Answers
Answer:
The value of k is;
[tex]k=-7.1842[/tex]Explanation:
Given the equation:
[tex]-3\cdot16^{-k-7}+8=3[/tex]To solve, let us subtract 8 from both sides;
[tex]\begin{gathered} -3\cdot16^{-k-7}+8-8=3-8 \\ -3\cdot16^{-k-7}=-5 \end{gathered}[/tex]then, we can then divide both sides by -3;
[tex]\begin{gathered} \frac{-3\cdot16^{-k-7}}{-3}=\frac{-5}{-3} \\ 16^{-k-7}=\frac{5}{3} \end{gathered}[/tex]To solve further we need to take the logarithm of both sides;
[tex]\begin{gathered} 16^{-k-7}=\frac{5}{3} \\ \log 16^{-k-7}=\log \frac{5}{3} \\ (-k-7)\log 16=\log \frac{5}{3} \\ \text{dividing both sides by log 16, we have;} \\ \frac{(-k-7)\log 16}{\log 16}=\frac{\log\frac{5}{3}}{\log16} \\ -k-7=\frac{\log\frac{5}{3}}{\log16} \end{gathered}[/tex]finding the value of the log;
[tex]-k-7=0.1842\text{ (to 4 decimal place)}[/tex]solving for k;
[tex]\begin{gathered} -k-7=0.1842 \\ -k=0.1842+7 \\ -k=7.1842 \\ k=-7.1842 \end{gathered}[/tex]Therefore, the value of k is;
[tex]k=-7.1842[/tex]Related Questions
Taylor and Emily are painting banners for their Halloween Party. Taylor’s banner is 8 inches tall and 564 inches wide. The area of Emily’s banner is 10 times as large as the area of Taylor’s banner. What is the area of Emily’s banner, in square inches?
Answers
Answer:
[tex]45120 in^2[/tex]
Step-by-step explanation:
Area of Taylor's Banner (AT): [tex]A_T = 8*564=4512 in^2[/tex]
Area of Emily's Banner (AE): [tex]A_E=10*A_T[/tex]
Plugging in AT: [tex]A_E = 10 * 4512 = 45120 in^2[/tex]
The Area of Emily's Banner is 45120 inch²
What is Area of rectangle?The Area of rectangle is the product of its length to its width.
i.e., Area of rectangle= length x width
Given:
Taylor’s banner : 8 inches tall and 564 inches wide.
Area of Taylor's Banner= l x w
= 8 x 564
= 4512 inch²
and, area of Emily’s banner is 10 times as large as the area of Taylor’s banner.
So, Area of Emil's Banner= 10 x 4512
= 45120 inch²
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Please help me do my Math Homework ASAP, it is attached.
Answers
Answer:
Step-by-step explanation:
he altitude of a triangle is increasing at a rate of 3.000 centimeters/minute while the area of the triangle is increasing at a rate of 4.000 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 9.500 centimeters and the area is 88.000 square centimeters?
Answers
The altitude exists 9.500 centimeters and the area exists 88.000 square centimeters is [tex]$ -\frac{9.26316}{4.75d}[/tex].
What is meant by the altitude of a triangle?A line segment passing through a triangle's vertex and running perpendicular to the line containing the base is the triangle's height in geometry. The extended base of the altitude is the name given to this line that contains the opposing side. The foot of the altitude exists the point at where the extended base and the height converge.
A triangle's altitude is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.
Let A be the area of the triangle
h be the altitude
b be the base
The formula that relates the three is the area of a triangle
A = (1/2) bh
Note that anything listed as a "rate" is a derivative value.
dh (rate of change of altitude) = 3.000 cm/min
dA (rate of change of area) = 4 cm²/min
h = 9.500 cm
A = 88.000 cm²
Consider that both b and h are changing in this situation, so we have to treat them both as variables. This means we have to use the product rule, inserting the derivatives where applicable.
dA = (1/2) × db × h + (1/2)b × dh
substitute the values in the above equation, we get
4 = (1/2) × db × 9.5 + (1/2) b × 3.000
88 = (1/2) × b × 9.5
b = 18.52631
Now, looking back at our derivative
4 = (1/2) × db × 9.5 + (1/2) × 18.52631 × 3.000
simplifying the above equation, we get
4 = 4.75 db + 13.26316
b =[tex]$ -\frac{9.26316}{4.75d}[/tex]
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a communication system consists of n components, each of which will, independently, function with probability p. the total system will be able to operate effectively if at least one-half of its components function. (a) let x denote the number of functioning components out of the n components. what is the distribution of x? (b) what is the probability that a 5-component system will function? (c) for what values of p is a 5-component system more likely to operate effectively than a 3-component system?
