What is the solution to the equation below? Round your answer to two decimal places.ex = 0.5A.x = 3.16B.x = -0.69C.x = -0.30D.x = 1.65
Answers
Solve the equation:
\(e^x=0.5\)Since the variable is an exponent, we need to use logarithms. The base of the exponential is the number e, the base of the natural logarithms, thus:
\(\ln e^x=\ln0.5\)Applying the power rule for logarithms:
\(x\ln e=\ln0.5\)Since ln e = 1:
\(x=\ln0.5\)Using a calculator:
x = -0.69
Related Questions
Ashley earned $40,000 last year. If the first $16,000 is taxed at 10% and income above that is taxed at 21%, how much does Ashley owe in tax? HELP ASAP
Answers
Hello,
I hope you and your family are doing well!
If Ashley earned $40,000 last year and the first $16,000 is taxed at 10% and income above that is taxed at 21%, the amount of tax that Ashley owes can be calculated as follows:
The first $16,000 of Ashley's income is taxed at a rate of 10%, so the amount of tax on this portion of her income is $16,000 * 10% = $1,600.
The remaining $24,000 of Ashley's income is taxed at a rate of 21%, so the amount of tax on this portion of her income is $24,000 * 21% = $5,040.
The total amount of tax that Ashley owes is the sum of these two amounts or $1,600 + $5,040 = $6,640
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Happy to help!
9(7y+5)-4(-6y-1
6(5f+4)-2(6f-4)
Answers
Answer: 9(7y+5)-4(-6y-1) simplifies to 87y + 49.
6(5f+4)-2(6f-4) simplifies to 18f + 32
Step-by-step explanation:
To simplify the expressions:
9(7y+5)-4(-6y-1)
Distribute the 9 and -4:
63y + 45 + 24y + 4
Combine like terms:
87y + 49
Therefore, 9(7y+5)-4(-6y-1) simplifies to 87y + 49.
6(5f+4)-2(6f-4)
Distribute the 6 and -2:
30f + 24 - 12f + 8
Combine like terms:
18f + 32
Therefore, 6(5f+4)-2(6f-4) simplifies to 18f + 32
solve for x
(look at photo)
Answers
By definition of proportion, the value of x is,
⇒ x = 80
We have to given that;
In a triangle,
Perpendicular = 60
Now, By Pythagoras theorem we get;
60² = 36² + y²
3600 = 1296 + y²
y² = 3600 - 1296
y² = 2304
y = 48
Hence, By definition of proportion;
⇒ x / 48 = 60 / 36
⇒ x = 80
Thus, By definition of proportion, the value of x is,
⇒ x = 80
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1.2 Generate a three-column table where you evaluate how learning takes place according to: • Piaget • Vygotsky • Bruner (15)
Answers
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
Here's a three-column table evaluating how learning takes place according to Piaget, Vygotsky, and Bruner:
Theorist Approach to Learning Key Concepts
Piaget Constructivism 1. Schema: Individuals actively construct their knowledge through assimilation and accommodation, organizing information into mental structures called schemas. 2. Stages of Development: Learning occurs through cognitive development stages, from sensorimotor to formal operational, where individuals progressively acquire more complex mental abilities. 3. Active Exploration: Children learn best through hands-on exploration and interactions with the physical world.
Vygotsky Sociocultural Theory 1. Zone of Proximal Development (ZPD): Learning takes place within the gap between a learner's actual developmental level and their potential level with guidance from a more knowledgeable other. 2. Social Interaction: Learning is facilitated through social interactions with peers and adults, such as cooperative learning and scaffolding. 3. Cultural Tools: The use of language, symbols, and cultural artifacts plays a central role in cognitive development and learning.
Bruner Constructivism 1. Scaffolding: Instruction should provide support and guidance tailored to the learner's current abilities to help them progress to higher levels of understanding. 2. Discovery Learning: Learners construct knowledge by actively exploring and discovering concepts and relationships on their own. 3. Spiral Curriculum: Learning is organized in a spiral manner, revisiting key concepts and building upon previous knowledge in a progressive and interconnected way.
While Piaget, Vygotsky, and Bruner have different perspectives on how learning occurs, they all emphasize the active role of the learner in constructing knowledge and the importance of social interaction and cultural influences in the learning process.
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Referring to the figure, the two rectangles shown have
equal areas. Find the value of x.
