Answer:
B. 2x-3
Step-by-step explanation:
14 and 21 have a common factor which is 7 so divide both by 7 to get 2x-3.
Answer:b
Step-by-step explanation: took the test
In a random sample of 8 customers, what is the probability that exactly 4 of them will use the Self-Checkout?
In the box below, give your answer correct to 3 significant figures. If you are correct, you will receive a CORRECT message here.
The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.
What is binomial probability?Binomial probability is the probability based on the binomial distribution.
The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.
The binomial distribution formula is:
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
P = binomial probability
x = number of times for a specific outcome within n trials
{ⁿ \ ₓ} = number of combinations
p = probability of success on a single trial
q = probability of failure on a single trial
n = number of trials
Random sample, n = 8
Specific outcome within n trials = 4
pˣ = 0.5⁴
= 0.0625
qⁿ = (1 - 0.5)⁸ ⁻ ⁴
= 0.5⁴
= 0.0625
Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ
= 8/4 x 0.0625 x 0.0625
= 2 x 0.0625 x 0.0625
= 0.0078125
= 0.008
Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.
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HELPPPPPPPPPPPPPPP!!!!!
f(1) = -1
Step-by-step explanation:Quadratic equations form the shape of a parabola, which looks like a U-shape.
Graph
To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.
Equation
We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.
f(1) = 1² - 2f(1) = -1This also shows that f(1) = -1.
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation.
Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot.
У = -16x^2 + 246x + 100
The rocket reaches a maximum height of 1045.6 feet.
How to find the maximum height of a parabola by quadratic formula
The height of the rocket under free fall is described by a parabola and parabolas are explained by second order polynomials, whose form are:
y = a · x² + b · x + c
Where:
a, b, c - Real coefficients.x - Time, in seconds.y - Height, in feet.The maximum height can be found by means of discriminant of the quadratic formula associated with following variant:
a · x² + b · x + (c - y) = 0
Discriminant
b² - 4 · a · (c - y) = 0
b² = 4 · a · (c - y)
b² / (4 · a) = c - y
y = c - b² / (4 · a)
If we know that a = - 16, b = 246 and c = 100, then the maximum height reached by the rocket is:
y = 100 - 246² / [4 · (- 16)]
y = 1045.563 ft
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solve the given differential equation by undetermined coefficients. y'' + 2y = −18x2e2x
The general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (-9x^2)e^(2x).
The given differential equation is y'' + 2y = −18x^2e^(2x)
To solve this equation by undetermined coefficients, we first find the characteristic equation of the homogeneous equation, which is r^2 + 2 = 0.
The solutions to this equation are r = i and r = -i. Therefore the general solution to the homogeneous equation is yh(x) = c1 cos(x) + c2 sin(x)
Now, we use the method of undetermined coefficients to guess the form of the particular solution. Since the non-homogeneous term is −18x^2e^(2x), we guess that the particular solution is of the form
yp = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x).
Substituting this into the differential equation, we get
y'' + 2y = (6Ax + 2B)e^(2x) + 2Cxe^(2x) = −18x^2e^(2x)
Equating the coefficients of the like terms, we get:
6A = 0, 2B = −18, and 2C = 0
Solving for A, B and C, we get A = 0, B = −9 and C = 0
Therefore, the general solution to the differential equation y'' + 2y = −18x^2e^(2x) by undetermined coefficients is y = (Ax^3 + Bx^2)e^(2x) + Cx^2e^(2x) = (-9x^2)e^(2x)
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Lucas is selling 4 pears for $5.45. How much will 5 pears
cost?
Answer:
6.8125
Step-by-step explanation:
An arithmetic sequence is defined by fn = 7 + 8(n – 1). What is the value of f1
Answer:
f(11) = 87
Step-by-step explanation:
substitute n = 11 into f(n) , that is
f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87
What is 249 rounded to the nearest 10?
