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
the shape of the density curve for a dataset is like a triangle. that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. if we standardize this dataset by calculating the standard scores, what is the geometrical shape of the density curve for the standardized dataset?
Answers
It will be similar to the original triangle.
The shape of the density curve for a dataset is like a triangle, that is, as we move to the left of the horizontal axis, it starts from zero height, then rises linearly until some peak, then declines linearly until reaches zero, then stays zero from there onward. If we standardize the dataset by calculating the standard scores, the geometrical shape of the density curve will more or less be the same. i.e., similar to the original triangle. Scale of it will be just changed.
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24PS-10 Question Help In a certain chemical, the ratio of zinc to copper is 3 to 14. A jar of the chemical contains 294 grams of copper. How many grams of zinc does it contain?
Answers
the ratio of zinc to copper is 3 to 14, that menas that for each 3 grams of zinc there are 14 grams of copper, so we can made a rule of three to find
Tara's office recycled a total of 60 kilograms of paper over 3 weeks. How many weeks will it take Tara's office to recycle a total of 80 kilograms of paper? Solve using unit rates.
Answers
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We can desribe 15x-10 as an expression.
We would describe 6x-2<35 as an
Answers
We can describe 15x-10 as an expression.
We would describe 6x-2<35 as an inequality.
What is an inequality?In mathematics, inequalities characterize the connection between two non-equal numbers. Inequality means being unequal. If two values are not equal, we use the "not equal symbol". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
An inequality in mathematics is a relationship that makes a non-equal comparison between two integers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In the illustration above, there's a less than sign. This means that it's an inequality.
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Elisa gets a tax free allowance of $6000 and pays tax at 25% on the next $20 000. She pays tax at a rate of 30% on the rest. If she earns $72000 per year, how much tax must she pay?
Answers
a bakery uses 3 3/5 cups of oats to make 2 4/7 pounds of oatmeal cookies how many cups of oats are required per pound of cookies
Answers
Answer: 7/5 or 1 2/5
Step-by-step explanation:
Ok so the bakery uses 3 3/5 cups cups of oats for 2 4/7 POUNDS of cookies.
You need to find the unit price.
So to get from 2 4/7 to 1, you need to divide 2 4/7 by 2 4/7
You need to do the same thing to 3 3/5 cups.
3 3/5 as an improper fraction is 18/5
2 4/7 as an improper fraction is 18/7
Now to divide you need to keep, change, and flip
keep the 18/5, change the sign to multiplycation, and flip the 18/7 to 7/18
18/5*7/18=7/5
7/5 or 1 2/5 pounds of outs are required to make 1 pound of oatmeal cookies
Determine whether each triangle below will form a unique triangle, no triangle or more than one triangle based on the criterion given.
Answers
Answer:
A: A unique triangle
B: A unique triangle
C: More than a triangle
In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither. Find the probabillity that a student chosen at random has both
Answers
9/25
Step-by-step explanation:
students who have either cat or dog =25-3=22
students who have both= 15+16-22= 9
probabillity that a student chosen at random has both= 9/25
Renting a roller rink for your birthday costs $300 plus $9 per person. The total charge for your party was $534. Translate this information into an equation using x to represent the number of guests at your party.
Answers
The equation using x to represent the number of guests at your party is 300 + 9x = 534
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Let x represent the number of guests at your party.
Here, renting a roller rink for your birthday costs $300 plus $9 per person. This will be:
300 + 9x = 534
Collect like terms
9x = 534 - 300
9x = 234
Divide
x = 234 / 9
x = 26
The number of guest is 26.
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5/3x+1/3x=11 1/3+8/3x
Answers
Answer:
-111/2
Step-by-step explanation:
Please look at the attachment below! :D
Which line is perpendicular to a line that has a slope
of 1?
Oline MN
Oline AB
Oline EF
Oline JK
Answers
JK is perpendicular to a line that has a slope
What is Slope?
The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).
Two lines, L1 and L2, with slopes m1 and m2 are perpendicular if
m1 x m2 = -1.
In our case m1 = 1
1 x m2 = -1
m2 = -2
so the slope of the perpendicular line is -2.
( -2 x (1) = -1).
As x increases, the line with a slope of -2 increases. Line JK is the only line displayed that fits this. Line AB cannot be the solution because it is "falling" as x grows.
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If angles of the triangle are In 2:3:7 then find all the angles
Answers
Answer:
Since all triangle angles sum to 180 then we can say
2x + 3x + 7x = 180
12x = 180
x = 15
There fore the angles are
2 * 15 3 * 15 and 7 * 15 or
30 45 and 105
Those 3 total 180 degrees
Step-by-step explanation:
i need help with this sorry I cant give much
Answers
Answer:
[tex]\frac{11}{20}[/tex]
Step-by-step explanation:
2[tex]\frac{3}{4}[/tex] ÷ 5
Convert mixed number fraction to improper fraction
[tex]\frac{11}{4}[/tex] ÷ 5
To divide fractions we turn the second fraction (the one you want to divide by) upside down (this is now called a reciprocal) and we multiply
[tex]\frac{11}{4}[/tex] × [tex]\frac{1}{5}[/tex] = [tex]\frac{11}{20}[/tex]
Nicholas is saving money to buy a new video game. He started with $25 and after 3 weeks of doing chores he had $70.
