The solution for 4ˣ⁺³ = 7 using change of base formula is -1.596
How to solve 4ˣ⁺³ = 7 using the change of base formula log base b of y equals log y over log b?To solve 4ˣ⁺³ = 7 using change of base formula log base b of y equals log y over log b, we are going to use logarithm rules.
If f(x) = g(x), then ln(f(x)) = ln(g(x)). Thus,
ln( 4ˣ⁺³) = ln(7)
Using log rule:
[tex]\log _{a} x^{b} = b \log _{a}(x)[/tex]
ln (4ˣ⁺³) = ln(7)
(x+3) · ln(4) = ln(7)
(x+3) · ln(2²) = ln(7)
(x+3) · 2ln(2) = ln(7)
x+3 = ln(7) / (2ln(2))
x = [ln(7) / (2· ln(2))] - 3
x = -1.596
Thus, the solution is x = -1.596
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Answer:
Did he round up?
Step-by-step explanation:
For what values of a and m does f(x) have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1? f (x) = startfraction 2 x superscript m baseline over x a endfraction
Using the concept of vertical and horizontal asymptotes, it is found that the function will have a horizontal asymptote at y = 2 and a vertical asymptote at x = 1 for a = -1 and m = 1.
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.In this problem, the function is:
[tex]f(x) = \frac{2x^m}{x + a}[/tex]
It has a vertical asymptote at x = 1, hence:
x + a = 0
1 + a = 0
a = -1
It has a horizontal asymptote at y = 2, hence:
[tex]\lim_{x \rightarrow \infty} f(x) = 2[/tex]
[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x + a} = 2[/tex]
[tex]\lim_{x \rightarrow \infty} \frac{2x^m}{x} = 2[/tex]
[tex]2^{m-1} = 2[/tex]
Then, since we want to simplify, the exponents at the numerator and the denominator have to be equal, hence m = 1.
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Can the sides of a triangle have lengths 2, 4, and 7?
Answer:
No, they can't
Step-by-step explanation:
According to the Triangle Inequality Theorem, the largest side cannot be greater than the sum of the other two sides.
2+4= 6<7
As you can see from this Equation NOT any two side are greater than the third making this NOT possibly be a tringle.
2+7=9>4
4+7=11>2
Alcohol is a major contributor to high percentages of academic problems and college dropouts. question: alcohol is a major contributor to high percentages of academic problems and college dropouts. true false not sure increasing alcohol consumption lowers gpas. question: increasing alcohol consumption lowers gpas. true false not sure students who drink more heavily miss classes at the same rate as other students. question: students who drink more heavily miss classes at the same rate as other students. true false not sure students who drink more study less. question: students who drink more study less. true false not sure students with a 2.0 gpa (c) consume twice as many drinks on average than students with a 4.0 gpa (a).
The correct decision for the statements are
True--->Alcohol is a major contributor to high percentages of academic problems and college dropouts. True--->Increasing alcohol consumption lower GPAs. False--->Students who drink more heavily miss classes at the same rate as other students.True----> Students who drink more study less. False----> Students with a 2.0 GPA (C) consume twice as many drinks on average than students with a 4.0 GPA (A).This is further explained below.
What is Alcohol?Generally, alcohol is a colorless liquid that is volatile and combustible. It is created during the natural fermentation of carbohydrates and is the component that gives wine, beer, spirits, and other beverages their intoxicating properties. Additionally, alcohol is utilized as an industrial solvent and as fuel.
In conclusion, The appropriate response for each of the statements is
Alcohol is a significant factor in the large percentage of students who struggle academically and drop out of college, which is true. It's true that drinking more alcohol brings a drop in GPA. Students who consume more alcohol miss the same number of courses as students who consume less alcohol. This statement is false. Students who drink more spend less time studying, which is true. Students with a grade point average of 2.0 (C) drink on average two times as much alcohol as students with a grade point average of 4.0 (A) (A).
