Answer: 10
Step-by-step explanation: any number to the first power is the number being multiplied
Answer: 10
Step-by-step explanation: Any number to the first power equals the same number, for example: 4 to the first power is 4, or in this case 10 to the first power = 10.
Mark is doing a course.There are 5 tests on the course. He needs a mean score of 10 to pass. In his first 4 tests his mean score is 12. What score does he need in the 5th test to pass the course
Mark needs a score of 2 on the 5th test to pass the course
How to calculate the mean score needed by Mark to pass the courseLet X be the score Mark needs to get on the fifth test to pass the course.
To find X, we can use the formula for the mean of five numbers:
(mean of 5 numbers) = (sum of the 5 numbers) / 5
We know that Mark needs a mean score of 10 to pass, so:
10 = (total score on all 5 tests) / 5
Multiplying both sides by 5, we get:
50 = total score on all 5 tests
We also know that Mark's mean score on the first four tests is 12, so:
(mean score on the first four tests) = (total score on the first four tests) / 4
12 = (total score on the first four tests) / 4
total score on the first four tests = 48
To pass the course with a mean score of 10, Mark needs a total score of 50, and he has already scored 48 on the first four tests. Therefore, he needs to score:
X = 50 - 48
X = 2
Mark needs a score of 2 on the fifth test to pass the course with a mean score of 10.
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Compute the area of the triangle, if x equals 3 less than 6.
I AM SUFFERING
The area of the triangle ABC is, 9 sq units.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.
Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know, The area of a triangle is (1/2)×base×height.
Given, x equals 3 less than 6 which is,
x = (6 - 3).
x = 3.
Now, The base of the triangle is x units and the height is 2x units.
Therefore, The area of the triangle is,
= (1/2)×(3)×2(3).
= 9 sq units.
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a worker earned #80 per hour for a 38 hour week in a company. the company pays overtime at a time and a half. in a week he earned #3640. find the total numbers of hours he worked that week?
The worker worked 38 + 5 = 43 hours that week.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's break this problem down into two parts.
Part 1: Calculating the base pay for the 38 hours worked
The worker earned #80 per hour for a 38-hour week, so the base pay for those 38 hours would be:
Base pay = #80/hour x 38 hours = #3040
Part 2: Calculating the overtime pay for the additional hours worked
To find out how many hours were worked beyond the 38-hour week, we can use the fact that the total pay for the week was #3640. We know that the base pay for 38 hours was #3040, so the remaining #600 must be the overtime pay.
Since the company pays overtime at a time and a half, we can use this to find out how many hours were worked beyond the 38-hour week:
Overtime pay = (#80/hour x 1.5) x (number of overtime hours)
We can rearrange this equation to solve for the number of overtime hours:
Number of overtime hours = Overtime pay / (#80/hour x 1.5)
Number of overtime hours = #600 / (#80/hour x 1.5) = 5
Therefore, the worker worked 38 + 5 = 43 hours that week.
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could you help with these questions ?
a. The equation of the tangent plane is z = 1 + x.
b. The point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.
c. The other points on the graph of f(x) whose tangent plane contains the line l are (-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
(a) The partial derivatives of f(x) at this point:
∂f/∂x = 2x + y²
∂f/∂y = x² + 2xy
Evaluating these at (0,1), we get:
∂f/∂x(0,1) = 1
∂f/∂y(0,1) = 0
So the equation of the tangent plane is:
z = f(0,1) + ∂f/∂x(0,1)(x-0) + ∂f/∂y(0,1)(y-1)
z = 1 + x
(b)
The plane T(0,1) contains the line l:
2x = y = (z+3)/2
Substituting y = 2x and z = 2y-3, we get:
z = 2(2x) - 3 = 4x - 3
So any point on the line l can be written as (x, 2x, 4x-3).
Substituting these values into the equation of the plane, we get:
4x-3 = 1 + x
3x = 4
So x = 4/3, y = 8/3, and z = 5.