Answers
Answer:
x = 2
Step-by-step explanation:
the area (A) of a rectangle is calculated as
A = length × breadth
given the rectangles have equal areas then equating the two areas gives
4x × 9 = 4(6x + 6) , that is
36x = 24x + 24 ( subtract 24x from both sides )
12x = 24 ( divide both sides by 12 )
x = 2
Help please been stuck on this
Answers
Step-by-step explanation:
The rules for significant digits are:
Non-zero digits are always significant.Zeros between significant digits are also significant.Trailing zeros are significant only after a decimal point.To round each number to one digit, round to the first digit.
a) 300,000
b) £200
c) 20,000 km
I need to use factorial the! When you use the binomial probability formula and I need to show step-by-step for for a through c
Given the number of trials and the probability of success, determine the probability indicated: (Hint use binomial distribution formula use factorials ! in showing your work)
n = 15, p = 0.4, find P(4 successes)
n = 12, p = 0.2, find P(2 success )
n = 20, p = 0.05, find P(at most 3 successes)
(hint for c.
P (at most 3 successes) = P(x ≤3)= P(x= 0) + P(x = 1)+ P(x = 2)+ P(x = 3)
Answers
Using the binomial distribution, it is found that the probabilities are:
P(X = 4) = 0.1268.P(X = 2) = 0.2835.\(P(X \leq 3) = 0.9841\)What is the binomial distribution formula?The formula is:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.Exercise 1:
The parameters are:
n = 15, p = 0.4, x = 4.
Then:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 4) = C_{15,4}.(0.4)^{4}.(0.6)^{11} = 0.1228\)
Exercise 2:
The parameters are:
n = 12, p = 0.2, x = 2.
Then:
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 2) = C_{12,2}.(0.2)^{2}.(0.8)^{10} = 0.2835\)
Exercise 3:
The parameters are:
n = 20, p = 0.05.
The probability is:
\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)
Using the binomial formula for each value and adding them:
\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9841\)
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Mariana's recipe calls for 2 cups of sugar to make 12 cupcakes. Which ratio of cups of sugar to cupcakes is equivalent to Mariana's recipe?
Answers
Answer:
2:12
Step-by-step explanation:
The ratio of cups of sugar to cupcakes is equivalent to 1:6.
Given that Mariana's recipe calls for 2 cups of sugar to make 12 cupcakes.
What is the ratio?The ratio is the comparison of two quantities. It is generally represented by a fraction.
2 cups of sugar: 12 cupcakes = 2:12
2:12 = 2/12 =1/6 =1:6
So, the ratio of cups of sugar to cupcakes is equivalent to 1:6.
Therefore, the ratio of cups of sugar to cupcakes is equivalent to 1:6.
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Type the correct answer in the box.
Fill in the missing term in the equation.
(1 + 2)(2+1) + blank
= 5(2+i)
Answers
(1 + 2)(2 + 1) + blank
= 3(3) + blank
= 9 + blank
Expanding the right side of the equation:
5(2 + i)
= 10 + 5i
Since the left side of the equation (9 + blank) is equal to the right side (10 + 5i), we can deduce that the missing term should be equal to 1i.
Therefore, the missing term in the equation is "1i".
You paid $6.99 for a shirt that was 70% of what was the original price of the shirt?
Answers
Answer:
$23.3
Step-by-step explanation:
you can use ratios to solve this:
$6.99/x=0.30/0.100 then cross multiply to get 0.3x=6.99
So, 6.99 divided by 0.3 = 23.3
so the original price is $23.3
HELP PLEASEEEE!!!!!!!!!!!!!!!!!
Answers
Answer:
172 cm²
Step-by-step explanation:
The surface area of a rectangular prism is given by the formula
A = 2(w * l + h * l + h * w)
where w = width, h = height and l = length
Each prism shown in the figure has
l = 8, w = 2 and h = 3
It is obvious that the prisms should be joined so that the length is doubled for the surface area to be maximized
The surface area of each prism is 2(2 x 8 + 3 x 8 + 3 x 2) = 92
The new prism will have double the length but the same height and width
so l = 16, w = 2 and h =3
Area = 2(2 x 16 + 3 x 16 + 3 x 2) = 172 cm²
factorize completely (2x+2y) (x-y)+(2x-2y)(x+y)
Answers
Explanation:
(2x + 2y)(x - y) + (2x - 2y)(x+y)
= 2(x+y)(x-y) + 2(x-y)(x+y)
= 2(x^2 - y^2) + 2(x^2 - y^2)
= (2 + 2)(x^2 - y^2) (combine like terms)
= 4(x^2 - y^2)
5 (15pts, 5pts each) In △ABC below, ED = 6 cm, EC = CB, and AC ⊥ BE . If AC = 12 cm and AB = 13 cm:
Answers
Answer:
i dont even understand this can u pls place an attachment of the problem pls
True or false: 12 + 18 is equivalent to 6(2+3).