Answers
A Communication system consists of n components.
a) Binomial distribution,
P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾
b) For 5-component system,
P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5
c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.
Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .
(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.
(b) Now , 5-component system is function . That is n=5
Probability that 5-components system will function is P(X= 5)
= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)
(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is
⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵
Whereas the corresponding probability for a 3-components system
³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3
³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³
5-Component system is better than 3-Components system if
10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³
=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²
Which reduce to
3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0
either p> ½ or p <1
=> p belongs to ( 0.5, 1)
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What is the slope of the line that passes through the points (-6, 1) and (-6,-4)?
Write your answer in simplest form.
Answers
Answer:
The slope is undefined
Step-by-step explanation:
help me answer this question please
Answers
Answer:
sum = -15/2
Step-by-step explanation:
Given the formula for the n-th term of a sequence is n(n-8)/√(n+3), you want the sum of the 1st and 6th terms.
First termThe first term is found by substituting 1 for n:
1(1 -8)/√(1 +3) = 1(-7)/√4 = -7/2
Sixth termThe sixth term is found by substituting 6 for n:
6(6 -8)/√(6 +3) = 6(-2)/√9 = -12/3 = -4
SumThe sum of the first and sixth terms is ...
-7/2 +(-4) = -(7/2 +8/2) = -15/2
sum = -7 1/2
find the product
6x/(-2)
Answer:
-12xy
Answers
The result of the expression given as 6x/(-2) is -3x
How to determine the product?From the question, the expression is given as
6x/(-2)
The above expression is a quotient expression
So, we start by rewritting it as a product
This is represented as
6x/(-2) = 6x * 1/(-2)
Remove the bracket
So, we have the following equation
6x/(-2) = 6x * 1/-2
Evaluate the product
6x/(-2) = -3x
Hence, the value of the expression is -3x
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In a certain tourism destination, 28% of the city's residents work in the hospitality industry. 55% of residents are age 40 or younger, and 15% of residents are people age 40 or younger who work in the hospitality industry. What percentage of the employed population are people older than 40 who do not work in the hospitality industry?
A. 13%
B. 17%
C. 32%
D. 45%
Answers
The percentage of the employed population are people older than 40 who do not work in the hospitality industry is B. 17%.
How to calculate the percentage?The city's residents work in the hospitality industry = 28%
The residents that are age 40 or younger, and 15% of residents are people age 40 or younger = 55%
Those who work in the hospitality industry that are younger than 40% = 15%
Therefore, those that don't work in the industry will be:
Percentage of 40 or older - Percentage of those working
= (100 - 55%) - 28%
= 45% - 28%
= 17%
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Which of the following best estimates the sum 1 1 2 3 B 0.5 0.8
Answers
we have
1/2 +1/3
Remember that
1/2=0.5
1/3=0.33 -----> rounded 0.3
so
0.5+0.3=0.80
Answer: please help
Step-by-step explanation: I don’t know what the answer is I need help
helpppppp math its hard for me
Answers
Step-by-step explanation:
You would start off with solving inside, the parenthesis, and you would get -8/27.
Then, your would solve the 1 1/4 - 3/4 and get 1/2.
You then have to multiply -8/27*1/2, which is -4/27.
Lastly, you divide by negative 4.
-4/27 divided by -4.
You have to flip it to multiply the reciprocal, and you get -4/27*-1/4.
Since negative times negative is positive, the answer would be 1/27.
Answer:
1/27
Hope this helped! :)
Carrie wants to make a wallpaper border to go around the top of her room. She wants the border to look something like the illustration below.