Therefore, the point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.
(c) To find all other points on the graph of f whose tangent plane contains the line l, we need to find the intersection of the graph of f with the plane T(0,1) + λ(2,0,1), where λ is a scalar. This gives us the system of equations:
x² + y²xy = 1 + x + 2λ
2x + y² = 0
y - 1 = λ
Solving for x and y in terms of λ, we get:
y = λ + 1
x = -(y²)/2 = -(λ+1)²/2
Substituting these values into the first equation, we get:
(λ+1)² + (λ+1)²(-(λ+1)²/2) = 1 - (λ+1)²/2 + 2λ
Simplifying and solving for λ, we get:
λ = -1/2, -1/4
Therefore, the other points on the graph of f(x) whose tangent plane contains the line l are:
(-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)
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Find the missing side measurements
Can anyone help me with this question
The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
From the given graph,
The zeros of function are x=-3, x=2 and x=5.
So, the number of zeros are 3 and the degree of the polynomial is 3.
The relative maximum from the given graph is (2, 0).
The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.
Here, the leading coefficient is negative.
The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.
Here, the multiplicity is 2.
Therefore, options B, C, D and E are the correct answers
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(2 -7) (-2 --7) slope intercept form
The answer is m = 0.
Paul finished his 800 meter race in 2 minutes and 2 seconds. Jeff finished in 121
seconds. Who finished first? (Remember, the person with the lowest time finishes first.) show work
Answer:
To compare the times of Paul and Jeff, we need to convert Paul's time to seconds.
Paul's time = 2 minutes 2 seconds = (2 x 60) + 2 = 122 seconds
Now we can compare their times:
Paul's time: 122 seconds
Jeff's time: 121 seconds
Jeff finished first since he has the lowest time.
Answer: To compare the times of Paul and Jeff, we need to convert Paul's time to seconds:
2 minutes and 2 seconds = 2 × 60 seconds + 2 seconds = 122 seconds
Now we can compare their times:
Paul finished in 122 seconds
Jeff finished in 121 seconds
Since Jeff's time is lower than Paul's time, Jeff finished first.
Step-by-step explanation:
Look at the stem-and-leaf plot of scores on a science test. Stem 6 7 8 9 10 Leaf 4,7 0, 0, 0, 3, 6, 9, 9 2, 2, 5, 8 1, 4, 4, 7, 7 0, 0, 0, 0 Key 6 4 = 64 How many students scored more than 70 but less than 80?
The number of students who scored more than 70 but less than 80 is zero.
What is the stem-and-leaf diagram?A stem-and-leaf diagram is a quantitative analysis of a collection of data points that are separated into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).
To find the number of students who scored more than 70 but less than 80, we need to look at the stem-and-leaf plot and count the number of leaves that fall within this range.
Stem 7 has a leaf of 6, which represents a score of 76. Therefore, at least one student scored between 70 and 76.
The stem 8 has leaves of 2, 5, and 8, which represent scores of 82, 85, and 88, respectively. Therefore, no students scored between 76 and 80.
Therefore, the number of students who scored more than 70 but less than 80 is zero.
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Yamilet works in a jewelry store and receives 12% commission when she makes a sale. how much commIssuing will she receive for selling an $8,125 ring
Answer: To find out how much commission Yamilet will receive for selling an $8,125 ring, we need to multiply the price of the ring by her commission rate, which is 12% or 0.12 in decimal form.
Commission = Price of ring x Commission rate
Commission = $8,125 x 0.12
Commission = $975
Therefore, Yamilet will receive a commission of $975 for selling an $8,125 ring.
Step-by-step explanation:
calculate the unit rate.
