Answer: x=3
Step-by-step explanation:
[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]
Divide both parts of the equation by 4:
[tex]x=3[/tex]
The perimeter of a rectangle 60 and the width is 14, what is the length of the rectangle.
The required length is 16 units in the given rectangle.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
The perimeter of a rectangle = 2(L+W)
Where W is the width of the rectangle and L is the length of the rectangle
We have been given that the perimeter of a rectangle is 60 and the width is 14
To determine the length of the given rectangle.
P = 2(L+W)
Here P = 60, and W = 14
60 = 2(L + 14)
60/2 = L + 14
30 - 14 = L
L = 16
Thus, the required length is 16 units in the given rectangle.
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14. Which of the following is a mixed number?
Α. 2.3
B.5%
C.2%2
D.25
Answer:
A. 2.3
Step-by-step explanation:
because it become 23/10 when you turn it into a fraction
Jada has $260 to spend on flowers for school celebration. She decides that the only flower that she wants to buy are roses and carnations. Roses cost $1.50 each and carnations cost $0.65 each. Jada buys enough roses so that each of the 75 people attending the event can take home at least one rose. Let x be the number of roses and y be the number of carnations.
a. Write an inequity to represent the constant “that every person takes home at least one rose”
b. Write an inequality to represent the cost constraints?
R ≥75 will be the inequality to symbolize the need that each individual bring home at least one rose, and for the cost requirement, it will be, 1.45R + 0.65C ≤ 200.
What is inequality?
A connection that compares two numbers or other mathematical expressions unequally is known as an inequality in mathematics. Most frequently applied when comparing two numbers on the number line that differ in size.
Given:
Jada has $200 she can use to buy flowers. Each carnation costs $0.65 and a rose costs $1.45, so 75 guests may leave with at least one rose.
Jada has a total of $200.
Let R be the number of roses Jada bought.
There will be 75 persons in all present at the event.
As a result, the cost of R roses at $1.45 each is 1.45R.
Combined with roses C: Jada bought carnations.
Currently, each carnation costs $0.65.
Cost of C carnations at $0.65 per flower, then, equals 0.65C.
Inequality will serve as a restraint that requires everyone to bring home at least one rose,
[tex]R \geq 75[/tex]
There will be inequality that represents the cost limitation.
[tex]1.45R + 0.65C \leq 200[/tex]
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For Questions 1-4: Evaluate the expression
7x+8xy-72y
O 366
O 376
O-366
O-376
when x=-2 and y=4
Step-by-step explanation:
7x+8xy-72y
Since x=-2 and y=4
Then u just input it
7(-2)+8(-2)(4)-72(4)
-14-64-288
-366
When solving a system of equation Jared found?
Nicole and Jared are both accurate. To generate an equation with just one variable, you can solve for either variable and then use the equivalent expression.
In the given question, when solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation.
Nicole found x = y - 10 for the same equation and substituted y - 10 for x in the other equation.
We have to check who is correct.
Nicole and Jared are both accurate. To generate an equation with just one variable, you can solve for either variable and then use the equivalent expression. You can then resolve. In contrast to Nicole, who would have produced a one-variable equation that can be used to solve for y, Jared would have produced an equation with just one variable that can be used to get the value of x.
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The right question is:
When solving a system of equations, Jared found y = x + 10 for one equation and substituted x + 10 for y in the other equation. Nicole found x = y - 10 for the same equation and substituted y - 10 for x in the other equation. Who is correct? Explain.
Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
The number of tickets that will be sold is 5,560.
What is division?
A division is one of the fundamental mathematical operations that divides a larger number into smaller groups with the same number of components. How many total groups will be established, for instance, if 20 students need to be separated into groups of five for a sporting event? The division operation makes it simple to tackle such issues. Divide 20 by 5 in this case. 20 x 5 = 4 will be the outcome. There will therefore be 4 groups with 5 students each. By multiplying 4 by 5 and receiving the result 20, you may confirm this value.
Ticket sales for Six Flags White Water totaled $94,520 this summer.
Tickets for the water park cost $17 each.
The number of tickets that will be sold is = $94,520/17 = 5,560.
Hence the number of tickets that will be sold is 5,560.
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Solve this system using the substitution method.
-2x – y = -7
x + 7y = 10
Solve using the substitution method and be sure to show all of your work.
Using the substitution method equation form is x is 3 and y is1
What is substitution method?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies.Finding the value of any variable from one equation in terms of another variable is the first step in the substitution method. For instance, if there are two equations,-2x – y = -7 and x + 7y = 10, Applying the replacement approach begins with this.One of the equations' initial variable should be solved for, and the answer should be inserted into the other equation.Form of Point: (3 , 1 )
Equation Form: x = 3 and y =1
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Which of the following can be a representation of a function?