The answer is A Reflection
This question is answered
Answers
Since Carrie wants to make a wallpaper border to go around the top of her room. She wants the border to look something like the illustration below. This is a Reflection
What is transformation?A transformation is an operation that is performed on a picture. Transformations are classified into four types: translations, reflections, dilations, and rotations. In transformations, reflections are achieved by flipping a shape or figure across a line of reflection, a point of reflection, or a plane of reflection.
A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. The line of reflection is formed when an image reflects through a line. A figure is said to reflect another figure when every point in one figure is equidistant from every point in another figure.
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The dial on a combination lock contains markings which represent the numbers from 0 to 39. How many 3- number combinations are possible if the first and the second must be different odd numbers, while the third number must not be an odd number?.
Answers
There are 64000 distinct combinations .
The dial for the standard combination lock is fastened to a spindle. The spindle travels through many wheels and a drive cam inside the lock. Every number has one wheel, hence the number of wheels in a wheel pack depends on how many numbers are in the combination.
The lock uses the numbers 0 to 39 and has 64,000 distinct combinations.
How many possible three-number combinations are there?
You have 10 options for the first digit, 9 options for the second digit, and 8 options for the third digit, giving you 10x9x8 = 720 if you want all three possible numbers with no duplication of the digits.
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PLEASE HELP
what is the value of x? justify each step
AC= 32
Answers
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.
Explain about the value?Value in mathematics is a number that represents the outcome of a computation or function. In the aforementioned example, you may inform your teacher that 5 + 6 Equals 30 or that x + y = 9 if x = 6 and y = 3. A variable or constant can also be referred to as a value.
X has a value of 3. The following is a list of the arguments made for each step.
Adding more line segments
Rule of substitution (b)
c) Simplifying by incorporating related terms
d) Compiling terms for lies
e) Multiplying each side by 8
AB = 2x
BC = 6x + 8
AC = 32
AB plus BC equals AC. (Extension rule)
addition of a line's individual segments
2x + 6x + 8 = 32 (Substitution rule) (Substitution rule)
replacing AB, BC, and AC in the formula AB + BC = AC
8x + 8 = 32 (Simplification) (Simplification)
2x + 6x + 8 = 32, simplified adding comparable terms
8x = 24 (Assembling similar terms)
8x = 32 - 8
8x = 24
x = 3 (Divide both sides by 8) (Divide both sides by 8)
8x / 8 = 24/8
x = 3
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a=3,k=12,z=6,h=4 Evaluate the algebraic expression z+15=?
Answers
since z=6, so z+15 is equal to 21
or a+k+z=21
Solve for .
4x4<8 AND 9x + 5 > 23
Answers
Answer:
solve for what? x or y? or anything another
Step-by-step explanation:
if x
1.
[tex] - \sqrt[4]{2} \sqrt[4]{2} [/tex]
2.
[tex]x = (2 \: or \: \infty )[/tex]
so hope it help
question 8 a large hotel chain sees about 500 customers per week. a data analyst working there is gathering data through customer satisfaction surveys. they are anxious to begin analysis, so they start analyzing the data as soon as they receive 50 survey responses. this is an example of what? select all that apply.
Answers
The sampling strategy used in this problem is an example of:
Failing to include diverse perspectives in the collection.Failing to choose a large enough sample size.What is sampling?Sampling is when a subset of an entire population is studied, to verify whether characteristics of the sample can be expanded to the entire population.
The sample has to be representative of the population, that is, large enough, hence it should contain all the subsets of the population.;
In the context of this problem, the chain sees about 500 customers a week and they receive the responses from 50 of them. This is a not large enough sample size, hence it could cause biased results, meaning that the perspective of the entire population will not be considered.
In the context of this problem, the survey are anonymous, and the objective of a survey is generally not to reward the participants, hence the last two options are false.
What is the missing information?The options are given as follows:
Failing to include diverse perspectives in the collection.Failing to choose a large enough sample size.Failing to reward customers for participating in the survey.Failing to collect data anonymously.More can be learned about sampling at https://brainly.com/question/9910540
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find the Length of an arcade of a circle whose central angle is 212° and radius is 5.3 inches. round your answer to the nearest tenth.