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To model some data Gwyn ran an exponential regression and found the regression equation to be y = 6.72 x 0.996x
Answer:
y=6.72x^0.996x
Step-by-step explanation:
Which ordered pair is a solution to the equation 2x − 3y = 1?
The ordered pair that is a solution to the equation 2x − 3y = 1 is; (2, 1)
How to find the solution that is an ordered pair?
We are given the equation;
2x - 3y = 1
Now, the ordered pair that is a solution simply means the least whole numbers for x and y that will make the equation valid.
Now, since the coefficient before x is bigger than the coefficient before y which is negative, then it means x must be larger than y. Thus, let us try x = 2 and y = 1 to get;
2(2) - 3(1) = 1
This makes the equation valid.
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a typist can type 495 words in 15 minutes. How many words can she type in 25 minutes?
Answer:
They can type 825 words in 25 minutes.
Step-by-step explanation:
First, we need to find how many words they can type per minute. To do that, we need to divide 495 by 15.
[tex]495 \div 15 = 33[/tex]
Now, we know how many words per minute, and the question is how many words they can type in 25 minutes. So to find our answer, we need to multiply 33 by 25, since 33 is how many words in one minute.
[tex]33 \times 25=825[/tex]
So now we know our answer: 825 words in 25 minutes.
Which digit in 125 734 016 has a value of 20 000 000?
Step-by-step explanation:
in a number like 125,734,016
the right most position has the weight 10⁰ = 1
so, 6×1 = 6.
the second right most position has the weight 10¹ = 10.
so, 1×10 = 10
the third right most position has the weight 10² = 100.
so, 0×100 = 0
the 4th right most position has the weight 10³ = 1000.
so, 4×1000 = 4,000
the 5th right most position has the weight 10⁴ = 10000.
so, 3×10000 = 30,000
the 6th right most position has the weight 10⁵ = 100000.
so, 7×100000 = 700,000
the 7th right most position has the weight 10⁶ = 1000000.
so, 5×1000000 = 5,000,000
the 8th right most position has the weight 10⁷ = 10000000
so, 2×10000000 = 20,000,000
and so on.
as we can see, the 2 (the 8th most position from the right or the second position from the left) has the value of 20,000,000.
A radioactive substance decays exponentially. A scientist begins with 110 milligrams of a radioactive substance. After 20 hours, 55 mg of the substance remains. How many milligrams will remain after 26 hours
Answer:
44.7 mg
Step-by-step explanation:
The equation for exponential decay can be written in the form ...
y = a·b^(t/p)
where 'a' is the initial value, 'b' is the decay factor, 'p' is the period over which the decay factor is applicable, and t is time in the same units as p.
SetupUsing the above equation, we have ...
a = initial value = 110 mg
b = decay factor = 55/110 = 1/2 over time period p=20 hours
Then the equation is ...
y = 110·(1/2)^(t/20) . . . . amount remaining after t hours
SolutionWe want the amount remaining after 26 hours. That will be ...
y = 110·(1/2)^(26/20) ≈ 44.67
About 44.7 milligrams will remain after 26 hours.
El triángulo ABC es equilátero y L, M y N son los puntos medios de BC, AB y CA respectivamente. Si MN = 3, ¿cuál es el valor de ML?
The value of ML = 3, using the mid-point theorem of triangles.
According to the midpoint theorem, "the line segment of a triangle crossing the midpoints of two sides of the triangle is said to be parallel to its third side and also half the length of the third side."
In the question, we are given that triangle ABC is an equilateral triangle, and L, M, and N are the midpoints of BC, AB, and CA respectively.
Thus, by the midpoint theorem, we can say that:
MN || BC, and MN = (1/2)BC,ML || AC, and ML = (1/2)AC, andNL || AB, and NL = (1/2)AB.Assuming AB = BC = AC = x units, we get:
MN = (1/2)BC = x/2,ML = (1/2)AC = x/2, andNL = (1/2)AB = x/2.