All of the above can be a representation of a function:
A graph can be used to visualize a function.A table can be used to show input and output values.An equation can be used to express the relationships between the inputs and the outputs.Which of the following can be a representation of a function?Option D. All of the aboveA function can be represented in a variety of ways, such as:
A graph is a useful tool for visualizing the relationship between inputs and outputs of a function. A table can be used to represent the inputs and outputs of a function.An equation can be used to express the relationship between the inputs and outputs.All of these methods are valid representations of a function and can be used to explore and better understand the function.
Since the question is not complete, here's the full task:Which of the following can be a representation of a function?
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Suppose that you and a friend are playing cards and you decide to make a friendly wager. The bet is that you will draw two cards without replacement from a standard deck. If both cards are diamonds, your friend will pay you $615. Otherwise, you have to pay your friend $37.
Step 2 of 2 :
If this same bet is made 621 times, how much would you expect to win or lose? Round your answer to two decimal places. Losses must be expressed as negative values.
If this same bet is made 621 times,then we expect to lose of $4514670
Probability
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
The bet is done 621 times then expected value is that we may have a loss of $4514670.if the bet is that is heart comes we will get $615 and lose $37 if not comes.
$615 if hearts come and lose $37 when not comes and bet is made 621 times. Calculate the expected win after 621 times.
There are 578 hearts in the standard deck of cards.
Probability is the chance of happening an event among all the events possible. The formula of calculating probability is as under:
Probability= number of items/ total number of items.
When two cards are chosen at random without replacement then the probability of getting two hearts is 578/52*577/51
=333,506/2652
=125.75
When two cards are chosen at random without replacement then the probability of not getting two hearts is 1-125.75
=124.75
When bet is made only 1 time expected value will be 125.75*615-124.75*37
=77,336.25 - 4,615.75
=-72720.5 means we are expecting to lose $2.05.
When bet is made 762 times then the expected value will be -72720*621= 4514670.
Then the expected value when bet is made 621 times is that we will lose $4514670 .
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1 Apply Ana is bowling. She pays $4 per game and $7 to rent shoes. After three games, each additional game is free. Is the total cost to bowl a function of the number of games played?
Answer:
game is free. Is the total cost to bowl a function of the
Step-by-step explanation:
let t be a binary search tree with n nodes. when t is linear the search algorithm makes key comparisons in the unsuccessful case
Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes n key comparisons, in unsuccessful case.
The BST (Binary Search Tree) is a tree where all nodes on the left and right sides of a given node are larger and less than each other.
The nodes of the BST are not kept in a continuous location because it is a non-linear data structure. The element is absent from the list in the best-case scenario, making it a worst-case scenario.
The worst-case temporal complexity for linear structures is O. (n).
In the worst scenario, there will be n key comparisons.
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The right question is:
Let T be a binary search tree with n nodes, in which n > 0. When I is linear, the search algorithm makes.......................... key comparisons, in unsuccessful case.
Compute the surface integral ∫ ∫S F⋅dS, where F = , over the plane
33x−19y+z=1,0≤x,y≤1, oriented by the upward-pointing normal.
The surface area is 131 square units.
What is Surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies
An upward point normal to the plane 33x−19y+z=1,0≤x,y≤1 is is
N=<33,−19,1>
Therefore F⋅N=33y−19z+x
Since the plane is defined by the equation z=1+19y-33x
the dot product becomes 33x−(33y−19z+x)+x=628x-328y-19
The limits of integration are given as 0≤x≤1, 0≤y≤1
Therefore the surface integral becomes
∫ ∫S F⋅dS= [tex]\int\limits^1_0 \int\limits^1_0{(628x-328y-19)dy} \, dx[/tex]
=[tex]\int\limits^1_0{(628x-183)} \, dx[/tex]
=314x²-183x|₀¹
=131
Hence, the surface area is 131 square units.
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Suppose the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi ), for i =1, . . . , n, is 1. Which of the following statements do you think would be INCORRECT? Evaluate each expression and give reasons
(a) Ëεi =Yi âËYi =0, for all i =1, . . . , n.
(b) Mean Squared Error =0.
(c) The coefficient of determination R^2 =1.
(d) nâ i=1 (Yi âYbar)^2 = nâ i=1 (ËYicap âYbar ^)2
(e) SE(Ëμ(x))=1.
