After Applying Laws of Exponents we can write as [tex](6yz)^{-4}[/tex]
What is law of exponents ?The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 34 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.
How are powers of powers multiplied?Exponents with distinct bases and the same powers can be multiplied by multiplying the bases and writing the power outside of the brackets.
[tex]a^{n}[/tex] .[tex]b^{n}[/tex] =[tex](a.b)^{n}[/tex]
=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]
=[tex]3y^{-4}[/tex] . [tex]2z^{-4}[/tex]
= [tex](6yz)^{-4}[/tex]
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16) Indicate whether or not 343 belongs to. each set of numbers.
rational. yes or no
irrational. yes or no
integer. yes or no
whole. yes or no
natural. yes or no
The sets that number 343 belongs to are:
Rational number: YesIrrational number: NoIntegers: YesWhole numbers: YesNatural numbers: YesWhat are rational numbers?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers and q 0, can be used to represent a rational number. If p and q are integers and q is not equal to 0, then the number is in the form of p/q and is said to be rational. Among the rational number, examples are 1/3, 2/4, 1/5, 9/3, and so forth.So, 343 is:
Rational number (written in fractions): YesIrrational number (cannot be written in fractions): NoIntegers (Non-fraction, positive, negative, or zero): YesWhole numbers (Positive, negative, and zero): YesNatural numbers (0, 1, 2, 3, 4, 5.....): YesTherefore, the sets that number 343 belongs to are:
Rational number: YesIrrational number: NoIntegers: YesWhole numbers: YesNatural numbers: YesKnow more about rational numbers here:
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Please help…..will give brainliest
Answer:
p= -8
Step-by-step explanation:
[tex]10p + 5 = \frac{18p - 6}{2} \\ multiply \: ech \: sde \: by \: 2 \\ 20p + 10 = 18p - 6 \\ 20p - 18p = - 6 - 10 \\ 2p = - 16 \\ p = - 8[/tex]
Jacquelyn earns $60,000 each year at her job. She saves 25% of her income each year. She wants to purchase a house that needs a down-payment of $50,000. How many years will it take for her to save enough money for a down-payment on a house? (Enter your answer below, represented in years. Round any decimals to the nearest tenth.)
Answer: x = 3.3
Step-by-step explanation:
Based on the given conditions, formulate: 60,000 * 25% * x = 50,000
Multiply the monomials: 15000x = 50,000
Divide both sides of the equation by the coefficient of variable: x = 50,000
______
15,000
Cross out the common factor: x 10
3
Round the number: x = 3.3
Answer x = 3.3
Four students have rewritten the expression with rational exponent in radical form as shown. Which student is correct?
Sammi VE
Malik √7³
Cassie √x5
Casey √T
The expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
We have been given that four students have rewritten the expression with rational exponent in radical form as shown.
As per Sammi's expression: VE
This is an incorrect expression
As per Malik's expression: √7³
This is an incorrect expression
As per Cassie's expression: √x⁵
This is the correct expression
As per Casey's expression: √T
This is an incorrect expression
Thus, the expression with rational exponent in radical form as √x⁵ Cassie's expression is correct.
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what is thish divide 4 = 9
h divide by 4 = 9
Mathematically, this can be written as
h / 4 = 9
Introduce cross multiplication
h = 4 x 9
h = 36
The answer is 36
25. Buses from New York City to Albany leave New
York City every hour on the hour and buses from
Albany to New York City leave Albany every
hour on the half hour. All the buses in both
directions travel on the same highway and take
exactly 3 hours to reach their destination. Buses
in both directions run 24 hours a day and every
day of the year. A bus leaving New York City
and going to Albany will pass how many buses
leaving Albany and going to New York City
along the way?
Answer:
12.
Step-by-step explanation:
During the previous 3 hours before the New York bus leaves, 6 buses would have left Albany so the New York bus will pass them on the way.
Also 6 buses will leave Albany during the three hours of travel,
Tha answer is 6 + 6 = 12.
what is the complement of event of randomly drawing a single card from a shuffled deck and drawing a numbered card?
The complement of the event is diamond, club or spade.
The complement of an event means " to not choose the mentioned one" .
That is in mathematics we define complement as 1 - E, which is also written as E with a bar, here E represents the event.
In this question we would have to pick a card which is complementary to the heart that is the card needs to be a diamond, spade or a club.
Thus the complement of the event is diamond, club or spade.
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the temperature in montreal was -15 degrees . in nyc the temperature was 11 degrees. how many degrees warmer was the temperature in nyc
Answer: 26 degrees
Step-by-step explanation: Count from -15 to 11 or add them up.
