which equation is equivalent to 2^3x = 10
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2^{3x} = 10}[/tex]
[tex]\large\textsf{Take the logarithm to both sides:}[/tex]
[tex]\mathsf{log(2^{3x}) = log(10)}[/tex]
[tex]\mathsf{3x \times (log(2)) = log(10)}[/tex]
[tex]\large\textsf{Simplify it:}[/tex]
[tex]\mathsf{3x = \dfrac{log(10)}{log(2)}}[/tex]
[tex]\large\textsf{Simplify this as well:}[/tex]
[tex]\mathsf{3x = 3.321928}[/tex]
[tex]\large\textsf{Divide 3 to both sides of your current equation:}[/tex]
[tex]\mathsf{\dfrac{3x}{3} = \dfrac{3.321928}{3}}[/tex]
[tex]\large\textsf{Lastly, simplify that last bit of the equation:}[/tex]
[tex]\mathsf{x = \dfrac{3.321928}{3}}[/tex]
[tex]\mathsf{x = 1.107309}[/tex]
[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{x = 1.107309}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]five percent of all vcrs manufactured by a large electronics company are defective. a quality control inspector randomly selects three vcrs from the production line. what is the probability that exactly one of the three vcrs is defective?
The probability that exactly one of the three vcrs is defective is 0.1354
x = total number of trials = 3 VCRs
x = number of successes = number of defective VCRs = 1
n- x = 3 -1 = 2
p = P(success) = 0.05
q = P(failure) = 1 -p = 1 – 0.05 = 0.095
In this question we are applying binomial distribution strategy: it is always applied to find the probability that an outcome will occur x times in n performances or experiment.
P (x = 1) = 3C1 (0.05)1 (0.95)2
= 3 (0.05) (0.9025)
= 0.1354
Therefore, the probability of exactly one of the three VCRs being a defective one is 0.1354
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Write an equation that equals 2,456
Answer:
2400+56=2456 OR
2500-44=2456
Answer:
Step-by-step explanation:
614x4=2,456
How am I supposed to find out how what angle EFG is so I can solve this problem?
let's recall that an angle bisector, bisects = cuts into two equal halves.
Check the picture below.
Write the negation of the hypothesis and the
negation of the conclusion for each conditional.
SEE EXAMPLES 3 and 4
24. If the sum of the interior angle measures of a
polygon is 180, then the polygon is a triangle.
the negations of the hypothesis and conclusion for the given conditional statement are:
not P = "The sum of the interior angle measures of a polygon is not 180°"
not Q = "The polygon is not a triangle"
How to write the negations of the hypothesis and conclusion?For two defined propositions P and Q, we define a conditional statement as a sentence of the form:
If P, then Q.
Particularly in this case, P is called the hypothesis and Q is called the conclusion of the conditional statement.
For the given one:
"If the sum of the interior angle measures of a polygon is 180, then the polygon is a triangle."
We will have that the hypothesis is:
The sum of the interior angle measures of a polygon is 180°
The conclusion will be:
The poñyogn is a triangle.
Now we want to negate these two, it is really simple, for the hypothesis we will have that the sum of the interior angles can be any number but 180°, then we can write the negation as:
"The sum of the interior angle measures of a polygon is not 180°
Similar for the conclusion, we just need to state that the polygon is not a triangle, we will get:
"The polygon is not a triangle"
Then the negations of the hypothesis and conclusion for the given conditional statement are:
not P = "The sum of the interior angle measures of a polygon is not 180°"
not Q = "The polygon is not a triangle"
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The Great Wall of China, built in the 7th century BCE, is about 1 x 10^4 miles long. The Panama Canal, built over 2 thousand years later, is about 5 x 10^1 miles long. Use these numbers to complete the sentence below. Write your answer in standarered form, without using exponets. The Great Wall of China is about ____ times longer then the Panama Canal what is the answer?
The Great Wall of China is about 200 times longer then the Panama Canal
How many times longer is the Great Wall of China?Scientific notation is used to compress large numbers into smaller numbers. In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. An examples of 100 expressed in scientific notation is 1 x 10².
In order to determine the difference in the length of the great wall of China and the Panama Canal, divide the length of the Great wall of China by the length of the Panama Canal.
(1 x [tex]10^{4}[/tex]) ÷ (5 x [tex]10^{1}[/tex])
(1/5) x [tex]10^{4 - 1}[/tex]
0.2 x [tex]10^{3}[/tex]
2 x [tex]10^{3 - 1}[/tex]
2 x10² = 200
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write the negation of the proposition. then state the truth value of the original proposition and its negation. antarctica is in the northern hemisphere.
The negation is "antarctica is not in the northern hemisphere" & the truth value of the original proposition is FALSE and its negation is TRUE.
The sentences that can be classified as true or false , but not both are called as propositions.