Answers
Answer: True
Step-by-step explanation:
Chloe is fundraising for her school by selling rolls of wrapping paper and packages of bows •she manages to sell 18 rolls of wrapping paper and 22 packages of bows for a total of $308.80 on her first day of sales. •she does better on her second day of sales. She sells 25 rolls of wrapping paper and 29 packages of bows for a total of $415.90
Answers
1)
a)
Let x be the cost of rolling paper and y be the cost of bows.
b)
Given that Chloe sell 18 rolls of wrapping paper and 22 packages of bows for a total of $308.80
The cost of 18 rolls of wrapping paper =18 times x=18x
The cost of 22 packages of bows =22 time y=2
What is the value of x in the diagram below?
A.
6
B.
4
C.
5
D.
3
Answers
Answer:
\(\boxed{3}\)
Step-by-step explanation:
We can use ratios to solve since the sides are proportional.
\(\frac{18}{x} =\frac{48}{8}\)
Cross multiply.
\(48x=18 \times 8\)
Divide both sides by 48.
\(\frac{48x}{48} = \frac{18 \times 8}{48}\)
\(x=3\)
The value of x in the given triangle is 3.
What are similar triangles?Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Given are two similar triangles,
Therefore, they have the same ratio of corresponding sides
18/48 = x/8
x = 3
Hence, The value of x in the given triangle is 3.
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A musician
produced 2000 compact discs of his music . He sold 125 of the discs.Four were returned because they were defective. Based of the amount of discs sold, what is the predicted total of defective discs?
Answers
Answer:
64
Step-by-step explanation:
I'm assuming this is what the question means, so basically every 4/125 discs are defective, and 125 fits into 2000, 16 times so you multiply 4/125*16/16 so you get 64/2000.hope this helps
Clipper Company sells two types of nail clippers. One focuses on the economy oriented customer and the other aims to satisfy the high-end clientele. The economy clipper costs $4 and has a sales price of $9. The high-end model costs $8 and sells for $13. Fixed costs associated with this product line amount to $66,120. Economy clippers constitute 70 percent of the market with the remaining 30 percent being high-end clippers. Based on this information what is the total break-even point (the total number of economy line plus the number of high-end clippers)? Note: Round your final answer to nearest whole number.
Answers
The total break-even point for both products is 16,530 units.
What does break-even point mean?A breakeven point is used in a variety of business and finance situations. It is the level of production at which total production revenue equals total production costs in accounting terms.
Given data
Selling price of economy clipper = $9
Cost of economy clipper = $4
Selling price of high-end model= $13
Cost of high-end model = $4
To calculate the break-even point, we need to determine the total fixed costs and the total variable costs for each product.
Variable costs for the economy clipper:
= $9 (sales price) - $4 (cost)
= $5
Variable costs for the high-end clipper:
= $13 (sales price) - $8 (cost)
= $5
Total variable costs for both products:
= (70% * $5) + (30% * $5)
= $5
The break-even point can be calculated using the formula:
Total fixed costs / (Price - Variable costs)
= $66,120 / ($9 - $5)
= $66,120 / $4
= 16,530 units.
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Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
Answers
Answer:
56π/3 m³ or 58.64 m³------------------------------------------------
Find the sum of the volumes of the two given cones.
Cone volume:
V = 1/3 πr²hCone 1, d = 4m, h = 8m:
V = 1/3 π*(4/2)²*8 = 32π/3 m³Cone 2, r = 2m, h = 6 m:
V = 1/3 π*2²*6 = 8π m³Total volume:
V = 32π/3 + 8π = 56π/3 m³ = 58.64 m³ (rounded)arrange the following in descending order - 5, 0, -15, 2.5, 2.05
Answers
Answer:
2.5, 2.05, 0, -5, -15
Step-by-step explanation:
for negative numbers the bigger is worth less
Determining the sale price of a home is an important task for city assessors, as it helps the city project future tax revenue. Regression models using the physical characteristics of a home to predict the sale price is standard practice for many assessors. A random sample of 724 homes sold in Ames, Iowa, between 2006 and 2010 was obtained to build such a model for the city of Ames. The assessor considered the following variables in their initial model:
Variable Description
LotArea Lot size (in thousands of square feet)
LivingArea Living space (in thousands of square feet)
Bedrooms Number of bedrooms
Rooms Number of rooms
Fireplaces Number of fireplaces
Bath Number of bathrooms
Age Age of the home (in years)
Price Sale price of the home (in thousands of dollars)
Below is the output obtained from the statistical software.