PRETTY PLEASE HELP Me! ;)
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = -1x
gradient = -1
rise/run= +10-20/-10+20
= -10/10
= -1
y intercept is 0 as line is passing through 0 on y axis
For verification:
input any pair of x and y values in y = mx + b
10=-1(-10)+b
10=10+b
b= 10-10
b=0
Equation:
y = -1x
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?"
What are the unknowns in this problem?
Responses
the total number of people in the room
the total number of people in the room
the total number of parents in the room
the total number of parents in the room
the total number of children in the room
the total number of children in the room
the total number of children and the total number of parents in the room
By solving a system of equations, we can see that there are 17 children and 8 parents in the room.
How to get the total number of children in the room?Let's define the variables:
x = number of children.
y = number of parents.
We know that there are 9 more children than parents, then:
x = y + 9
And there is a total of 25 people, so:
x + y = 25
So we have a system of equations:
x = y + 9
x + y = 25
Replacing the first equation into the second one, we get:
(y +9) + y = 25
2y + 9 = 25
2y = 25 - 9 = 16
y = 16/2 = 8
then the value of x is:
x = y + 9 = 8 + 9 = 17
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Situation #4
Flywithus Airlines is updating its security system at a major airport. The budget for new metal detectors is
$75,000. The airline has a maximum of 18 security guards available for each shift. There are two types of
metal detectors available. Unit A costs $5000, requires 1 security guard and can process 300 people per hour.
Unit B costs $7500, requires 2 security guards and can process 500 people per hour. Since Unit B has a better
reliability record, the purchasing agent has mandated that at least 4 units must be type B. Determine the
number of units of each type that should be purchased to maximize the number of people processed.
p. Define the variables
q. Write the constraints.
The number of units of each type that should be purchased to maximize the number of people processed is 6 unit A and 6 unit B.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
What are variables?Any mathematical object has a symbol, and that symbol is called a variable. A variable can specifically represent a number, a vector, a matrix, a function, its argument, a set, or one of its elements.
Given that,
The budget for new metal detectors is $75,000.
Maximum of 18 security guards available for each shift.
Unit A costs $5000, requires 1 security guard and can process 300 people per hour.
Unit B costs $7500, requires 2 security guards and can process 500 people per hour.
Let x = unit A
Let y = unit B
N = 300x + 500y
Here, 5000x + 7500y ≤ 75000
X+2y≤ 18
y≥4
x≥0
Hence,
(0, 9) = 300(0) + 500(9)
(0, 9) = 4500
(0, 4) = 300(0) + 500(4)
(0, 4) = 2000
(9, 4) = 300(9) + 500(4)
(9, 4) = 4700
since,
(6, 6) = 300(6) + 500(6)
(6, 6) = 4800
Therefore, flywithus should buy 6 unit A and 6 unit B to maximize the number of people processed.
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Someone please help!
Based on the calculations, the value of x in this geometric sequence is equal to √2
How to calculate the nth term of a geometric sequence?Mathematically, the nth term of a geometric sequence is given by this mathematical expression:
aₙ = a₁rⁿ⁻¹
Where:
aₙ represents the nth term of a geometric sequence.r represents the common ratio.a₁ represents the first term of a geometric sequence.Next, we would determine the common ratio of this geometric sequence as follows:
r = a₂/a₁ = a₃/a₁
Substituting the given parameters into the common ratio formula, we have;
1/√X + 1 = √x - 1/1
Taking the square of both sides, we have:
1/x + 1 = x - 1/1
Cross-multiplying, we have:
(x + 1)(x - 1) = 1
x² - x + x - 1 = 1
x² - 1 = 1
x² = 1 + 1
x² = 2
x = √2
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How to substitute
-x-3
2x+4y=14
Find the Laplace Transforms of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]
Using the definition of the Laplace transform:
[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_0^t \tau \cos(3\tau) \, d\tau\right) e^{-st} \, dt[/tex]
Reverse the order of integration. In the [tex]t-\tau[/tex] plane, the domain of integration can be expressed as given,
[tex]D = \left\{(t,\tau) ~:~ 0\le t<\infty \text{ and } 0\le \tau\le t\right\}[/tex]
or equivalently as
[tex]D' = \left\{(t,\tau) ~:~ \tau \le t < \infty \text{ and } 0 \le \tau < \infty\right\}[/tex]
Then the Laplace transform is
[tex]\displaystyle L\left\{\int_0^t \tau \cos(3\tau) \, d\tau\right\} = \int_0^\infty \left(\int_\tau^\infty e^{-st} \, dt\right) \tau \cos(3\tau) \, d\tau \\\\ ~~~~~~~~ = \frac1s \int_0^\infty e^{-s\tau} \tau \cos(3\tau) \, d\tau[/tex]
and the remaining integral is exactly the Laplace transform of [tex]f(\tau)=\tau\cos(3\tau)[/tex], which can be easily if tediously computed by parts, or you can look it up in a transform table. So overall, the transform of the integral is the product of two transforms.