Thus, the triangle LMN is an equilateral triangle.
Thus, MN = ML = NL.
Given MN = 3, we can write the value of ML = 3.
Thus, the value of ML = 3, using the mid-point theorem of triangles.
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The given question is in Spanish. The question in English is:
"Triangle ABC is equilateral and L, M, and N are the midpoints of BC, AB, and CA respectively. If MN = 3, what is the value of ML?"
PLS HELP ITS DUE IN 9 MIN AND IM CONFUSED AND I DON’T WHAT TO DO ANSWER ASAP ILL GIVE BRAINIESTTTTT
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 20% of people are likely to invest in portfolio A, 30% are likely to invest in B, and 50% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing either stocks or bonds from portfolio C?
Considering the given tree diagram, there is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
At each node, the sum of the probabilities is of 1, hence:
0.2 + 0.3 + Z = 1.
Z = 0.5.
There is a 0.5 = 50% probability of an investor choosing either stocks or bonds from portfolio C.
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The lifespan of a car battery averages 5 years. Suppose the battery lifespan follows an exponential distribution. What is the probability that the battery lasts more than 3 years
The probability that battery lasts more than 3 years is [tex]e^{-0.6 }[/tex].
Parameter of Exponential Distribution
It is given that the average lifespan of the car battery = 5 years
⇒ μ = 5
And, we have to find the probability that the car battery lasts more than 3 years.
Now, the relation between the parameter of exponential distribution, λ and average, μ is given as,
1/ λ = μ
⇒ λ = 1/5
Calculating the Probability
The probability for the car battery to lasts more than 3 years is given by P(N>3). Here, N is the lifespan of the car battery.
P(N>3) = 1 - P(N≤3)
P(N>3) = 1-F(4)
Here, F is the exponential distribution for the lifespan of the car battery.
P(N>3) = 1-(1-e^(-λn))
P(N>3) = [tex]e^{-3/5}[/tex]
Thus, the required probability is,
P(N>3) = [tex]e^{-0.6 }[/tex]
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A spherical ball of wax with a radius of 8 inches is melted and poured into a container shaped like a rectangular prism with a 14 inch x 16 inch base. What is the height of the melted wax in the new shape
It is expected the height of the melted wax in this shape is 9.57 inches, this height would make the volume remain constant.
What is the volume of the spherical ball?The volume of a sphere can be calculated using the formula V = 4/3 πr³. Let's use this formula to calculate the volume of the spherical ball of wax:
V = 4/3 π8³ V = 4/3 π 512V= 4/3 x 3.1416 x 512 V =2144.66 cubic inchesWhat is the height of the new shape?Considering the volume should be the same (2144.66 cubic inches) and the volume of this shape can be calculated by multiplying the sides, this would be the equation:
2144.66 = 14 x 16 x y ( unknown value)y= 2144.66 / 14 x 16y = 9.57This means the height would be 9.57 inches.
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Help me please, I'm stuck
Answer:
Gradient: 5
y-intercept: (0, 15)
Step-by-step explanation:
The gradient is usually just the same as the slope, so if we write the equation in slope-intercept form, y = 5x+15, the coefficient of x value (5) is the slope. The y-intercept is when x equals 0. Plug that in to get y = 15.
PLEASE HELP!!!
Review the table of values for function k(x).
x
k(x)
–19.1
37.5
–19.01
37.95
–19.001
37.995
–19.0001
37.9995
–19
undefined
–18.9999
43.9995
–18.999
43.995
–18.99
43.95
–18.9
43.5
What is Limit as x approaches negative 19 plusk(x)?