Answer: 250
Step-by-step explanation:
249 is closer to 250 than 240
Answer:
Step-by-step explanation:
249 is rounded to closest to 250
A teacher gave her students two tests. If 45% of the students passed both tests and 60% passed the first test. What is the probability that a student who passed the first test also passed the second?
Answer: We can use the concept of conditional probability to find the probability that a student who passed the first test also passed the second. Conditional probability is the probability of an event occurring given that another event has already occurred.
The probability that a student who passed the first test also passed the second is the probability of both events occurring (passing both tests) divided by the probability of the first event occurring (passing the first test).
We can use the information provided to calculate this probability:
Probability of passing both tests = 0.45 (45%)
Probability of passing the first test = 0.60 (60%)
Probability of passing both tests given that the student passed the first test = (Probability of passing both tests) / (Probability of passing the first test) = 0.45 / 0.60 = 0.75
So the probability that a student who passed the first test also passed the second is 0.75 or 75%.
It means, if we know that a student passed the first test, there's a 75% chance that the student also passed the second test.
Step-by-step explanation:
Aunt Sue used 1/6 teaspoon of vanilla to make 2/12 containers of pudding. How much vanilla is in one container of pudding?
The amount of vanilla in one container of pudding is given as follows:
One teaspoon.
How to obtain the amount of vanilla?The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.
The rule of three is defined as follows:
1/6 teaspoon - 2/12 containers.
x teaspoon - 1 container.
The first line can be simplified as follows:
1/6 teaspoon - 1/6 containers.
(as 2/12 = 1/6).
Hence there is one teaspoon of vanilla in one container of pudding.
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16) Similar triangle 5
r
4
X
h
*) find y if h= 3
*) find X
find r
71
3
P
The values of the variables in the similar triangles are y = 2.25 units, x = 5 units and r = 3.75 units
How to find the variables in the similar triangles?Similar triangles are triangles that have the same shape, but possibly different size. Two triangles are similar if and only if their corresponding angles are congruent, that is, they have the same measure. When two triangles are similar, their corresponding side lengths are in proportion.
Since the triangles are similar. We write:
h/y = y/3
Since h = 3, we have:
3/4 = y/3
y = 9/4 = 2.25 units
x = √(4² + h²) (Pythagoras theorem)
x = √(4² + 3²) = 5 units
r = √(y² + 3²)
r = √(2.25² + 3²) = 3.75 units
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Can you please help me i want to know the steps to solve this problem i dont want the answer so i can learn to do this on my own
Answer:
Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so
1+(6-8)=?
X^5 = -5 complex numbers using square roots
Poopy man is my husband uwu
anyways ur answer is 3^x
help I can't do math :')
1.20C + 3 >= 13.50
Where C is the number of chores Janie does.
On the left side of the inequality, 1.20C represents the amount of money Janie earns from doing chores, and 3 represents the amount of money she already has. The inequality states that the sum of the money she earns from doing chores and the money she already has must be greater than or equal to the cost of the CD (13.50).
This inequality can be simplified:
1.20C >= 10.50
C >= 8.75
Thus, Janie could do at least 8.75 chores to have enough money to buy the CD, since she can do fractions of chores.
Answer:
3 + 1.2 c > 13.50
Step-by-step explanation:
First of all, let's write an equation that gives us the income Janie gets for doing chores. As she earns 1.20 (I will omit the $ symbol for simplicity) for each chore c she makes we can write income depending on the amount of chores as:
income(c) = 1.2 c
If she does 1 chore she gets 1.2, if she does 4 chores she gets 4.8 and so on for any c (obviously c is positive as she can do negative chores).
So, her total money will be the sum of what she earns for chores and the money she already has: 3.
money (c) = 3 + 1.2 c
If she does 2 chores she has 3+2.4=5.4 and so on for any c.