The unit rate for the problems are;
a. 50pages/hour
b. 4points / game
c. 8 car washed /hour
d. 8 ounces of peanut/ dollar
What is unit rate?A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 100 yards in 10 seconds, you ran on average 10 yards in 1 second.
a. The unit rate = number of pages/ time
= 100/2 = 50pages/hour
b. The unit rate = number of points /number of games
= 20/5 = 4 points per game
c. The unit rate = number of car washed/ time
= 40/5 = 8car washed per hour
d. unit rate = number of ounces of peanut/ number of dollars
= 20/2.5 = 8 ounces of peanut per dollar
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Complete the ordered pairs that lie on the graph of function h. Type the correct answer in each box. Use numerals instead words. h(x){-x^2-6x-9, x<-2 (1/3)x-4,-2_ 2
The values of the piecewise function {h(x)} for different values of {x} is given above.
What is algebraic expressions?An algebraic expression is a made up of terms both constants and variables. For example, we can write -
2x + 3y + z
5x + y
x + 8y
Given is the relation as -
y = {- x² - 6x - 9 for x < - 2}
y = {x/3 - 4 for x > - 2}
The given function is a piecewise function. We can write the values for different values of {x} as -
{x} = - 4
y{4} = - (-4)² - 6(-4) - 9 = - 1
{x} = - 3
y{-3} = - (-3)² - 6(-3) - 9 = - 0
{x} = - 1
y{-1} = -1/3 - 4= -4.3
{x} = 0
y{-1} = 0/3 - 4 = - 4
Therefore, the values of the piecewise function {h(x)} for different values of {x} is given above.
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The demand equation for a certain item is p=14-x/1000 and the cost equation is c(x)=7000+4x. Find the marginal profit at a production level of 3000 and interpret the result.
Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.
what is equation ?An equation in mathematics is a claim made regarding the equivalence of two expressions. It includes one or more variables (unknown values) and describes how those variables and/or constants relate to one another. For instance, the line on a coordinate plane denoted by the equation y = 3x + 5 has a y-coordinate that is equivalent to three times the x-coordinate plus five. Three and five are constants in this equation, while x and y are factors. Finding the value(s) of the dependent variables) that make the equation true is one way to answer an equation. In the example above, we can enter y = 11 into the equation .
given
We must first determine the revenue function, which is provided by, in order to determine the marginal profit at a production level of 3000:
14x - x/1000x = R(x) = xp(x) = 14x - x2/1000
where the demand function is given by p(x) = 14 - x/1000.
The benefit function is next, and it is provided by:
P(x) = R(x) - C(x) = (10x - x2/1000 - 7000) + (4x) = 14x - x2/1000
where the cost function, C(x), equals 7000 plus 4x.
We must take the derivative of the profit function with regard to x and evaluate it at x = 3000 in order to determine the marginal profit:
P'(3000) = 10 - 3/5 = 9.4
Because the cost equation is c(x)=7000+4x, the marginal profit at a production level of 3000 is $9.4 per unit.
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Question Which is closest to the surface area of the figure below? 1463.8 m squared 578.1 m squared 923.2 m squared 3692.6 m2
The closest option to the cone area is 923.2 m².
What is a cone?A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.
To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:
A = [tex]\pi[/tex]r² + [tex]\pi[/tex]rℓ
where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.
First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.
h² = ℓ² - r²
h² = 19.3² - 14²
h ≈ 11.48 feet
Now we can compute the surface.
A = [tex]\pi[/tex](14)² + [tex]\pi[/tex](14)(19.3)
A ≈ 923.2 square feet
So the closest option to the cone area is 923.2 m².
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I think of a number, treble it and take 6 from my answer.
If the result is 18, find the number.