Option (e) SE(u(x)) = 1 is incorrect about the sample correlation coefficient between two random variables X and Y based on a set of bi-variate points (X i , Yi )
The examination of the relationship between two variables is possible using bivariate analysis, which also has many real-world applications. It seeks to determine whether there is a link between the variables and how strong it is.
You can examine an association or causality hypothesis using bivariate analysis. It also aids in the prediction of dependent variable values based on changes in an independent variable.
The correlation coefficient (R) is a numerical value that ranges from -1 to 1. It reveals the strength of the linear relationship between the two specified variables.
The coefficient is referred to as Pearson's correlation coefficient when used to describe a linear regression.
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Please help!!! What is the slope intercept equation for this line
Answer:
y = - [tex]\frac{1}{4}[/tex] x - 1
Step-by-step explanation:
y = mx + b
Slope:
The m is the slope in the equation. Look at the two points given. If you start at the point on the left, you go down 1 and 4 to the right. 1/4
Y-intercept:
The y intercept is the b. It is where the line crosses the y axis. It crosses at -1
Answer:
y = - (1/4)x - 1----------------------------------------
Slope- intercept form:
y = mx + b, where m- slope, b- y-interceptUse two points on the graph:
(0, - 1) and (4, - 2)The first point is a y-intercept, b = - 1
Find the slope:
m = (- 2 - (-1)) / (4 - 0) = - 1/4The line is:
y = - (1/4)x - 1Find the third derivative of the function y=6x-x2/x2
As Mercury revolves around the sun, it travels at a speed of approximately 30 miles per second. Convert this speed to kilometers per second. At this speed, how many kilometers will Mercury travel in 15 seconds? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Therefore , 48 kilometers per second is the speed of Mercury as it orbits the Sun. Mercury's distance from Earth is 96 kilometers in 2 seconds.
What are speed and an example?An object's speed can be determined by calculating the distance it covers in a given amount of time. For instance, an automobile is moving at 70 miles per hour if it covers 70 miles in an hour (miles per hour).
Here,
The speed of Mercury as it orbits the Sun is 30 miles per second.
In kilometers/second, Mercury's rate of rotation around the Sun
= 30 1.6 kilometers per second
= 48 kilometers/second
Mercury will move right now in 2 seconds.
=> equals 48 + 2 kilometers
=> 96 kilometers.
Therefore , 48 kilometers per second is the speed of Mercury as it orbits the Sun. Mercury's distance from Earth is 96 kilometers in 2 seconds.
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a landscape architect wishes to enclose a rectangular garden on one side by a brick wall costing $40/ft and on the other three sides by a metal fence costing $20/ft. if the area of the garden is 142 square feet, find the dimensions of the garden that minimize the cost.
The dimensions of the rectangular garden which minimize the cost is equal to 9.6ft and 14.6ft respectively.
As given in the question,
Cost of brick wall is equal to $40/ft
Cost of metal fencing is equal to $20/ft
Let 'x' and 'y' are the dimensions of the rectangular garden
Area of the rectangular garden = 142 square feet
⇒ 142 = xy
⇒x = 142/y
Costing of four side fencing 'C' = 40x + 20x + 20y + 20y
⇒ C = 60x + 40y
⇒C = 60(142/y) + 40y
⇒C = 8520/y + 40y
Differentiate with respect to y
dC/dy = -8520/ y² + 40
Put dC/dy = 0
-8520/ y² + 40 = 0
⇒y² = 8520/40
⇒y = √213
⇒ y= 14.6 ft
⇒ x= 142/14.6
= 9.7 ft
Therefore, the dimensions of the rectangular garden with the given area which minimize the cost is equal to 14.6ft and 9.7ft.
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Write the equation for a vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full
minor x-axis length of 4 units.
The equation of the verticallly-oriented ellipse is x²/4 + y²/25 = 1
What is the equation of a vertically-oriented ellipse?The equation of a vertically-oriented ellipse centered at the origin with major axis y axis is given by
x²/b² + y²/a² = 1 where a > b
How to find the equation of the verticallly-oriented elipse centerd at the origin?Given that the vertically-oriented ellipse centered at (0,0) with a full major y-axis length of 10 units and a full minor x-axis length of 4 units.
We have that the length of major axis 2a = 10
⇒ a = 10/2
⇒ a = 5
Also, the length of minor axis 2b = 4
⇒ a = 4/2
⇒ a = 2
So, given the equation of the vertically-oriented ellipse,
x²/b² + y²/a² = 1 where a > b
Substituting the values of the variables into the equation, we have that
x²/b² + y²/a² = 1 where a > b
x²/2² + y²/5² = 1
x²/4 + y²/25 = 1
So, the equation is x²/4 + y²/25 = 1
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Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in gallons) in its tank. When graphed, the function gives a line
with a slope of 5.9. See the figure below.