Answers
70-25=$45
$45/3 = $15
PLEASE HELP URGENT HELP PLEASE!!!!!!!!!!!!!!!!
Answers
Answer:
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
Step-by-step explanation:
separate y from everything
[tex]w = y(h - 5c^{3})[/tex]
now divide everything by the thing in the parenthesis
[tex]\frac{w}{h - 5c^{3}} = y[/tex]
now flip it
[tex]y = \frac{w}{h - 5c^{3}}[/tex]
that is your answer
Use point-slope form to write the equation of a line that passes through the point (-12,15) with slope −1.
Answers
Answer: y = -1x + 3
Step-by-step explanation:
Point-Slope form: y - y1 = m(x-x1)
Replace the form with the values provided:
y - 15 = -1(x+12)
Once you get this, you need to get y by itself in order to get it in slope intercept form.
Distribute:
y -15 = -1x - 12
Add -15 to the right side:
y = -1x + 3
What’s the answer plss
Answers
Answer: 8.4cm
Step-by-step explanation:
sin cos tan
SOH CAH TOA
It is cos because CAH does not have opposite (o) in it and we want to find the opposite.
O is opposite (opposite angle)
A is adjacent (next to angle)
H is hypotenuse (opposite right angle)
This is how I remember it
Cos(61)*17.4=8.435
8.4cm
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
Responses
A 18
B 18 2/3
C 19
D 19 2/3
Answers
Answer:
the answer for your question is option A
Answer:b
Step-by-step explanation:
the interest rate on a five-year certificate of deposit (cd) for banks in south florida in 2018 was normally distributed with a mean of 2.28 percent and a standard deviation of 0.37 percent. 1. what proportion of these banks had an interest rate less than 2.5 percent?
Answers
The proportion of these banks that had an interest rate less than 2.5 percent is 0.724.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 2.5
μ = mean = 2.28
σ = standard deviation = 0.37
z-score = (2.5 - 2.28) / 0.37
z-score = 0.22 / 0.37
z-score = 0.5946
To get the proportion, find the probability that corresponds to the z-score in the z-table. (see attached images)
z-score = 0.5946
By interpolating the values,
probability = 0.724
proportion = 0.724
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Please help last question and super confused!! ASAP
Given the function:
h(x) = -2/3x+4/5
Find the following values
A) h(3)
B) h(4)
C) h(-1/2)
Answers
h(3)= -2/3(3) +4/5
h(3) = -1 + 4/5
h(3) = -1/5
h(4) = -2/3(4) + 4/5
h(4) = -8/3 + 4/5
h(4) = -40/5 + 12/5
h(4) = -28/5
h(-1/2) = -2/3(-1/2) + 4/5
h(-1/2) = 2/6 + 4/5
h(-1/2) = 1/3 + 4/5
h(-1/2) = 5/15 + 12/15
h(-1/2) = 17/15
Mr. Reed is drawing a blueprint of a rectangular patio. The width of the patio is 40 3/4 feet shorter than twice its length. The perimeter of the patio is 86 1/2 feet. What is the length of the patio?
Answers
Answer:
length = 28 feet
Step-by-step explanation:
let length = x
width = 2x - 40 3/4
= 2x - 163/4
= 2x - 40.75
perimeter of a rectangle = 2(l+w)
according to the question:
86 1/2 = 2(l+w)
86.5 = 2(x + 2x - 40.75)
86.5 = 2(3x - 40.75)
86.5 = 6x - 81.5
86.5 + 81.5 = 6x
thus, x = 28
A deck of cards was shuffled and after each shuffle, the suit of the top card was recorded. The table shows theprobability of each outcome. What is the probability that the top card is not a heart?
Answers
Answer:
[tex]0.72[/tex]Explanation:
Here, we want to get the probability that the top card is not a heart card
Mathematically, the sum of the probability that an event will occur and that the event will not occur is 1
Let the event that a heart card is the top card be H
[tex]P(H)\text{ + P(H') = 1}[/tex]We already have P(H) as 0.28
Thus:
[tex]\begin{gathered} 0.28\text{ + P(H') = 1} \\ P(H^{\prime})\text{ = 1-0.28} \\ P(H^{\prime})\text{ = 0.72} \end{gathered}[/tex]suppose that the lifetime of a transistor is a gamma random variable x with mean of 24 weeks and standard deviation of 12 weeks. what is the probability that the transistor will last between 12 and 24 weeks?