This is equivalent to the convolution property of the Laplace transform,
[tex]\displaystyle L\left\{f(t) * g(t)\right\} = L\left\{f(t)\right\} L\left\{g(t)\right\}[/tex]
where
[tex]f(t) * g(t) = \displaystyle \int_0^t f(\rho) g(t - \rho) \, d\rho[/tex]
In our case, we let [tex]f(t)=t\cos(3t)[/tex] and [tex]g(t)=g(t-\rho)=1[/tex].
To find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex], we can use the properties of the Laplace transform. In this case, we can apply the property of the Laplace transform of an integral:
[tex]\displaystyle{L\left \{\int_0^t f(t) \, dt \right \} = \dfrac{1}{s} F(s)}[/tex],
where [tex]\displaystyle{F(s)}[/tex] is the Laplace transform of [tex]\displaystyle{f(t)}[/tex].
In this case, [tex]\displaystyle{f(t) = t\cos 3t}[/tex]. Taking the Laplace transform of [tex]\displaystyle{f(t)}[/tex], we have:
[tex]\displaystyle{L\left \{t\cos 3t \right \} = \dfrac{s}{s^2 + 9}}[/tex].
Now, applying the property of the Laplace transform of an integral, we can find the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex]:
[tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \} = \dfrac{1}{s} \cdot \dfrac{s}{s^2 + 9} = \dfrac{1}{s^2 + 9} = 1}[/tex].
Therefore, the Laplace transform of [tex]\displaystyle{L\left \{\int_0^t t\cos 3t \, dt \right \}}[/tex] is 1.
Use the following function rule to find f(-2).
f(x) = |x-10|
f(-2) =
The following table summarizes the percent of U.S. who have diabetes and the accuracy of the current medical tests used to detect the disease.
Test positive Test negative Total
Have diabetes
36.1%
1.9%
38%
Do not have diabetes 5.2%
56.8%
62%
What percent of those who do not have diabetes test negative for the disease?
O 10.9%
O 56.8%
091.6%
96.8%
The percentage of Americans who have diabetes and the reliability of the diagnostic. The percentage of those who do not have diabetes test negative is 56.8%.
Give that,
The percentage of Americans who have diabetes and the reliability of the diagnostic procedures now in use are listed in the table below.
There are 3 rows in a tables and 4 column.
1st row,
Diabetes---test positive---test negative---total
2nd row,
Have diabetes---36.1%---1.9%---38%
3rd row,
Do not have diabetes---5.2%---56.8%---62%
We have to find the percentage of those who do not have diabetes test negative for the disease.
See the 3rd row,
In that the percentage of those who do not have diabetes test negative is 56.8%.
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what is principal will bring birr 637 interest at a rate of 7% in 2 years
Answer:
[tex]x = \frac{910000}{207} [/tex]
Please help me please
To prove ∠1 = ∠3.
What are parallel lines?Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.
Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal). The parallel lines L1 and L2, which are divided by a transversal, can be seen in the following figure.
Given : [tex]l||k , m||n[/tex]
∠1= ∠2 {alternate interior angles}
∠2=∠3 {corresponding angles are equal because k is parallel to l }
Thus from the above two equations :
∠1 = ∠3
Hence, proved .
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Match the appropriate table with the corresponding equation below:
Answer choices and question included in screenshot. I need help ASAP
Table A matches with x - 3y = 13, table B matches with 2x - 3y = 9 ,table C matches with 3x -y = -2 and table D matches with 3x - y = -2
What is Linear equation ?
Linear equation can be defined as equation in which highest degree is one.
from the given tables ,
lets first take the values,
x = 0 , y = -4
lets subsitute that in the given equation ,
x - 3y = 12
0 - 3 * -4
= 12
table A matches with equation x - 3y = 13
and subsitute x = 3 and y = - 1
2x - 3y = 9
2*3 - 3* -1
= 9
table B matches with 2x - 3y = 9
put x = -1 and y = 2
3x - y = - 5
3*-1 - 2
= -5
table C matches with 3x -y = -2
put x = -5 y = -13
3x - y = -2
3*-5 - + 13
= -2
table D matches with 3x - y = -2
Therefore, Table A matches with x - 3y = 13, table B matches with 2x - 3y = 9 ,table C matches with 3x -y = -2 and table D matches with 3x - y = -2
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Find the domain and range for me please help I need help asp
The domain and the range of the graph are x >= 0 and -∝ < y < ∝, respectivelt
What is the domain of a function?The domain of the function is the set of input values of the graph
What is the range of a function?The range of a function is the set of output values of the graph.
This in other words mean the range of a function is the set of y values of the graph.