Answer:
number is 8
Step-by-step explanation:
let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so
3n - 6 = 18 ( add 6 to both sides )
3n = 24 ( divide both sides by 3 )
n = 8
that is the number thought of is 8
Consider an annuity-immediate with monthly payments for twenty years. The
payments are level in the course of each year, then increase by 2% for the next year. Find the present value of this annuity if the initial payment is $1,000 and
i=4%
The present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To solve this problem, we need to first find the monthly interest rate since the payments are made monthly. The monthly interest rate can be found by dividing the annual interest rate by 12:
i = 4% / 12 = 0.3333% per month
Next, we need to find the present value of the annuity. We can use the formula for the present value of an annuity-immediate:
[tex]PV = P * (1 - (1 + i)^{-n}) / i[/tex]
where PV is the present value, P is the monthly payment, i is the monthly interest rate, and n is the number of payments.
The first year, the payments are level, so we can use the formula with n = 12 to find the present value of the payments for the first year:
[tex]PV1 = 1000 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$11,887.87[/tex]
For the second year, the payments increase by 2%, so the monthly payment for the second year will be:
P2 = 1000 * 1.02 = $1,020
We can then use the formula again with n = 12 to find the present value of the payments for the second year:
[tex]PV2 = 1020 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$12,061.92[/tex]
We can continue this process for the remaining 18 years, increasing the payment by 2% each year. The total present value of the annuity is the sum of the present values of each year's payments:
PV = PV1 + PV2 + ... + PV20 = $189,468.24
Therefore, the present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.
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The question is present in the image
The correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, an expression, [tex]\sqrt[3]{24} \sqrt[4]{32}[/tex], we need to simplify it,
Factoring them,
24 = 2 x 2 x 2 x 3
32 = 2 x 2 x 2 x 2 x 2
Therefore,
[tex]\sqrt[3]{24} = 2\sqrt[3]{3}[/tex]
[tex]\sqrt[4]{32} = 2\sqrt[4]{2}[/tex]
[tex]\sqrt[3]{24} \sqrt[4]{32}[/tex] = [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
Hence, the correct option for the given expression is [tex]4\sqrt[3]{3}\sqrt[4]{2}[/tex]
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Please Help me!
Which of the following inequalities would represent the graph shown?
Answer:
f(x)>[tex]\sqrt{1-x}[/tex]
Step-by-step explanation:
because it is above the x axis it is >
Because it is -x is moves to the right
because it is a dotted line and not solid it is >
solver for y 2x-3y=3
Answer:
[tex] y = \dfrac{2}{3}x - 1 [/tex]
Step-by-step explanation:
[tex] 2x - 3y = 3 [/tex]
Subtract 2x from both sides.
[tex] -3y = -2x + 3 [/tex]
Divide both sides by -3.
[tex] y = \dfrac{-2}{-3}x + \dfrac{3}{-3} [/tex]
[tex] y = \dfrac{2}{3}x - 1 [/tex]
I need help with this please
What is the value of w? W+3/4 =w-2/2
As a result, 7 is the number of w that solves the problem.
What do the denominators mean?In mathematics, a denominator is the lowest integer in a proportion that indicates how many equal portions are split into a whole. It is a fraction's division. In this case, the fraction is 4, so there are four components overall.
To solve for w in the equation (W+3)/4 = (W-2)/2, we can start by cross-multiplying to eliminate the denominators:
2(W+3) = 4(W-2)
Expanding the brackets:
2W + 6 = 4W - 8
Simplifying:
2W = 14
W = 7
Therefore, the value of w that satisfies the equation is 7.
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Hi! I will give brainliest for anyone who answers this correctly. Thank you so much!
Tanisha read 4 books in 5 months If she reads at a constant rate how many books did she read each month give your answer as a whole number or a fraction in the simplest form. Help!!!!
Answer:
She read 4/5 of a book per month
Step-by-step explanation:
4/5= 4/5per month
Step-by-step explanation:
To find out how many books Tanisha read each month, we can use the formula:
books read per month = total number of books ÷ total number of months
Using the information given in the problem, we know that Tanisha read 4 books in 5 months. So we can plug those values into the formula:
books read per month = 4 ÷ 5
Simplifying the fraction by dividing the numerator and denominator by their greatest common factor, which is 1, we get:
books read per month = 4/5
Therefore, Tanisha read 4/5 of a book per month, or equivalently, 0.8 books per month.