37.5
38
43.5
44
which of the answer choices could be the one missing data item for the following set, if the mode is 12? 7, 12, 9, 15, 12, 7, 9, 7, 12, 15 a. 15 b. 9 c. 7 d. 12
Answer: D. 12
Step-by-step explanation: The mode is the most popular number in a set of numbers. In this set, there are 3 sevens, 3 twelves, 2 nines, and 2 fifteens. If the mode is twelve, you need one more 12 because there are the same amounts of twelves and sevens. So that means the answer is 12!
A store sells about 30 pants each week for Nu 800 each. The owner expects to lose one sale each week for every increase in price of Nu 40.
a) Write an expression to represent the
i) new price of a pant after n Nu 40 price increases.
ii) expected number of pants that will be sold weekly after n price increases. b) Write a function to represent the expected weekly sales as a function of the number of price increases of Nu 40. c) Use the function to determine the price that will maximize totally sales.
The new price after the price increase of Nu 40 will be Nu 840.
How to calculate the price?The price of a pant after n Nu 40 price increases will be:
= 800 + 40
= 840
The expected weekly sales as a function of the number of price increases will be:
= n - 1) × 800
= (30 - 1) × 800
= 29 × 800
= 23200
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how do u multiply 1x100000000000000000000000000000??
By using mind ig -,-
Hope Helpful ~
The power of the algebraic expression
7xy + 3xy² - x³y² + 4 is
The power of the algebraic expression 7xy + 3xy² - x³y² + 4 is 1.
How to estimate the power of algebraic expression?An expression that denotes repeated multiplication of the exact factor exists named a power. The number 5 stands named the base, and the number 2 exists named the exponent. The exponent equals the number of times the base exists utilized as a factor.
Given: 7xy + 3xy² - x³y² + 4
An expression that represents repeated multiplication of the same factor is called a power.
So, the power of the given expression will be 1.
Therefore, the correct answer is 1.
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Select the correct answer from each drop-down menu.
Given: line AB ||line DC and DF_~BF
Prove: DFC _~BFA
Angles are formed when two or more lines intersect. Angles are majorly measured in degrees.
The required proof is as shown below:
Whenever a transversal passes through two parallel lines, angles are formed which have some similar properties.
STATEMENTS REASONS
1. AB ║DC Given.
2. < FDC ≅ < FBA Alternate angle theorem.
3. <AFB ≅ < DFC Vertical opposite angle rule.
4. DF ≅ BF Given
5. ΔDFC ≅ Δ BFA Angle-Angle-Side property
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For the equation y = -2/5 x + 2, explain what x -values would be best to choose for making a table of ordered pairs. Be sure to explain why.
The x values to make a suitable ordered pair must be a multiple of 5
How to determine the best x values?The function is given as:
y = -2/5x + 2
The slope of the above equation is:
m = -2/5
The above is a fraction with a denominator of 5.
So, the x values to make a suitable ordered pair must also be a multiple of 5
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Your professor selects three students from your Stats class to form a study team. How many study teams are possible from a class of 30 students
Total number of teams are 10
Linear EquationAn equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation is one that includes a variable, such as x.
As given in the problem,
total number of students in class=30
now professor want to create study teams .
one team consist of 3 members,
lets suppose professor will form n teams
So,
3×n=30
solve this equation to get value of n
n=30÷3
n=10 teams
hence total number of teams are 10 .
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can someone please help mee (will give brainliest 20 points!!!)
Answer:
a.) C(x) = 10x + 8,000
Step-by-step explanation:
The fixed cost does not change regardless of the variable. Therefore, it should be attached to no variable. However, the variable cost does depend on the number of alarms and thus should be attached to the variable.
This makes the algebraic expression:
C(x) = 10x + 8,000
Your graph should look very similar to this. Keep in mind that our axis are slightly different. You can plot specific points on your graph by plugging random "x" values into your algebraic expression and finding the subsequent "y" values.
Can you please find x?
Answer:
x=7
Step-by-step explanation:
The angle of a straight line is 180 degrees, so let's just say the other angle to the right of 15x+34 is "a" that means that 15x + 34 + A = 180, and since the sum of interior angles of a triangle is 180 degrees, that means that 29 + A + 12x + 26 = 180, and we can define A using this equation in terms of x.