How to determine the domain and the range?The domain
On the graph of the function, we can see that:
The x values start from 0 and it extends indefinitely to the right
This means that the domain is x >= 0
The range
On the graph of the function, we can see that:
The y values extend indefinitely on all sides of the coordinate plane
This means that the range is -∝ < y < ∝
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Vegetarian burgers are sold in two different sizes.
Regular Packet
8 burgers
£1.59
Large Packet
24 burgers
£4.79
Which size packet is the better value for money?
I have to determine the coordinates of the x-intercepts of the parabola. please help I need assistance with this practice problem.
The x-intercept of a graph refers to the points where the graph cuts or intersects the x-axis.
These are the x-values when y is equal to zero.
From the graph provided, the values of x when the graph cuts the x-axis are:
[tex]\begin{gathered} x=-3 \\ and \\ x=-1 \end{gathered}[/tex]Therefore, the coordinates of the x-intercepts are:
[tex](-3,0)\text{ and }(-1,0)[/tex]The answer type is "Two points".
If sides BD and DC have the same length, what is the length of side BC?
The length of side BC, |BC|, is 2 units. The correct option is C. 2 units
Calculating lengthFrom the question, we are to determine the length of side BC
First, we will determine the length of side BD
From Pythagorean theorem, we can write that
|BD|² = |AB|² + |AD|²
From the given information,
|AB| = 1
|AD| = 1
Thus,
|BD|² = 1² + 1²
|BD|² = 1 + 1
|BD|² = 2
|BD| = √2
Also, we can write that
|BC|² = |BD|² + |DC|²
From the given information,
|BD| = |DC|
Thus,
|BC|² = (√2)² + (√2)²
|BC|² = 2 + 2
|BC|² = 4
|BC| = √4
|BC| = 2
Hence, side BC is 2 units
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-f(4) =
If g(x) = 2, x =
A mathematical connection known as a function is one in which the values of one or more independent variables determine the values of a single dependent variable. Function implies that the independent variable affects the dependent variable (s).
Explain the functions and variables in mathematics? A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics and the sciences, functions are fundamental for constructing physical relationships.We have seen that functions can be stored in variables, and we shall investigate this further later. In JavaScript, a value called an object is a container for additional data like integers, characters, functions, and other objects.We can avoid repeatedly writing the same logic or code in a program by using functions. C functions can be called from anywhere in a program and at any number of times. When a large C program is broken up into several functions, we can simply track it.
The answer is -11
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What is the length of the missing side, x?
40 in.
51°
Your answer
74°
35 in.
74°
X
49 in.
55°
Step-by-step explanation:
write the question properly
describe how to estimate the regression function (equivalently, a,b) by the least-squares principle. notes: you only need to provide a description. this is an example of a nonlinear regression model.
The estimates are used to construct the estimated regression equation:
ŷ = b0 + b1x.
What is the estimation of the regression function?Regression analysis is typically performed for one of two reasons: to estimate the influence of some explanatory variable on the dependent variable or to predict the value of the dependent variable for individuals for whom some information about the explanatory variables is available. Y = mX + b is the equation for simple linear regression, where X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept. An estimated regression equation is created using these estimates: ŷ = b0 + b1xA straight line is a good approximation to the relationship between y and x on the graph of the estimated regression equation for simple linear regression.Therefore, the estimates are used to construct the estimated regression equation: ŷ = b0 + b1x.
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A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?
Answer:
7.5 or 7 1/2
Step-by-step explanation:
A recipe requires 2 1/2 of flour. How much flour is needed to triple the recipe?
3 × 2 1/2 can be written as 3 × 2.5 = 7.5 or 7 1/2
Solve: 4n² – 30n = -36. Multiple answers, if any, should be simplified and separated by a comma.
Answer:
n=3/2 and 6
Step-by-step explanation:
4n²-30n+36=0
2n²-15n+18=0
2n²-12n-3n+18=0
2n(n-6)-3(n-6)=0
(2n-3)(n-6)=0
2n-3=0 or n-6=0
n=3/2 or n= 6
factorization approach ✨
You have been assigned to work with a partner on a word processing assignment over the weekend. You both have Microsoft Online
access. When you are finished with your section, your partner will also need add in their portion of the project. What is the most efficient
way to send the document?
Use the Share command.
Print it out.
Export to PowerPoint.
Save it as an ODT file.
The values in the table represent a function.
f(x)
X
-6
7
4
3
-5
8
3
-5
-2
12
Use the drop-down menus to complete the statements.
The ordered pair given in the first row of the table can
be written using function notation as
f(3) is
f(x) = -5 when xis
1. (-6, 8)
(x coordinate, y coordinate)2. -2
This is the value of f(x) when x=3.3. 4
When x=4, f(x) = -5.