Now we need her money to be greater or equal to 13.50 in order to buy the CD. The inequality is:
money (c) > 13.50
3 + 1.2 c > 13.50
We can go further and solve it. First lets subtract 3 in both sides:
12 c > 10.50
Now, divide both sides by 1.2:
c > 10.50 / 1.2
c > 8.75
So, she needs at least 8.75 chores to earn enough money to buy the CD. As she can do fractions of chores the answer is 8.75 chores. Is she couldn't do fractions she would need at least 9 chores.
what is the midpoint between (-7,-9) and (-0.5,-3)
The midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)
The midpoint between two points in a Cartesian plane is the point that is equidistant from both points and is located exactly in the middle of the line segment connecting the two points. To find the midpoint, we need to average the x-coordinates and the y-coordinates of the two given points.
Given the points (-7,-9) and (-0.5,-3), the midpoint can be found by:
averaging the x-coordinates (-7 + -0.5) / 2 = -3.75
averaging the y-coordinates (-9 + -3) / 2 = -6
So, the midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)
Alternatively, the midpoint formula is:
(x1+x2)/2 , (y1+y2)/2
So for the given points,
(x1,y1)= (-7,-9) and (x2,y2)= (-0.5,-3)
Midpoint (x,y) = (-7+(-0.5))/2 ,(-9+(-3))/2
= (-3.75,-6)
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A diamond speculator used the line with equation
y = 5000x250 to estimate the price of diamond
rings.
5) What would the speculator predict fot he price of the
0.29-carat diamond ring?
6) What would the speculator predict fot he price of the
0.21 -carat diamond ring?
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
y = 5000x - 250
y = 5000 * 0.29 - 250
y = 1200
A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.
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(9.42x10^4)(6.45x10^2)
Simplify using a scientific calculator.
Write each answer in scientific notation.
Sone help me understand how to do this
60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (9.42×10⁴)(6.45×10²)
We have to find the value of the expression.
9.42×6.45×10²×10⁴
60.759×10²×10⁴
Bases are same then the powers will be added.
60.759×10⁶
Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).
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1/2(x-5)=9 what is the value of x
Answer:
23
Step-by-step explanation:
1/2-2.5=9
1/2x=9+2.5
x=11.5/0.5
x=23
Which table represents only values described by the relationship between t and w?
w = t + 11.2
The table of w = t + 11.2 is:
t w
0 11.2
1 12.2
2 13.2
3 14.2
4 15.2
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
w = t + 11.2
The table can be calculated as,
When t = 1, w = 1 + 11.2 = 12.2
When t = 2, w = 2 + 11.2 = 13.2
When t = 3, w = 3 + 11.2 = 14.2
When t = 4, w = 15.2
So on..
Thus,
t w
0 11.2
1 12.2
2 13.2
3 14.2
4 15.2
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For the following two numbers, find two factors of the first number such that their product is the first number and their sum is the second number.
36,13
The two factors of the first number 36 which their sum is equal to 13 are 4 and 9.
What is factor of a numberFactor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.
The first number 36 have the following factors:
1, 2, 3, 4, 6, 9, 12, 18, and 36.
the factors 4 and 9 will be the factors in question because;
4 × 9 = 36
4 + 9 = 13
Therefore, 4 and 9 are the two factors of 36 that their product is the first number 36 and their sum is the second number 13.
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Determine the distance between the points (-2,3) and (5,-3):
The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
What is the distance?The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.
This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.
So, we have the points:
(-2, 3) and (5, -3)
Distance formula: d=((x2 - x1)² + (y2 - y1)²)
Insert values and calculate as follows:
d=((5 - (-2))² + (-3 - 3)²)
d=((7)²+(-6)²)
d=√85
d=9.21
Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.
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Represent Multiplication of
Whole Numbers by Fractions
raw a visual model to find the product.
2x
ME Critique Reasoning Barbara picked 36 apples. She
needs to put of the apples in a basket. Barbara says she
will put 12 apples in the basket. Is Barbara correct? HELP MEE
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
what is fraction ?A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.
given
she is correct as Barbara picked 36 apples
in one time she put 12 apples in the basket
Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x
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Mr. Coupe and his friend have 2,798
paddle balls to split among 40 hoppers.