Original equation (sum of interior angles)
A + 29 + 12x + 26 = 180
Combine like terms
A + 12x + 55 = 180
Subtract 12x and 55 from both sides
A = -12x + 125
Original equation (since a line is 180 degrees)
15x + 34 + A = 180
Substitute -12x + 125 as A
15x + 34 + (-12x + 125) = 180
Combine like terms
3x + 159 = 180
Subtract 159 from both sides
3x = 21
Divide both sides by 3
x = 7
Pls help me
Here is a sequence of numbers
Answer:
a) Perfect square.
b) 9
Step-by-step explanation:
The given numbers are perfect squares.
64 = 8*8
49 = 7*7
36 = 6*6
25 = 5*5
16 = 4*4
So, the next number will be 3 *3 = 9
.
Which equation represents a circle with a center (-5, -6) and a radius of 5?
The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.
How to Write the Equation of a Circle?The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².
Given the following:
Center (-5, -6) = (h, k)
Radius = 5 = r
Plug in the values into the formula
(x + 5)² + (y + 6)² = 5²
(x + 5)² + (y + 6)² = 25
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There are 752 cal in 8 ounces of a certain ice cream how many calories are there in 2 pounds
Given Circle G with radius r, what is the formula for the area of the segment (unshaded region)
Answer:
Option D
Step-by-step explanation:
The triangle ABJ is equitorial
So area
√3/4r²Then mBJ is a arc which is 1/6th of circle
Area.
π/6r²So area of unshaded region
πr²/6-√3/4r²r²(π/6-√3/4)Answer:
[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector JGB is 60°.
As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.
Interior angles of a triangle sum to 180°. Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.
Area of an equilateral triangle:
[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]
As the side length of the given equilateral triangle is the radius (r):
[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]
To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :
[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]
Substituting the angle in radians, the area of the sector is:
[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]
Therefore, the solution is option D.
Henry walked on a flat field 9 meters due north from a tree. He then turned due east and walked 24 feet. He then turned due south and walked 9 meters plus 32 feet. How many feet away from his original starting point is Henry
Henry was 40 feet away from his original starting point. Using Pythagorean's theorem it is calculated.
What is the Pythagorean theorem?The theorem says that,
In a right-angled triangle, the sum of squares of the lengths of two arms (opposite and adjacent sides) is equal to the square of the hypotenuse.
I.e, Consider a right-angled triangle ΔABC, where AC is the hypotenuse side of the triangle. So, according to the theory,
AC² = AB² + BC²
Calculation:It is given that,
Henry walked on a flat field,
9 meters - towards the north
24 feet - towards the east
9 meters + 32 feet - towards the south
This can be shown in the diagram below.
In the diagram, the distance from the starting point is X, and the last point is S.
To find the distance between these two points, a line is joined as shown in the diagram. Thus, it is formed as a right-angled triangle.
So, according to the Pythagorean theorem,
XS² = (24)² + (32)²
(here 32 feet is the only distance from the assumed point to the endpoint)
⇒ XS² = 1600 = 40²
∴ XS = 40 feet
So, Henry is 40 feet away from the original starting point.
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Find the measures of the numbered angles in each rhombus.
Answer:
Step-by-step explanation:
2=27
3=27
5=27
1=126
4=126
The new video came console was priced at $400 when it was released last year. This year, the price decreased by 15% during the holiday sale period. The game manufacturer recently announced that the same console will be re-release with new updates and expanded functionality. The retail price will be 25%greater then the previous sale price . When the game concise is re-released whatcwill be the retail price?
A) 360
B)425
C)380
D415
Answer:
B
Step-by-step explanation:
15% off means 85 % of original price
400 * .85 now increase this price by 25%
400* .85 * 1.25 = $425