With 48 gallons of fuel in its tank, the airplane has a weight of 2383.2 pounds. What is the weight of the plane with 77 gallons of fuel in its tank?
Airplane
weight
(in pounds)
2383.2
48
Amount of fuel
(in gallons)
pounds
48
Answer:
To find the weight of the plane with 77 gallons of fuel in its tank, we can use the linear equation for the weight of the plane in terms of the amount of fuel in its tank. The equation has the form:Weight = m * Fuel + bWhere m is the slope of the line, which is 5.9, and b is the y-intercept, which is the weight of the plane when the amount of fuel is 0. We know that the weight of the plane with 48 gallons of fuel is 2383.2 pounds, so we can use this information to solve for b:2383.2 = 5.9 * 48 + b
b = 2383.2 - 5.9 * 48
b = 2383.2 - 280.8
b = 2102.4Now that we have the value of b, we can plug it back into the equation to find the weight of the plane with 77 gallons of fuel:Weight = 5.9 * 77 + 2102.4
Weight = 456.3 + 2102.4
Weight = 2558.7 poundsSo the weight of the plane with 77 gallons of fuel in its tank is 2558.7 pounds.
Step-by-step explanation:
Identify the perimeter and area of the figure.
50 cm; 42 cm2
50 cm; 54 cm2
34 cm; 54 cm2
34 cm; 42 cm2
Answer:
Perimeter 34 cm
Area 42 [tex]cm^{2}[/tex]
Step-by-step explanation:
Perimeter:
Perimeter is the measurement of the distance around the figure. I started on the far left of the rectangle and then went around counter clockwise.
3 + 3 + 3 + 5 + 3 + 3 (this is not labeled, but I see that the other sides is 3)
+3 + 5 + 3 + 3
8(3) + 2( 5) = 24 + 10 = 34
The perimeter is 34 cm
Area:
Area of the rectangle
a = l x w
a = 10(3) = 30
Area of the triangle
a = 1/2 (l x w)
a = 1/2(4 x 3) = 1/2(12) = 6
There are 2 triangles so the area of both is 12
Total area: 30 + 12 = 42
The area is 42 [tex]cm^{2}[/tex]
for which equation is 0 not a solution x 5 4 6 x 4 4 3 x 0 x 9 9
On solving the provided question we can say that the answer is third one , that equation is 3 x = 0.
What is quadratic equation?Any equation that can be written in standard form, with x denoting an unknown value and a, b, and c denoting known integers, is referred to as a quadratic equation in algebra. In general, it is assumed that a > 0; equations with a = 0 are thought to be degenerate since they become linear or even more basic.
Here,
thus ,the given equation :
x - 5 = 4
6 x + 4 = 4
3 x = 0
x + 9 = 9
Thus , the given equation 3 x = 0 have 0 as its solution.
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for any given flight, an airline tries to sell as many tickets as possible. suppose that on average, 10% of ticket holders fail to show up, all independent of one another. knowing this, an airline will sell more tickets than there are seats available, and hope that there is a sufficient number of ticket holders who do not show up to compensate for its overbooking. using the central limit theorem, determine n, the maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane. use the 1/2-value-correction (called de moivre-laplace approximation) in your calculation.
The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 324.
The maximum number of tickets an airline should sell on a flight with 300 seats so that it can be approximately 99% confident that all ticket holders who do show up will be able to board the plane is 326. This is calculated using the 1/2-value correction (de Moivre-Laplace Approximation). The 1/2-value correction assumes the normal distribution is symmetric, with the mean in the middle of the distribution. This means that the probability of being above the mean is equal to the probability of being below the mean. Since the airline wants to be 99% confident that all ticket holders who do show up will be able to board the plane, this means that the airline needs to sell enough tickets such that the probability of being above the mean (300 tickets sold) is 99%. Using the 1/2-value correction, the airline needs to sell 326 tickets to achieve this confidence level.
This is calculated as follows: P(x > 300) = 0.99 P(x < 300) = 0.01 Using the 1/2-value-correction:
P(x = 300 + 0.5) = 0.99
Therefore, x = 300 + 0.5=> x = 300.5 => x = 326
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Which of the following is √ 48 simplified?
Answer:
4√3
Step-by-step explanation:
√48
If we factor it out we will get
√4^2 ⋅ 3
Then we pull terms out from under the radical
4√3
So, the answer is 4√3
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Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.
Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude?
Both gyms charge the same monthly rate and the same membership fee.
Liam can conclude that the price and monthly rate of both the gyms are equal.
