒ θ = 0.0523π
So, the polar coordinate is (6.08, 0.0523π)
Therefore, the polar coordinate of given cartesian coordinate (-6, -1) is
(6.08, 0.0523π)
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HELP PLEASE!!
20 points for grabs
Step-by-step explanation:
....................
Solve for d.
5+d > 5−d
Answer:
d>0
Step by Step Explanation:
Let's solve your inequality step-by-step.
5+d>5−d
Step 1: Simplify both sides of the inequality.
d+5>−d+5
Step 2: Add d to both sides.
d+5+d>−d+5+d
2d+5>5
Step 3: Subtract 5 from both sides.
2d+5−5>5−5
2d>0
Step 4: Divide both sides by 2.
2d/2>0/2
d>0
Answer:
3
Step-by-step explanation:
You could put 3 because 5+3 is greater than 5-3.
Ken can run m miles at a
pace of 6.30 minutes per
mile. He ran slower for 10
minutes to warm up.
Write an equation that
represents the total time,
t, Ken spent running.
Equation that represents the total time t (in minutes) Ken spent running is = 10 + m/6.30.
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation
How to solve such time related questions?
The key concept for solving such questions is the relationship between speed, distance and time.
The relationship between them is Distance = Speed x Time
Total time t (in minutes) =Initial Time + distance/speed
Given :-
Distance = mSpeed = 6.30 miles per hourInitial Time = 10 minThus,
t = 10 + m/6.30.
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The length of a spring with no applied force acting on it is 10.00 centimeters. Juanita applied different forces to the spring and recorded the new lengths of the spring in a table. She also graphed a scatterplot from the results in the table. Based on the scatterplot, which equation BEST represents these data?
Answer:
the second option L = 0.05F + 10
Step-by-step explanation:
the first one
F = 0.05L + 10
does not make any sense, as for length = 10 the force has to be 0. but this function here gives us
0.05×10 + 10 = 0.5 + 10 = 10.5
which is clearly not 0. so, this is wrong.
the second one is correct.
L = 0.05F + 10
it is not perfect, but it is the only one describing the first data points well. like, when F = 0, then L = 10.
the third
L = 0.05F
fails already at the beginning F = 0, as it gives us L = 0 instead of 10. this is wrong.
the fourth
F = 0.05L
fails also already at the beginning. for L = 10 we need to have F = 0. but instead we get F = 0.5. this is wrong.
one end of a tent is a triangle. the height of the triangle is 1.5 m and the base is 2.5 m. what is the area of the triangle?
Answer:
1.5×2.5/2=1.875.
Step-by-step explanation:
We all know that area of triangle is base into hight upon 2.
give the volume of the cylinder below
Answer:
B. 126 [tex]\pi[/tex]
Step-by-step explanation:
The volume for a cylinder is: Area of the base x Height
The base is a circle with a diameter of 6cm.
The formula to find the area of the base is: radius x radius x pi
In this case, the radius is 3 (6/2) so the area will be 9pi.
Now that we know that area of the base, all we need to do is multiply the height, which is 14cm.
9 pi x 14 = 126 pi
So B. 126 pi is the correct answer!
Answer:
126π
option B is the correct answer
The slope of the line shown in the graph is __ and the y-intercept of the line __
Answer:
slope
(0, 6) and (-9, 0)
0 - 6 / -9 - 0 = -6/-9 = 2/3
y intercept is when the line intercepts the y axis and x = 0
The slope of the line shown in the graph is 2/3 and the y-intercept of the line is 6
Answer:
slope is 2/3
y intercept is 6
Step-by-step explanation:
We can find the slope of the line by using two point
(-9,0) and (0,6)
The slope formula is
m = ( y2-y1)/(x2-x1)
= ( 6 - 0) /( 0 - -9)
= (6-0)/(0+9)
= 6/9
= 2/3
The y intercept is where it crosses the y axis ( the value where x is 0)
The y intercept is 6
can someone please help me(20 points will give brainliest!!!)
Answer:
g(2) = 16; g(-2) = 4; g(a) = 3a + 10; 3(a+2) = 3a + 16
Step-by-step explanation:
We want to substitute the value in the parentheses on the left-hand side for the value of x on the right-hand side
Thus, g(2) = 3(2) + 10 = 6 + 10 = 16
g(-2) = 3(-2) + 10 = -6 + 10 = 4
g(a) = 3(a) + 10 = 3a + 10
g(a + 2) = 3(a + 2) + 10 = 3a + 6 + 10 = 3a + 16
What is the slope of the line that passes through the points (9, 2) and
(9,27)? Write your answer in simplest form.
Answer:
Slope (m) = infinity
Step-by-step explanation:
Given points:
⇒ (9, 2) and (9, 27)
In order to find the slope of these points, we must use the slope formula.
So the formula is ⇒ y₂ - y₁ / x₂ - x₁
Plug in the given points:
⇒ 27 - 2 / 9 - 9
Solve both the top and bottom (numerator and denominator):
⇒ 25 / 0
Divide:
⇒ Undefined.
(Anything divided by zero is undefined).
ts
The table below represents the concessions sold at the last three basketball games. The
games were held on different days and times.
Friday night
Saturday morning
Tuesday night
Total
Candy Hot Dogs
148
94
78
320
102
27
150
279
Nachos
108
42
97
247
Total
358
163
325
846
What is the approximately probability of a person going to a Saturday morning game and
buying nachos?