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2 people are going to equally share 5 kg of chocolate. How many kilograms of chocolate should each person get?
Thabo is x years old and Lizzie is y years old. Write down algebraic expression for: Thabo's age in 6 year's time
The algebraic expression for Thabo is, Thabo's age in 6 years' time is x + 6.
What are the types of algebraic expression?There are three primary categories of algebraic expressions, including:
Numeral Expression. Binary Expression. Expression of a Polynomial
Monomial Expression: A monomial is an algebraic expression that only has one term.
Monomial expressions include 3x4, 3xy, 3x, 8y, etc. as examples.
A binomial expression is an algebraic expression with two terms that are opposite each other.
Binomial examples are 5xy + 8; xyz + x3; etc.
Polynomial Expression: In general, a polynomial expression is one that has several terms with non-negative integral exponents of a variable.
Given that, Thabo is x years old and Lizzie is y years old.
In 6 years, Thabo's age will be:
x + 6
Hence, Thabo's age in 6 years' time is x + 6.
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In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 214 answered "none," 280 said "one," 373 said "two," 153 said "three," and 53 responded with four or more. A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
Question content area bottom
Part 1
P(four or more cell phones)= enter your response here
(Round to three decimal places as needed.)
Based on the information, it can be inferred that the probability that a person has four or more cell phones in their home is 0.0494
How to find the probability that a person has four or more cell phones in their home?To find the probability that a person has four or more cell phones in their home, we must carry out the following mathematical procedure.
We must find the total number of people surveyed and the percentage that each group represents:
214 + 280 + 373 + 153 + 53 = 1,0731,073 = 100%214 = ?214 * 100% / 1,073 = 19.94%1,073 = 100%280 = %?280 * 100 / 1,073 = 26.09%1,073 = 100%373 = %?373 * 100 / 1,073 = 34.76%1,073 = 100%153 = %?153 * 100 / 1,073 = 14.25%1,073 = 100%53 = %?53 * 100 / 1,073 = 4.93%Now we must establish the probability. For this we must carry out the following mathematical procedure:
100% = 14.94% = ?4.94 * 1 / 100 = 0.0494According to the above, the probability that someone answers that four or more cell phones are used in her house is 0.0494.
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At a scouts' camp, there is sufficient food to last 72 scouts for 6 days. If 18 scouts do not turn up for the camp, how much longer can the food last for the other scouts?
The food will last the other scouts for 8 days
How to calculate the number of days the food will last?At a scout's camp, the food will last 72 scouts for 6 days
The first step is to multiply both values(the number of scouts and the number of days spent in the camp)
= 72 × 6
= 432
The number of scouts at the camp can be calculated by subtracting the number of scouts present from the number of days the scouts spent at the camp
= 72-18
= 54
The amount of food left can be calculated as follows
= 432/54
= 8
Hence the food will last for 8 days
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29 cents using 5 coins
Answer:
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro cents.
20 + 5 + 2 and two 1 cents will make 29 Euro c
Step-by-step explanation:
Answer: A quarter and 4 pennies
Step-by-step explanation:
25+4=29
What is the meaning of "that adds no new term"?
This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.
What is product?Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.
An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.
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Which Function is the inverse of the exponential function y= (3/2)^x ?
Step-by-step explanation:
To find the inverse of the exponential function y = (3/2)^x, we need to interchange the roles of x and y, and then solve for y.
So, starting with y = (3/2)^x, we can write:
x = (3/2)^y
To solve for y, we can take the logarithm of both sides with base 3/2:
log(3/2) x = y
Therefore, the inverse of the exponential function y = (3/2)^x is:
y = log(3/2) x
or in exponential form:
y = (log base 3/2) x
This function is the logarithmic function with base 3/2.