For Example , "Shirt is yellow" is a proposition whereas "a is less than 2" is not a proposition as the value of a is not fixed.
Negation of proposition means writing the opposite of the given proposition.
If the proposition is true then it's truth value is "True".
If the proposition is false then it's truth value is "False".
According to the given Question
The negation of the statement "antarctica is in the northern hemisphere" is "antarctica is not in the northern hemisphere"
The truth value of the original proposition is FALSE as Antarctica is in the Southern hemisphere.
The truth value of the negation is TRUE as Antarctica is not in the Northern hemisphere it is in southern Hemisphere.
Therefore , the negation is "antarctica is not in the northern hemisphere" & the truth value of the original proposition is FALSE and its negation is TRUE.
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Explain how to use addition with negative numbers.
Step-by-step explanation:
Adding A Negative Number
Now let's see what adding and subtracting negative numbers looks like:
add subtract +- goes down
We can add weights (we are adding negative values)
the basket gets pulled downwards (negative)
Example: 6 + (−3) = 3
is really saying
"Positive 6 plus Negative 3 equals Positive 3"
We could write it as (+6) + (−3) = (+3)
5) Three consecutive odd integers are such that the sum of the first and the third is 70.Find the integers
Solution : Three consecutive odd integers are 33,35,37
Three consecutive odd integers :
Odd numbers are whole numbers that when divided by 2 give the remainder as one. Odd numbers are written in the form 2x+1,x∈N where N is the natural numbers
the sum of the first and the third is 70.
1 st number is = a
2nd number = b
3rd number = c
Let the required one integer be x. We need three integers so one integer is x next odd integer can be written as x+2 and the third integer can be written as x+4
a+c = 70 ...1
a= x
b=x+2
c= x+4
for equation 1
x+x+4 = 70
2x+4 =70
2x= 70-4
2x= 66
x=66/2
x=33
a=33
b= x+2 =33+2 =35
c= x+4 = 33+4 = 37
Three consecutive odd integers are 33,35,37
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please help this is my question
find the value of x in each of the following here are the questions
2x=10
3x=27
Step-by-step explanation:
1)x=10/2=5
x=5
2)x=27/3=9
x=9
Please help! I cannot figure this out.
well, for the piece-wise function, we'd like to know f(-2), or namely what is f(x) when x = -2?
well, f(x) is 2 for x = -1
f(x) is 4 for x > -1
keeping in mind that in the negative side of the number line, the closer to 0, the larger, thus -1 is much larger than -1,000, so hmmm -2 is farther from 0 than -1 is, so -1 is larger than -2, so when x = -2, x < -1, and the function that applies when x < -1 is -(x+1)² + 4, so then
[tex]f(x)= \begin{cases} -(x+1)^2 + 4&\stackrel{-2}{x} < -1\\\\ 2&x=-1\\\\ 4&x > -1 \end{cases} \\\\\\ f(-2)\implies -(~~(-2)+1~~)^2 + 4\implies -(-1)^2+4\implies -(-1)(-1)+4 \\\\\\ -(1)+4\implies -1+4\implies \text{\LARGE 3}[/tex]
Answer: f(-2)=3
Step-by-step explanation:
[tex]f(x)=\left\{\begin{array}{ccc}-(x+1)^2+4\ for\ x < -1\\2\ \ \ \ for\ \ x=-1\\4\ \ \ for \ \ \ x > -1\end{array}\right[/tex]
[tex]-2\in(-\infty,-1)\\Hence,[/tex]
[tex]f(-2)=-(-2+1)^2+4\\f(-2)=-(-1)^2+4\\f(-2)=-1+4\\f(-2)=3[/tex]
|2x-3|=-1
Help solve
awaer
click here
Step-by-step explanation:
Write each expression as a single logarithm.
log₄2+log₄8
If the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.
Given that the expression is log₄2+log₄8.
We are required to express the given expression in single logarithm.
Product property of logarithm basically tells that says that the logarithm of a product is equal to a sum of logarithms and because logs are exponents, and we multiply like bases, we can add the exponents.
The expression is log₄2+log₄8.
log₄2+log₄8=[tex]log_{4}[/tex](8*2) (We are not required to write the base separately)
=[tex]log_{4}[/tex]16
Hence if the expression is log₄2+log₄8, then it will look like [tex]log_{4}16[/tex] in single logarithm form.
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Identify the equation that represents the sentence “Find two consecutive odd integers whose sum is 116”.
Multiple choice question.
cross out
A)
n
(
n
+
2
)
=
116
cross out
B)
n
(
n
+
1
)
=
116
cross out
C)
2
n
+
2
=
116
cross out
D)
2
(
n
+
2
)
=
116
Answer:
Answer: 57 & 59
Step-by-step explanation:
Let us assume first odd integer is 'x'
Then, next consecutive integer should be 'x+2'. RIGHT?