Answers
The length of the arc of the circle is 19.6 inches
We can find the length of the arc using the formula;
[tex]L\text{ = }\frac{\theta}{360}\text{ }\times\text{ 2}\pi r[/tex]where ;
[tex]\begin{gathered} \theta\text{ is central angle which is 212} \\ r\text{ is radius which is 5.3 inches} \end{gathered}[/tex]Substituting these values;
[tex]\begin{gathered} L\text{ = }\frac{212}{360}\text{ }\times\text{ 2 }\times\frac{22}{7}\text{ }\times\text{ 5.3} \\ \\ L\text{ = 19.618413} \\ \\ To\text{ the nearest tenth, this is 19.6 inches} \end{gathered}[/tex]The line perpendicular to y=-3x+4 that passes through the point (-3,-7)
Answers
Answer:
Step-by-step explanation:
A perpendicular line will have a sope that is the negative inverse of the reference line. The reference line is y = -3 + 4, with a slope of -3. The negative inverse would be -(-1/3) or (1/3).
The new line will take the form of y = (1/3)x + b, where b is the y-intercept (the value of y when x=0). We want the new line to go through point (-3,-7). We;ll need a value of b that will make that happen. To find b, enter the given data point and solve for b:
y = (1/3)x + b for (-3,-7).
-7 = (1/3)(-3) + b
-7 = -1 + b
b = -6
The new equation is y = (1/3)x - 6
See the attached graph.
Approximate the value of each irrational number. Explain your reasoning.
Part A
√30
Answers
To find the square root, we need to find out what number(s) can be multiplied by themselves to equal 30.
5 • 5 = 25
6 • 6 = 36
Because 30 is between 25 and 36, we know that the square root of 30 is between 5 and 6.
When we multiply 5 and 6 by themselves to find their square, we will find that 30 lies about halfway between 25 and 36. Upon calculation, the square root of 30 is 5.47, which to the nearest tenth is 5.5.
The square root of 30 ≈ 5.5.
is 12 an integer? Im getting confused answers
Answers
Answer:
Yes 12 is an Integer
Step-by-step explanation:
12 is a whole number that can be written without a fractional component, thus 12 is an integer.
NEEd HELP 9th grade asp
Answers
Answer:175/48
Step-by-step explanation:
May Someone Please Give Me The Answers To The Problems I Haven’t Done (Please Mark Which Ones They Are)Thank You!!
Answers
The simplest form of the ratios are:
(A) 3/1 = 3(B) 6/2 = 3(C) 18/6 = 3(D) 36/12 = 3What are ratios?An ordered pair of numbers a and b, written as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value.For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls).
So, the ratios in the simplest form are:
We can observe that the simplest form of all the ratios is similar which is 3.
Therefore, the simplest form of the ratios are:
(A) 3/1 = 3(B) 6/2 = 3(C) 18/6 = 3(D) 36/12 = 3Know more about ratios here:
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Santiago's car used 15 gallons to travel 525 miles. How far can he travel on 19 gallons?
Answers
Answer:
665
Step-by-step explanation:
the reasoning is because you divide 525/15 and you get 35 with that you multiply by 19 because you are seeing how far you can get with 19 gallons of gas .
665 miles Santiago can travel on 19 gallons of fuel.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
Given, Santiago's car used 15 gallons to travel 525 miles. Since,
Santiago travels in 15 gallons = 525 miles
Santiago travels in 1 gallons = 525/ 15 = 35
Santiago travels in 19 gallons = 35* 19 = 665
Therefore, Santiago can travel 665 miles on 19 gallons of fuel.
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Find the measure of the complement for the angle 1 degree
Answers
89 degrees
Explanations:
The sum of an angle and its complement is equal to 90 degrees.