The approximately probability that a person will go to the Saturday morning game and buy nachos is 18%.
What does approximate mean?Anything similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated. An estimated result can be obtained by rounding the values in a computation before carrying out the procedures.The word type "approximately" is an adverb.A value that is close to, higher than, as close to, and with the specified level of precision is known as an approximation value by the excess of a number.Approximately symbol ≈.The approximately probability of a person going to a Saturday morning game and buying nachos:
Probabaility= [tex]\frac{150}{846} *100[/tex]
=17.7%
Approximately=18%.
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corresponding angles are congruent =. which angle corresponds with 3
The angle that corresponds to 3 is angle 5
How to determine the angle that corresponds to 3?Corresponding angles are angles that are at the same relative position between parallel lines and transversal
These angles are congruent
From the figure, we have:
Angle 3 and Angle 5 are in the same relative position
Hence, the angle that corresponds to 3 is angle 5
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A student is trying to solve the system of two equations given below: equation p: y z = 6 equation q: 3y 4z = 1 which of these is a possible step used in eliminating the y-term? (y z = 6) ⋅ 4 (3y 4z = 1) ⋅ 4 (y z = 6) ⋅ −3 (3y 4z = 1) ⋅ 3
Option C is correct (y + z = 6) ⋅ −3
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.As per the statement -
A student is trying to solve the system of two equations given below:
Equation P: y + z = 6 ....[1]
Equation Q: 3y + 4z = 1 ....[2]
Multiply the equation [1] by -3 to both sides we have;
-3 .( y + z = 6 ) ⇒ -3y -3z = -18..........(3)
Add equation [2] and [3] to eliminate the y-term;
z = -17
Therefore, the possible step used in eliminating the y-term is, (y + z = 6) ⋅ −3
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The complete question is -
A student is trying to solve the system of two equations given below: Equation P: y + z = 6 Equation Q: 3y + 4z = 1 Which of these is a possible step used in eliminating the y-term?
(y + z = 6) ⋅ 4
(3y + 4z = 1) ⋅ 4
(y + z = 6) ⋅ −3
(3y + 4z = 1) ⋅ 3
C=22°, a = 14 m, b = 8 m find area of ABC to the nearest tenth
Answer:
21.0 m²
Step-by-step explanation:
The formula for the area of a triangle from two sides and the included angle is ...
A = 1/2ab·sin(C)
AreaUsing this formula, we find the area to be ...
A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²
The area of triangle ABC is about 21.0 square meters.
A sampling method is _________ when the individuals selected for one sample are used to determine the individuals in the second sample.
a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample
What is sampling?Sampling can be defined as a technique of selecting a subset of the population or individual members in order to make statistical inferences from them and estimate the entire characteristics of the whole population.
Sampling methods are used by researchers in market research to reduce the workload and also to research the entire population
It is time-friendly, cost-effective method and forms the basis of research design.
Some sampling methods are;
Simple random samplingSystematic samplingStratified samplingClustered samplingQuota samplingPurposive samplingIt can be said to be dependent when selecting from one sample affects another sample.
Thus, a sampling method is dependent when the individuals selected for one sample are used to determine the individuals in the second sample.
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Find the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0).
The equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and
r(1, 1, 0) is x + y + z = 2 .
According to the question
Let the points
p(0, 1, 1) = (x1,y1,z1)
q(1, 0, 1)= (x2,y2,z2)
r(1, 1, 0)= (x3,y3,z3)
now,
The equation of the plane through the points
i.e
The formula of equation of a plane passing through three non collinear points
[tex]\left[\begin{array}{ccc}x-x1&y-y1&z-z1\\x2-x1&y2-y1&z2-z1\\x3-x1&y3-y1&z3-z1\end{array}\right] = 0[/tex]
by substituting the values in the formula of equation of a plane
[tex]\left[\begin{array}{ccc}x-0&y-1&z-1\\1-0&0-1&1-1\\1-0&1-1&0-1\end{array}\right] = 0[/tex]
[tex]\left[\begin{array}{ccc}x&y-1&z-1\\1&-1&0\\1&0&-1\end{array}\right] = 0[/tex]
x(1) - (y-1)(-1) + (z-1)(1) = 0
x + y - 1 + z - 1 = 0
x + y + z = 2
Hence, the equation of the plane through the points p(0, 1, 1), q(1, 0, 1), and r(1, 1, 0) is x + y + z = 2 .
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Which equation represents the relationship shown in the
graph?
gradient = rise/run
= 2/1
= 2
So,it's the first option, y=2x
Hope this helps!
Jake volunteers to help out his younger brother's basketball team in his free time. One of his tasks is to ensure that all the basketballs have enough air in them. Given that a properly inflated basketball measures 8.8 inches across, what is the total volume of air inside six of Jake’s basketballs? Assume that the wall of each ball is infinitely thin.
Using the volume of a sphere, the total volume of air inside six of Jake's basketballs is of 2140.8 cubic inches.
What is the volume of a sphere?The volume of a sphere of radius r is given as follows:
[tex]V = \frac{4\pi r^3}{3}[/tex]
From the problem, since the properly inflated basketball measures 8.8 inches across, the diameter is of 8.8 inches, hence the radius is:
r = 8.8/2 = 4.4 inches.
Then the volume in cubic inches of a single ball is:
V = 4 x pi x (4.4)³/3 = 2140.8 cubic inches.
For the six balls:
6 x 356.8 = 2140.8 cubic inches.
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