Now, put in the form of equation:
x + (x+2) = 116
x + x + 2 = 116
2x + 2 = 116
2x = 116 - 2
2x = 114
x = 114 / 2 => 57
Now, put the value of 'x' in second step:
x + 2 => 57 + 2 = 59
Therefore, answer would be 57 & 59
help pls explain this to meeeeee
(image included)
The equation of the line passing through the given coordinate with the given slope is; y = 2x + 11
What is the equation of the line in point slope form?
The formula for equation of line in point slope form is;
(y - y1) = m(x - x1)
We are given the slope is 2
Now, if the line passes through the coordinate (-4, 3), then the equation of the line is;
(y - 3) = 2(x - (-4))
y - 3 = 2x + 8
y = 2x + 11
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HELP PLEASE!!! INEQUALITY WORD PROBLEM, MULTIPLE CHOICE.
Answer:
D.
Step-by-step explanation:
She gets 21$ for 6 hours of work, while the amount of tips is varied.
Answer: it would be A
Step-by-step explanation:
What is the value of the expression below when w = 9 and x = 8?
Answer:
9w7x
Submit Answer
Answer:
Step-by-step explanation:
4,536
Find the area of the triangle.
Do not include units (square units) in your answer.
Answer:
Step-by-step explanation:
The area is 6
because the base is 4 units and the height it 3 units, and base times height will give you 6.
Reginald wallace's gross weekly salary is $515. his weekly federal withholding is $55. the social securit
tax is 6.2 percent of the first $90,000. the medicare tax is 1.45 percent of gross pay. the state tax is 1.5
percent of gross pay. each week he pays $12.40 for medical insurance. how much is deducted from
wallace's weekly wages for state tax and medicare tax?
$17.67
$15.19
b. $12.22
d. $16.19
c.
a.
If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.
State tax and Medicare taxState tax=1.5 percent of gross pay
Medicare tax=1.45 percent of gross pay
State tax=$515 ×0.015
State tax= $7.725
Medicare tax=$515× 0.0145
Medicare tax = $7.4675
Hence:
State tax and Medicare tax=$7.725+$7.4675
State tax and Medicare tax=$15.1925
State tax and Medicare tax=$15.19 (Approximately)
Therefore If Reginald Wallace’s gross weekly salary is $515 and the Medicare tax is 1.45 percent of gross pay. The state tax is 1.5 percent of gross pay. The amount that is deducted from Wallace’s weekly wages for state tax and Medicare tax is: $15.19.
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can √2x/3y be simplified? yes or no?
If yes show your work if not Explain why not.
Note Show work or ill delete your answer....
The expression √3 + 5 cannot be simplified and the expression √2x/3y cannot be simplified
How to determine if the expressions can be simplified?Expression 1
The expression is given as
√3 + 5
The above expression is a combination of a radical expression and an integer
The radical expression √3 cannot be simplified
This means that the expression √3 + 5 cannot be simplified
Hence, the expression √3 + 5 cannot be simplified
Expression 2
The expression is given as
√2x/3y
The above expression is a combination of radical expressions
However, the radical expressions do not have a common factor
This means that the expression √2x/3y cannot be simplified
Hence, the expression √2x/3y cannot be simplified
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Complete question
can √3 + 5 be simplified if yes show your work if not explain why
can √2x/3y be simplified if yes show your work if not explain why
The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $ 1200 . The party must have 13 adult chaperones.
a. If every student who attends shares the facility cost equally, what function models the cost per student C with respect to the number of students n who attend? What is the domain of the function? How many students must attend to make the cost per student no more than $ 7.50 ?
a. If every student who attends shares the facility cost equally, the function model will be 1200/N
What is the domain of the function?
domain : 1 ≤ N ≤ (312 - additional adult chaperones) N ∈ Z
How many students must attend to make the cost per student no more than $ 7.50 ?1200/N ≤ 7.50
1200 / 7.50 ≤ N
N ≥ 1200/7.5
N ≥ 160
More than 160 students must attend to make the cost per student no more than $ 7.50
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i’m so lost please help i’m really trying to raise my grade
Answer:
A. x = 5
B. isosceles triangle
Under her cell phone plan, Bao pays a flat cost of $40.50 per month and $5 per gigabyte. She wants to keep her bill under $60 per month. Write and solve an inequality which can be used to determine gg, the number of gigabytes Bao can use while staying within her budget.
The number of gigabytes Bao can use while staying within her budget is 3.9 gigabytes.
How to illustrate the inequality?From the information, plan, Bao pays a flat cost of $40.50 per month and $5 per gigabyte and she wants to keep her bill under $60 per month.
The inequality will be:
40.50 + 5g < 60
where g = number of gigabytes
40.50 + 5g < 60
5g < 60 - 40.50
5g < 19.50
g < 19.50 / 5
g < 3.9
Therefore, the number of gigabytes will be less than 3.9 g.