Let the measure of the complement be "x"
Given the information below:
Angle = 1 degrees
Taking the sum of the angle and its complement will give:
[tex]x+1^0=90^0[/tex]Subtract 1 from both sides
[tex]\begin{gathered} x+1-1=90-1 \\ x+0=90-1 \\ x=89^0 \end{gathered}[/tex]Therefore the measure of the complement for the angle given is 89 degrees
{(7, 3), (4, 8), (-6, -5), (6, 6), (-1, 9) }
Domain:
Range:
Answers
Answer:
Domain: -6,-1,4,6,7
Range: -5,3,6,8,9
Step-by-step explanation:
The domain is the first element in each ordered pair. It is the x value. The range is the second element in each ordered pair. It is the y values.
Miss Davidson ran a sit-up competition among her P.E. students and monitored how many sit-ups each student could do. Number of sit-ups Number of students 76 3 79 5 175 2 X is the number of sit-ups that a randomly chosen student did. What is the expected value of X? Write your answer as a decimal.
Answers
Let the total number students be s. Then
s = 3 + 5 + 2= 10
x | Number of students(n) | Pr(x) | xPr(x)
---------------------------------------------------------------------------------
76 | 3 | 0.3 | 22.8
---------------------------------------------------------------------------------
79 | 5 | 0.5 | 39.5
--------------------------------------------------------------------------------
175 | 2 | 0.2 | 35
--------------------------------------------------------------------------------
[tex]\sum \text{xPr(x) = 22.8 + 39.5 }+\text{ 35 = 97.3}[/tex][tex]\text{ The expected value is }\sum \text{xPr(x)}[/tex]Therefore, the expected value of x is 97.3
can you please help me
Answers
We have to calculate the area and perimeter of ABC.
Area:
We can calculate the area by substracting from the area of the big triangle ABD the area of the little triangle BCD. Both are right triangles.
The area of ABD is:
[tex]A_{\text{ABD}}=\frac{b\cdot h}{2}=\frac{(15+5)\cdot12}{2}=\frac{20\cdot12}{2}=\frac{240}{2}=120[/tex]The area of BCD is:
[tex]A_{\text{BCD}}=\frac{b\cdot h}{2}=\frac{5\cdot12}{2}=\frac{60}{2}=30[/tex]Then, the area of ABC is:
[tex]A_{\text{ABC}}=A_{\text{ABD}}-A_{\text{BCD}}=120-30=90[/tex]The area of ABC is 90 cm^2.
Perimeter:
We calculate the perimeter by adding the length of the three sides. We know only 2 of the sides, so we have to calculate the other one (BC).
The length of BC can be calculated using Pythagorean theorem for the triangle BCD, so we can write:
[tex]\begin{gathered} BC^2=CD^2+BD^2=5^2+12^2=25+144=169 \\ BC=\sqrt[]{169}=13 \end{gathered}[/tex]Now, we can calculate the perimeter as:
[tex]P_{\text{ABC}}=AB+BC+AC=25+13+15=53[/tex]The perimeter is 53 cm.
Please help me I don’t know it
Answers
Answer:
angle 4 and 5 are interior angles, and 3 and 6 as well
write the following statements as an algebraic expression or equation.you have twice as many apples as bananas.the choices are in the picture
Answers
ok
apples = a
babanas = b
a = 2b
find the number of terms in the sequence 1,-4,16,...,65536
Answers
Answer:
9 terms
Step-by-step explanation:
The sequence given is a geometric sequence
In a geometric sequence, the nth term of the sequence can be found by the formula
[tex]a_n = a_1r^{n-1}[/tex]
[tex]\text{where }\\\\ a_n = \text {nth term}\\\\\text{$a_1 = $ first term}\\\\\text{$r = $ common ratio}[/tex]
In the given sequence,
a₁ = 1
r = -4
aₙ = 65536
So we get the relation:
65536 = 1· (-4)ⁿ⁻¹
65536 = (-4)ⁿ⁻¹
It is clear that n-1 has to be even so that the power of 4 is positive.
Substituting x = n -1 where x is even gives us
4ˣ = 65536
If we take logarithms to the base 4 on both sides we get
=> x = [tex]\log_465536 = 8\\\\[/tex]
Since x = n - 1 and x = 8, n = 9
So the 9th term in the series is 65536