How many will be in each hopper?
MULTIPLICATION
Estimate:
Solve:
DIVISION
Answer:
To find out how many paddle balls will be in each hopper, you can divide the total number of paddle balls by the number of hoppers.
paddle balls ÷ hoppers = paddle balls per hopper
2798 ÷ 40 = 69.95
So there will be approximately 69.95 paddle balls in each hopper. Since it's not possible to put 0.95 of a paddleball in a hopper, you can round it to the nearest whole number. This means each hopper will have 70 paddleballs.
Step-by-step explanation:
What is the measure of each angle inside the figure (the value of x)?
(Hint-This equals 360° divided by the number of sides of the figure.)
Answer:
60
Step-by-step explanation:
360 degrees divided by 6 sides equal 60 degrees
Write a quadratic equation with solutions -3 and 4/7.
Which linear system could the graph represent?
Responses
A 4x + 4y = 4
x + y = 14x + 4y = 4 x + y = 1
B 2x − y = 4
x + 2y = −32x − y = 4 x + 2y = −3
C −x + y = 2
x + 2y = 2−x + y = 2 x + 2y = 2
D x + y = 2
2x + 2y = 8x + y = 2 2x + 2y = 8
Question 2
The system represented by the graph has how many solutions?
Responses
A 1
B 2
C 0
D infinitely many
The linear system could the graph represent is, x + y = 2 & 2x + 2y = 8
So, Option D is correct.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line for given two points is y-y₁ = y₂-y₁/x₂-x₁(x-x₁)
Given that,
The graph of linear system
first line intersects the x & y axes at (2,0) & (0,2) respectively
Similarly, second line intersects the x & y axes at (4,0) & (0,4) respectively
By using two point form of the line we can write equation for both the lines,
x + y = 2 _____ (1)
x + y = 4 _____ (2)
by multiplying 2 in equation (2)
2x + 2y = 8
Hence, The linear system is x + y = 2 & 2x + 2y = 8
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Find the length of the indicated side.
3/2X+6 =2/5x+9
The length of side AB is
If the equation be 3/2X+6 =2/5x+9 then the length of side AB is -15/11.
What is meant by equation?The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.
A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution, also known as the root of the equation, is the quantity for which the equation holds true. Even if the LHS and RHS are switched, an equation still holds true.
Let the equation be 3/2X + 6 = 2/5x + 9
simplifying the equation, we get
15x + 27 = 4x + 12
15x = 4x - 15
11x = -15
Divide both sides by 11, we get
[tex]$\frac{11 x}{11}=\frac{-15}{11}$$[/tex]
[tex]$x=-\frac{15}{11}$$[/tex]
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You deposit $2,000 in an account earning 3% interest compounded monthly.
a. How much will you have in the account in 20 years?
b. How much interest will you earn?
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]
[tex]A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}[/tex]
Show the relationship between the number of miles and the number of hours in the ratio 24 to 2
The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
What is the ratio?
A ratio is a mathematical comparison of two or more quantities. It is used to show the relationship between the sizes of different quantities or amounts. It is typically expressed as a ratio of two numbers, such as 24:2, with a colon separating the numbers.
The ratio of miles to hours is 24 to 2. This can also be written as 24:2 or 12:1. It means that for every 24 miles, 2 hours are required to travel that distance.
Hence, The ratio of miles to hours is 24 to 2, which can be written as 24:2 or 12:1.
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Which point on the number line represents the difference 2.6 - 1.2?
The answer is 1.4
What is the number line?In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.
Given here:
2.6-1.2=1.4
Hence, The answer is 1.4
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(4-347-12)-(8+7-27)
PLEASE HELPPPP
Answer:
=4-347-12-8-7+27
=-343
*Mark me brainliest -_- *_*
Answer: (4-347-12)-(8+7-27)= -343