Given, Lian is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee.
Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75.
we have to mention that what Lian can conclude,
As, substituting the first equation in the second one Liam got the price which is same in both the gyms.
So, Liam can conclude that the price and monthly rate of both the gyms are equal.
Hence, Liam can conclude that the price and monthly rate of both the gyms are equal.
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Compare the square root of 18 and twenty three fifths using >, <, or =. twenty three fifths is less than the square root of 18 twenty three fifths is equal to the square root of 18 the square root of 18 is greater than twenty three fifths the square root of 18 is less than twenty three fifths
Comparing the square root of 18 and twenty three fifths using an inequality is ✓18 < 23/5.
How to illustrate the inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
The square root of 18 will be 4.25
23/5 will be 4.6
Therefore, we can see that 4.6 is greater than 4.25.
In this case, ✓18 is less than 23/5.
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determine whether the function represents exponential growth or decay calculator
From the given information, Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.
What is exponential decay?The process of decreasing a sum at a constant percentage rate over time is referred to in mathematics as exponential decay. It may be written as the formula y=a(1-b)x, where y represents the final amount and a, b, and x, respectively, represent the initial amount and the decay factor.
The formula for an exponential function is where b is a positive integer that is not equal to 1.
Whether a function is an exponential growth or a decay depends on the value of b. If b > 1 or if b< 1, an exponential function exhibits exponential growth and exponential decline, respectively.
given,
[tex]= > y = 4(\frac{5}{6} )^x[/tex]
[tex]= > b = \frac{5}{6} < 1[/tex]
Therefore, the function [tex]= > y = 4(\frac{5}{6} )^x[/tex] is an exponential decay.
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The integer X, Y and Z each are perfect squares X greater than y greater than z greater than zero if x, y, z from an AP the smallest possible value of X is
49 is the smallest possible value of x.
Given: x, y, and z are three perfect square numbers.
What is the least x that can be?
Currently, we have three numbers by the stipulation:
x > y > z > 0
and AP has these figures.
Let's now list every perfect square from 1 to 10 in the following order: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
As a result, we can observe that 25 is equal to the product of 1 plus 49.
The possible outcomes are 1, 25, and 49.
If x = 49 and z = 1, then
x + z / 2 = y
49 + 1 / 2 = y
y = 50 / 2
y = 25
Y is therefore 25 and X is 49.
As a result, 49 is the lowest value of x that can exist.
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Explain why 1/2 is not equivalent to 2/5.
Answer:
as you can see on the picture, they both have same rectangle
1st figure is i divide it by 2 and shade 1 to get 1/2
2nd figure is I divide it by 5 and shade 2 to get 2/5
if we use LCD:
1/2 will become 5/10
2/5 will become 4/10
Therefore, proved that 1/2 is not equivalent to 2/5, on the other hand, 1/2 is greater than 2/5CREDITS:heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Which of the following is true about the above arrow diagram? It does not define a function because 2 is not mapped to any element of B It properly defines a function but it is not a one-to-one function It properly defines a function but it is not a one-to-one correspondence It properly defines a function but it is not onto Which of the following functions is a one-to-one function?
f: Z - Z, where f(n) = n2 + 6 f: R → R, where f(x) = 5x + 3 f: Z - Z, where f(n) = In - 1 f: R - R, where f(x) = 4x2
The given functions we proved and solved.
(1) given mapping is not a function because element 1 in domain has two distinct images 2 and 3.
For the function we must have for every element of domain there must be unique image in co-domain.
It does not define a function......(option First)
(2) As we know mod function always returns with positive sign
Therefore domain and co domain are already given to be integers.
Range set will set of non-negative integers.
(3) Here we have from the graph
f(-2) and f(0)=1
The only map satisfies these two conditions is:
f(x) = x+1
(4) The second function f:R→R such that f(x)=2x+7 is the ony one-one function.
Because f(x)=f(y)
2x+7=2y+7
2x=2y
x=y
Hence f(x) is one one.
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PLEASE HELP! I'LL MARK YOU AS THE BRAINIEST AND I'LL GIVE YOU A LOT OF POINTS!
Answer:
B) -2x+y=8
Step-by-step explanation:
First I looked at the graph and found the y-intercept and slope.
Y-intercept = 8
I found that because the point was the on the y-axis line like (0,8)
To find the slope I identified the next point. From the Y-intercept (0,8), you have to go down 8 units. Then I saw the point go left 4 units which makes it negative.
Slope = -8/4, which is also -2
Slope Intercept Equation (y=mx+b) would be: y=-2x+8
Then I compared it to the options and that's what I got.