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Which stem-and-leaf plot represents the data set?
{3.3, 4.5, 5.0, 4.4, 5.0, 2.2, 4.9, 3.3, 3.4, 2.0, 2.1}
A stem and leaf plot is a table used to display data. The 'stem' is shown on the left side of the table and shows the first digit or digits of data values. The 'leaf' is shown on the right side of the table and shows the last digit of the data value.
A stem and leaf plot displays numerical data by splitting each data point into a "leaf" (usually the last digit) and a "stem" (the leading digit or digits).
Split each data point into a stem and a leaf. The stem is everything before the final digit, and the leaf is the final digit. Write the stems in a vertical column and don't skip stems just because they don't have any data.
2
3
4
5
4
5
our stems are the 10 digit data.
2 ! 0 ,1, 2
3! 3, 4,
4! 4 , 5 , 9
5 ! 0
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what is the slope-intercept equation of the line that includes the points in the table?
If we have two pairs (x₁, y₁) and (x₂, y₂) on the table, use the following formula to get the slope:
a = (y₂ - y₁)/(x₂ - x₁)
How to get the slope for any table?
A general linear equation in the slope-intercept form can be written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Now, if the linear equation has a table with some values:
X Y
x₁ y₁
x₂ y₂
x₃ y₃
etc...
Then you can select any two of the pairs on the table, for example (x₁, y₁) and (x₂, y₂), and use the following formula to get the slope:
a = (y₂ - y₁)/(x₂ - x₁)
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Given ƒ(x) = −4x − 5, find ƒ(5)
The output value of f(5) in the given function f(x) = -4x - 5 is -25
What is the output value of f(5) in the given function?A function is simply a set of ordered pairs where each first element is paired with one and only second element and also no element in either pair is without a partner.
Given the data in the question;
f(x) = -4x - 5f(5) = ?To determine the output value of f(5), replace the variable x with 5 and simplify.
f(x) = -4x - 5
f(5) = -4(5) - 5
Perform the multiplication operation to remove the parenthesis.
f(5) = -4(5) - 5
f(5) = -20 - 5
f(5) = -25
Therefore, the output value of f(5) in the given function f(x) = -4x - 5 is -25.
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The loudness in decibels dB of a sound is defined as 10 log I/I₀ , where I is the intensity of the sound in watts per square meter (W / m²) . I₀ , the intensity of a barely audible sound, is equal to 10⁻¹²W/m². Town regulations require the loudness of construction work not to exceed 100 dB . Suppose a construction team is blasting rock for a roadway. One explosion has an intensity of 1.65x10²W/m² . Is this explosion in violation of town regulations?
b. What values should you use for I and I₀?
a) The explosion does violate the town regulation
b) The values are , I = [tex]1.65 * 10^{2} W/m^{2}[/tex] and [tex]I_{0}[/tex] = [tex]10^{-12} W/m^{2}[/tex]
The values that we have been given are
L = loudness of the sound = 10log(I/[tex]I_{0}[/tex])
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
[tex]I_{0}[/tex] = intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
Putting the required value in the equation of the loudness we get
a) L = [tex]10*log (\frac{1.65*10^{2} }{10^{-12} } )[/tex]
L = 10*14.217 dB = 1142.17 dB
And according to the town regulation the loudness of the construction work should not exceed 100dB.
Thus the explosion is in violation of the town regulation as it exceeds 100dB.
b) The respective values of I and [tex]I_{0}[/tex] are
I = intensity of the sound in watts per square meter = [tex]1.65 * 10^{2} W/m^{2}[/tex]
= intensity of barely audible sound = [tex]10^{-12} W/m^{2}[/tex]
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4(x - 3) + 14 = 7x - 3(x + 7)
Is this a conditional, identity, or contradiction equation
4(X-3)+14=7X-3(X+7)
or, 4X-16+14=7X-3X
or, 4X-7X+3X=(-21)+16-14
or, 0= -19
Hence, the answer is wrong but the process is right.
Solve for g: 3/4(4g + 5)=6
Make the non testable questions be testable questions. (Only 2) PLEASE HELP!!
"Which planet is the most interesting to study?"
"What happens if you do not eat breakfast?"
When the given non testable questions are made into testable questions, they become:
What planetary conditions are considered subjects of interest for study?How is your body affected when you do not eat breakfast?How to write testable questions?A testable question is one that requires the answer to be acquired by means of experimentation.
Instead of asking, "Which planet is the most interesting to study?" you could ask about the conditions that a planet has which are considered subjects of interest.
Also, instead of asking, "What happens if you do not eat breakfast?" you could ask about how the body is affected when we skip breakfast. This can be tested in an experiment that checks the body's functions when breakfast isn't eaten.
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