Answers
The probability that the transistor will last between 12 and 24 weeks is 0.424
X= lifetime of the transistor in weeks E(X)= 24 weeks
O,= 12 weeks
The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.
X~gamma([tex]\alpha ,\beta[/tex])
E(X)= [tex]\alpha \beta[/tex] [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks
V(x)= [tex]\alpha \beta ^{2}[/tex] [tex]\alpha[/tex]=24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)
P([tex]12\leq X\leq 24[/tex])
P([tex]12/6\leq G\leq 24/6[/tex])
P([tex]2\leq G\leq 4[/tex])
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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Answer:
Step-by-step explanation:
0.424 is the probability that the transistor will last between 12 and 24 weeks.
X= lifetime of the transistor in weeks E(X)= 24 weeks
Standard deviation= 12 weeks
Finding the parameters alpha and beta X~gamma(αβ)
E(X)= αβ β =6 weeks
V(x)=αβ^2 α =24/6= 4
Now we can find the solutions:
The excel formula used to create Figure one is as follows:
=gammadist(X,α,β,False)
P(12≤X≤24)
P(12/6≤G≤24/6)
P= 0.424
Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424
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Solve for x to the nearest tenth.
Answers
Answer:
x = 11.2 cms.
Step-by-step explanation:
I infer that the units are in centimeters.
8-3 = 5
One side = 5 cm
Other side = 10 cm
By the Pythagorean Theorem:
x² = 5² + 10²
x² = 25 + 100
x² = 125
√x² = √125
x = 11.18 cms
To the nearest tenth:
x = 11.2 cms
A sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich. After making sandwiches for and hour the shop owner has used 91 combined ounces of meat and cheese. How many ounces of meat were used?
Answers
The number of ounces of meat were used is 52 ounces.
Given that, a sandwich shop serves 4 ounces of meat and 3 ounces of cheese on each sandwich.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
There are 7 ounces of combined meat and cheese in each sandwich (4+3 =7)
Number of sandwiches can make with 91 ounce of meat and cheese
= 91/7
= 13 sandwiches
Number of ounces of meat = 13 × 4 = 52 ounces
Number of ounces of cheese = 13 × 3 = 39 ounces
Therefore, the number of ounces of meat were used is 52 ounces.
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1. Is 26 divisible by 2? (1 point)
ONO
O Yes, because 2 +6=8 and 8 is divisible by 2.
O Yes, because the last digit is 6, which is divisible by 2.
Answers
Answer:
Yes, because the last digit is 6, which is divisible by 2.
Step-by-step explanation:
The solution is, Yes, because the last digit is 6, which is divisible by 2.
What is division?Division is the process of splitting a number or an amount into equal parts.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
26 divisible by 2
i.e. 26/2 = 13
so, it is divisible.
now, we know that,
because the last digit is 6, which is divisible by 2.
Hence, The solution is, Yes, because the last digit is 6, which is divisible by 2.
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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
PLS HELP!!!
Building an A-frame dog house. Your club has decided to build and sell dog houses for a fundraising project. You found this dog house and set of plans by searching the net.
A customer has offered to pay extra if you will make one half the size called for in the plans. Take each of the 5 measurements shown in the drawing and find half of the measurement. Show your work to get full credit!
Answers
The one half of the dimensions of the frame dog house is obtained.
What is termed as the mixed fractions?A mixed fraction is a form of fraction that has both a whole number as well as a fractional part. An improper fraction could also be formed from a mixed fraction. To do so, follow the steps outlined below. Step 1: Multiply the mixed fraction's denominator by the whole number part.Step 2: Subtract the numerator from the product obtained in step 1.Step 3: In numerator/denominator form, compose the improper fraction only with sum obtained in step 2.For the given question, the dimensions of the frame dog house are given as;
Gusset plate:Height = 5 ³/₂ inchesBase = 3 ¹/₂ inchesFloor plate = 47 ¹/₄ inches Thickness = 2 inchesSlope = 45 ¹/₄ inchesConvert the following fraction in improper by the above method;
Gusset plate:Height = 13/2 inchesBase = 7/2 inchesFloor plate = 189/4 inches Thickness = 2 inchesSlope = 181/4 inchesNow, customer has offered to pay extra if you will make one half the size called for in the plans.
Multiply each dimension with 1/2.
Gusset plate:Height = 13/2 × 1/2 = 13/4 inchesBase = 7/2 × 1/2 = 7/4 inchesFloor plate = 189/4 × 1/2 = 189/4 inches Thickness = 2× 1/2 = 1 inchSlope = 181/4 × 1/2 = 181/8 inchesThus, the one half of the dimensions of the frame dog house is obtained.
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ASAP please Hurry
The number of issues of books from a library are given for the years 2001–2011. The numbers are in hundreds of thousands.
Answers
Answer:
See attached graph.
Step-by-step explanation:
Use DESMOS graphing software. Free.
The ratio of 1.4 to 26 is the same as the ratio of 2.8 to ____.