Estimate Std Error t value Pr(>|t|)
(Intercept) 100.55 6.167 16.31 < 0.0001
LotArea 0.99 0.144 6.86 < 0.0001
LivingArea 112.97 5.600 20.17 <0 .0001
Bedrooms −16.35 2.366 −6.91 < 0.0001
Rooms −0.51 1.667 −0.30 0.7613
Fireplaces 12.80 2.206 5.80 < 0.0001
Bat −13.60 3.459 −3.93 < 0.0001
Age−0.96 0.054 −17.86 < 0.0001
Number of Observations Residual Std Error R2 Adjusted R2
724 33.69 0.7686 0.7663
What is the response variable?
a. lot area
b. living area
c. age
d. sale price
What proportion of the variation in sale price does this multiple regression model explain?
a. .3369
b. .7686
c. .7663
d. 0.2314
Answers
What is the definition of perpendicular lines?
1.two lines that intersect in a way that forms right angles
2.two lines that intersect in a way that cuts both lines in half
3.two lines that intersect in a way that they share more than one common point
4.two lines that intersect in a way that forms two congruent angles
Answers
Answer:
Step-by-step explanation:
The correct definition of perpendicular lines is option 1: "Two lines that intersect in a way that forms right angles."
When two lines intersect to form four right angles (90-degree angles), they are said to be perpendicular to each other. The point at which the lines intersect is called the point of intersection.
Therefore, option 1 is the correct definitation of perpendicular lines.
Answer: 1. Two lines that intersect in a way that forms right angles.
Step-by-step explanation:
Hope this helped! :)
Dividing fractions word problems, please help I need it........
Answers
Answer:
25
Step-by-step explanation:
l x w = h
25 x 7.2 = 180
The length of the longer leg of a 30 60 90 triangle is 6. The hyp is 9.
State the solution in Simple Root Form:
State the solution to the nearest tenth:
Answers
Step-by-step explanation:
there is something severely wrong with the problem definition.
when the Hypotenuse = 9, there is no 30-60-90 triangle with a leg = 6.
and when we are just focusing that this is a right-angled triangle with the Hypotenuse = 9, then 6 cannot be the longer leg.
it is also not clear what the solution is supposed to be. the 2nd leg ? the area ? the perimeter ? the height(s) ? ...
what ?
so, all I can do here is to show you why I said what I said :
30-60-90 triangle with Hypotenuse = 9
then the longer leg is opposite of the 60° angle and therefore sin(60)×9 = 7.794228634...
the shorter leg is opposite of the 30° angle and therefore sin(30)×9 = 0.5×9 = 4.5
a right-angled triangle with Hypotenuse = 9, one leg = 6 gives us per Pythagoras for the other leg
9² = 6² + leg²
81 = 36 + leg²
45 = leg²
leg = sqrt(45) = 6.708203932...
so, you see, as stated above, there is no leg with the length 6 in such a 30-60-90 triangle.
and in a more general right-angled triangle, if one leg = 6, then the other leg is actually longer.
therefore, there is everything wrong with the problem definition.
Identify the exponent in the term -3X²
A. 3
B. x
C. minus sign ( - )
D. 2
Answers
x is the term which is manipulated to fit the expression.
(-) is what is done to the coefficient.
3 is the coefficient.
One batch of an ice cream recipe uses 9 cups of milk. A chef makes different amounts of ice cream on different days. Here are the amounts of milk she used:
Monday: 12 cups
Tuesday: 2212 cups
Thursday: 6 cups
Friday: 712 cups
How many batches of ice cream did she make on each of the following days?
Answers
Answer:
Just divide each amount by 9....so.....
Monday 12 / 9 = 4 / 3 = 1 + 1/3 batches
Tuesday 22 + 1/2 = 45/2
So (45/2) / 9 = 45 / 18 = 5/2 = 2 + 1/2 batches
Thurssday 6 / 9 = 2 / 3 batches
Friday 7 + 1/2 = 15/2
So (15/2) / 9 = 15 / 18 = 5 / 6 batches
Please help ya boy out please
Answers
Answer:
its a
Step-by-step explanation:
its a trust me
Ellen already knew 50 appetizer recipes before starting culinary school, and she will learn 4 new appetizer recipes during each week of school. After 73 weeks of culinary school, how many total appetizer recipes will Ellen know? Write and solve an equation to find the answer.
Answers
Answer:
342
Step-by-step explanation:
50+4x=y
x=73
which ones are rational and irrational ? 9.5 , 9.6 , or 9.7
Answers
9514 1404 393
Answer:
all are rational
Step-by-step explanation:
Any decimal number with a finite number of digits is rational.
__
A decimal number is irrational if and only if it has an infinite number of non-repeating digits in its fractional part.
what is the meaning of sequence in mathematic and
Answers
Answer:
A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
Step-by-step explanation: