1. To solve 3^(2x-1)=27, we first need to simplify 27 to power of 3: 27=3^3
3^(2x-1)=3^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
2x-1=3
Solving for x, we get:
2x=4
x=2
2. To solve 3^(x^2-3x)=81, we first need to simplify 81 to the power of 3: 81=3^4
3^(x^2-3x)=3^4
Next, we can use the property that if the bases are the same, the exponents must be equal:
x^2-3x=4
Solving for x, we can use the quadratic formula:
x=(-b±√(b^2-4ac))/(2a)
x=(-(-3)±√((-3)^2-4(1)(-4)))/(2(1))
x=(3±√(9+16))/2
x=(3±5)/2
x=4 or x=-1
3. To solve 4^(x+1)=64, we first need to simplify 64 to the power of 4: 64=4^3
4^(x+1)=4^3
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=3
Solving for x, we get:
x=2
4. To solve 4^(x+1)=1/64, we first need to simplify 1/64 to the power of 4: 1/64=4^(-3)
4^(x+1)=4^(-3)
Next, we can use the property that if the bases are the same, the exponents must be equal:
x+1=-3
Solving for x, we get:
x=-4
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1. IF HEIGHTS OF FEMALE COLLEGE STUDENTS ARE NORMALLY DISTRIBUTED WITH A MEAN OF 64 INCHES AND A STANDARD DEVIATION OF 10 INCHES, WHAT IS THE PROBABILITY OF RANDOMLY SELECTING A FEMALE COLLEGE STUDENT WITH A HEIGHT LESS THAN 63 INCHES.
2. WHAT IS THE PROBABILITY OF RANDOMLY SELECTING A FEMALE COLLEGE STUDENT WITH A HEIGHT BETWEEN 61 AND 69 INCHES?
3. WHAT IS THE PROBABILITY OF FINDING AN AVERAGE OF GREATER THAN 65 INCHES WITH A SAMPLE OF 35 FEMALE COLLEGE STUDENTS?
a)0.1587 (or 15.87%)
b)0.6827 (or 68.27%)
c)0.0228 (or 2.28%)
1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).
2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).
3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).
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RATIONAL EXPRESSIONS Solving a rational equation that simplifies to quadratic: Binomial... Solve for x 2-(5)/(x+7)=-(7)/((x-3)(x+7)) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". x
X = 7 & -7/2
First, use the distributive property to simplify the equation:
2 - 5/(x+7) = -7/(x-3)(x+7)
2(x-3)(x+7) - 5(x-3) = -7(x+7)
2x2 + 7x - 6x - 15 = -7x - 49
2x2 -13x - 49 = 0
This equation can be solved by factoring the binomial:
2x2 -13x - 49 = 0
2x(x-7) - 7(x-7) = 0
(2x-7)(x-7) = 0
Therefore, the solution for x is x = 7 and x = -7/2.
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The expression - 16x + 24x + 4.2 represents the height of a ball, in feet, × seconds after it is thrown. What does 4.2 represent in this context?
Answer:
4.2 represents the initial height of the ball.
Step-by-step explanation:
h(x) = -16x² + 24x + 4.2
At x = 0, h(0) = 4.2
4.2 represents the initial height of the ball.
Two cheeseburgers and one small order of fries contain a total of 1420 calories. Three cheeseburgers and two small orders of fries contain a total of 2290 calories. Find the caloric content of each item.
One cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Two cheeseburgers and one small order of fries contain a total of 1420 calories.
Three cheeseburgers and two small orders of fries contain a total of 2290 calories.
let the number of Calories in one cheeseburgers be x and in one fries be y.
So, the system of Equation is:
2x + y = 1420
3x + 2y= 2290
solving the above two equation
x= 550 and y= 320
So, one cheeseburgers have 550 Cal and on smalls Fries have 320 Cal.
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Use the Distributive
Property to express
24 + 36
Answer:
60
Step-by-step explanation:
24 + 36 = 60
You can use the Gold Digger for the distributive property! * Factor as if you want to find the Greatest Common Factor.
Answer this
………………..
The slope of the linear equation is; 0.5
The y-intercept of the Linear Equation is: 4.75
Yes the equation is proportional
What is the graph of the linear Equation?The equation we are given is expressed as;
y = ¹/₂x + 4³/₄
When x = 0,
y = ¹/₂(0) + 4³/₄
y = 4.75
When x = 1,
y = ¹/₂(1) + 4³/₄
y = 5.25
When x = 2,
y = ¹/₂(2) + 4³/₄
y = 5.75
When x = 3,
y = ¹/₂(3) + 4³/₄
y = 6.25
If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5
Thus, slope = 0.5
y-intercept = 4.75
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Function g is a transformation of f(x) = 2x. Compare the graphs of the functions. Select all that apply.
x= 1 2 3 4 5
g(x)= 1/8 1/4 1/2 1 2
In response to the query, we have that The two graphs are oriented and coordinates have the same form in common. The moment where the two graphs come together (1, 2).
what are coordinates?A coordinate system is a technique used in geometry to precisely locate points or other geometry objects on a manifold, also including Euclidean space, using one or more numbers or coordinates. A point or item on a two-dimensional sphere is located using a pair of numbers known as coordinates. The x and y positions are two numbers that describe a point's location on a 2D plane. a collection of integers that indicate exact locations. Typically, the figure has two numbers. The first number represents the front-to-back distance, while the second column represents the top-to-bottom distance. When there are 12 units below and 5 above, as in (12.5), this is an example.
f(1/x) = 2/(1/x) = 2x, where g(x) =
Hence, g(x) = f(1/x) is equivalent to f(x) = 2x.
The values of x and g(x) are as follows:
x= 1 2 3 4 5\sg(x)= 1/8 1/4 1/2 1 2
f(x) = 2x: (1, 2), (2, 4), (3, 6), (4, 8), (5, 10) (5, 10)
g(x) = f(1/x) = 2x: (1, 2), (1/2, 1), (1/3, 2/3), (1/4, 1/2), (1/5, 2/5)
The appropriate choices are thus:
A reflection of the graph of f(x) about the line y = x is the graph of g(x).
The two graphs are oriented and have the same form in common.
The moment where the two graphs come together (1, 2).
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In the equation T = 30 - 5h, the y-intercept is
and the coefficient is
Answer: The y-intercept is 30 and the coefficient is -5
Step-by-step explanation:
In the slope-intercept form (y = mx + b) b stands for your y-intercept, in this case, 30.
The coefficient is the number being multiplied by the variable, or in this case, the slope, or -5.
What are the coordinates of point D (3/4,3)
after it is reflected across the x-axis?
When a point is reflected across the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of the reflected point D, we simply change the sign of the y-coordinate of point D.
Given that the coordinates of point D are (3/4,3), its reflected point D' across the x-axis will have the coordinates (3/4, -3).
Therefore, the reflected point D' is located at the point (3/4, -3).
Coordinates are pairs of numbers used to identify the position of a point in a two-dimensional plane. In a Cartesian coordinate system, the two numbers represent the x-coordinate (the horizontal position) and the y-coordinate (the vertical position) of the point.
For example, the point (3, 5) has an x-coordinate of 3 and a y-coordinate of 5. This means that the point is located 3 units to the right of the origin (the point where the x- and y-axes intersect) and 5 units above the x-axis. Similarly, the point (-2, -1) has an x-coordinate of -2 and a y-coordinate of -1, which means that it is located 2 units to the left of the origin and 1 unit below the x-axis.
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The math coach is delivering boxes of books to classrooms. She has 495 books to deliver. Each box contains 15 books. She has already delivered 4 boxes. Write an equation, where b is the number of boxes of books, that the math coach still needs to deliver.
Answer:
The math coach has delivered 4 boxes of books, so the number of boxes she still needs to deliver is b. Each box contains 15 books, so the total number of books she still needs to deliver is 15b. She has 495 books to deliver in total. Therefore, we can write the equation:
15b = 495 - 4(15)
Simplifying the right-hand side:
15b = 495 - 60
15b = 435
Dividing both sides by 15:
b = 29
So the math coach still needs to deliver 29 boxes of books.
Which of the following expressions is equivalent to -2(-x^2-3)
A. 2x^2-6
B. 2x^2-3
C. 2x^2*3
D. 2x^2+6
Answer:
2(−x 2−3)
Simplify the expression
−2x 2−6
Factor the expression
−2(x 2+3)
Which rational number has a different value than the others?
A. 44%
B. 22/50
C. 0.44
D. 4/9
Two groups of hikers leave the same camp heading in opposite directions. The first group travels 2 miles north & 5 miles east. The second group travels 3 miles south and 7 miles west.
The distance between the two groups after the hikes is approximately 12.04 miles.
The Pythagorean Theorem: What is it?A right triangle's connection between its sides is described by the Pythagorean Theorem, a foundational idea in mathematics. It claims that the hypotenuse's square length, which is the side that faces the right angle, equals the sum of the squares of the lengths of the other two sides of any right triangle. The Pythagorean Theorem is frequently used to solve issues involving distance, velocity, and acceleration and has various applications in the disciplines of geometry, trigonometry, and physics.
The distance between the two groups serves as the hypotenuse of a right triangle, which is formed by the two pathways. The following formula can be used to determine the hypotenuse's length:
Distance = √((2+7)² + (5+3)²)
= √(9² + 8²)
= √(81 + 64)
= √(145)
≈ 12.04 miles
Therefore, the distance between the two groups after the hikes is approximately 12.04 miles.
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Solve the equation. Don't forget to first simplify each side of the equation, if possible. 2(2z-3)=3(z+3)
The solution to the equation is z = 15.
To solve the equation 2(2z-3)=3(z+3), we first need to simplify each side of the equation by distributing the numbers outside of the parentheses to the terms inside the parentheses.
On the left side of the equation, we have 2(2z-3). Distributing the 2 to the terms inside the parentheses gives us:
2(2z) - 2(3) = 4z - 6
On the right side of the equation, we have 3(z+3). Distributing the 3 to the terms inside the parentheses gives us:
3(z) + 3(3) = 3z + 9
Now we can rewrite the equation as:
4z - 6 = 3z + 9
Next, we want to get all of the z terms on one side of the equation and all of the constant terms on the other side. We can do this by subtracting 3z from both sides of the equation and adding 6 to both sides of the equation:
4z - 3z = 9 + 6
Simplifying gives us:
z = 15
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Which piecewise function represents the graph?
Answer:
A
Step-by-step explanation:
trust
An umbrella was sold for rupees 279 in the off season at a loos for 7% find original price of umbrella
Answer:
300
Step-by-step explanation:
x(100%-7%)=279
0.93x=279
x=300
PLEASE HELP
An insurance company monitors accidents at rock concerts.
When someone is injured while dancing in a mosh pit,
"moshing", the company collects information about the
victim. Some statistical data about the ages of those injured
is shown below..
N Mean
66 20.136
StDev Min Q1 Median Q3 Max
5.099 13 17
19
22 47
Using the data above, which of these ages is considered an
outlier?
22.0
19.0
29.5
25.5
The measure that is considered an outlier is the data-set is a measure of 29.5.
What is the interquartile range of a data-set?The interquartile range is calculated as the difference between the third quartile and the first quartile.
The values that are outliers are given as follows:
At least 1.5 IQR below Q1.At least 1.5 IQR above Q3.The quartiles for this problem are given as follows:
Q1 = 17, Q3 = 22.
Hence the IQR is of:
IQR = 22 - 17
IQR = 5.
Meaning that the outliers are given as follows:
Values that are at most 17 - 1.5 x 5 = 9.5.Values that are at least 22 + 1.5 x 5 = 29.5.More can be learned about interquartile range at brainly.com/question/12323764
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please help asap and show work
Answer:
(-3, -4)
Step-by-step explanation:
Rotating a point that has the coordinates (x,y) 180° about the origin in a clockwise or counterclockwise direction, produces a point that has the coordinates (−x,−y). Ari's error was that she rotated "N" by 90 degrees instead of 180 degrees, as the rule for a 90 degree rotation is (-y, x). Therefore, the correct coordinated for N' can only be (-3,-4)
Of the 34 cars in a parking lot, 20 are green, 8 are gold, and the rest are black. What are the odds against the next car leaving the lot being black?
A. 3:14
B. 3:28
C. 28:3
D. 14:3
This spinner has 6 equal sections. In simplest form, what are the odds in favor of spinning blue or green?
A. 1:2
B. 1:3
C. 3:1
D. 2:1
What are the odds against getting three tails when you flip three coins?
A. 1:1
B. 1:7
C. 1:8
D. 7:1
(You can do one answer if u want explaination would be helpful)
The odds against the next car leaving the lot being black = option(A) is correct option.
The odds against getting three tails when you flip three coins = option(B) is the correct option.
What is probability?
The potential of any random event's result is referred to as probability. To determine the likelihood that any event will occur is the definition of this phrase.
There 34 cars out of which 20 are green, 8 are gold and 6 are black.
So, The odds against the next car leaving the lot being black
= no. of black cars / no. of non black cars
= 6/28
=3/14 (A)
If three coins are flipped together,
the total number of outcomes will be = 2³ = 8
no. of outcomes getting three tails = 1
The odds against getting three tails when you flip three coins
= no. of outcomes getting three tails/ no. of outcomes not getting three tails
= 1/7 (option B)
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6. Construct a golden spiral that involves a golden rectangle with length 4 meters
1:1.618 (the golden ratio).
To construct a golden spiral that involves a golden rectangle with length 4 meters, first draw a 4 meter long line. Divide it into two segments, such that the longer segment has a ratio of 1:1.618 (the golden ratio) to the shorter segment.
Draw a right angle at the end of the shorter segment. This creates a square that has a side length of 4 meters. Draw an arc centered at the intersection of the two line segments with a radius equal to the shorter segment and connect the ends of the arc. This creates a golden rectangle with a length of 4 meters.
Draw a quarter circle at each corner of the golden rectangle and connect the endpoints. This creates a spiral, and it is a golden spiral if the ratio of the lengths of the two line segments is 1:1.618 (the golden ratio).
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Student Edition. Geometry. Volume 2 < 75 of 350---> 5. BLUEPRINTS Ezra is redrawing the blueprint shown of a stage he is planning to build for his band. By what percentage should he multiply the dimensions of the stage so that the dimensions of the image are the size of the original blueprint? What will be the perimeter of the updated blueprint? (Example 2) 10 units 4 units 8 units Long Description 10 units 2 units
Ezra should increase the stage's dimensions by the following factor in order to make the picture half the size of the original blueprint:
50%.
The modified blueprint will have a perimeter that is half that of the original layout.
What is a dilation?When the scale factor is multiplied by the coordinates of an image's vertices, the result is a dilatation, which alters the side lengths of a figure.
The scale factor of the dilation is supplied as follows because, for this issue, we want the updated stage's dimensions to be half those of the original stage.
k = 1/2.
Given that both the perimeter and the side lengths have the same unit, 50%, or half of the original stage's perimeter, will be represented by the updated stage's perimeter.
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select the number line that shows that two oppsite numbers have the sum of 0
Answer: I'd say A
Step-by-step explanation:
-1+1=0
an international company had 19700 employes in one country that is 22.9 percent of there employs, how many employies do they have in all
Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.
What formula is used to calculate a percentage?We must first divide the value by the whole sum, and then multiply the result by 100 to get the percentage.
Let's use algebra to solve the problem.
If 19,700 employees represent 22.9% of the company's total number of employees, we can write:
0.229 = 19,700 / Total number of employees
To find the total number of employees, we can isolate the variable on one side of the equation:
Total number of employees = 19,700 / 0.229
Using a calculator, we get:
Total number of employees = 86,026.2
Rounded to the nearest whole number, the international company has approximately 86,026.2 employees in total.
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50 points
dias older brother likes his hot chocolate made with 2 ounces of cocoa and 3 ounces of milk. Whose how chocolate is more chocolaty
Dina likes hers with 3 ounces of chocolate and 5 ounces of milk
Explains how u got the answer
Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.
How to define which is the more chocolaty recipe?The more chocolaty recipe is defined obtain the proportion of cocoa for each recipe.
The proportion of cocoa for each recipe is obtained dividing the amount of cocoa used by the sum of the amounts of cocoa and milk used.
Hence the proportion for Dina's older brother is calculated as follows:
2/(2 + 3) = 2/5 = 0.4 = 40% cocoa.
The proportion for Dina's is obtained as follows:
3/(3 + 5) = 3/8 = 0.375 = 37.5% cocoa.
40 > 37.5, hence Dina's older brother has a hot chocolate that is more chocolaty, as his recipe has a higher proportion of cocoa.
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help plsssssssssssssssssss
Answer: Third answer option, [tex]\sqrt{3} *\sqrt{12}[/tex]
Step-by-step explanation:
Both 3 and 9 are not irrational numbers, so the first option is incorrect.
The [tex]\sqrt{3}[/tex] is irrational, but 0 is not, so the second option is also incorrect.
The [tex]\sqrt{3}[/tex] and [tex]\sqrt{12}[/tex] are both irrational. Let us see if they result in a rational number when multiplied together;
[tex]\sqrt{3} *\sqrt{12} =\sqrt{3*12} =\sqrt{36} =6[/tex]
They do, so this answer option is correct.
Your favorite restaurant is at the intersection of Second Street and Washington Boulevard.
Second Street is on y =
-4
x + 4.
3
Washington Boulevard is on 7y = 3x -9. With the help of this map, can you figure out the
name of this eatery?
19-8
Answer:
To find the name of the restaurant, we need to find the intersection point of the two streets.
The equation of Second Street is y = (-4/3)x + 4/3.
The equation of Washington Boulevard is y = (3/7)x - 3/7.
To find the intersection point, we can set the two equations equal to each other:
(-4/3)x + 4/3 = (3/7)x - 3/7
Multiplying both sides by 21 (the least common multiple of 3 and 7) to eliminate fractions, we get:
-28x + 28 = 9x - 9
Bringing all the x terms to one side and all the constants to the other side, we get:
-37x = -37
Dividing both sides by -37, we get:
x = 1
Substituting this value of x into either equation, we can find y:
y = (-4/3)(1) + 4/3 = 0
Therefore, the intersection point of Second Street and Washington Boulevard is (1,0), which means the restaurant is located at that point.
Step-by-step explanation:
Evaluate each logarithm by using properties of logarithms and the following facts.
loga(x) = 3.1 loga(y) = 5.8 loga(z) = 1.1
(a) loga (xy)
(b) loga (x/z)
(c) loga (y7)
(d) loga (square root y)
Please explain how to figure these out. Thank you ! Any help is appreciated!
We can use the properties of logarithms to evaluate each expression. The properties of logarithms include:
1) loga (xy) = loga (x) + loga (y)
2) loga (x/z) = loga (x) - loga (z)
3) loga (x^p) = p loga (x)
4) loga (square root x) = (1/2) loga (x)
Using these properties, we can evaluate each expression as follows:
(a) loga (xy) = loga (x) + loga (y) = 3.1 + 5.8 = 8.9
(b) loga (x/z) = loga (x) - loga (z) = 3.1 - 1.1 = 2
(c) loga (y^7) = 7 loga (y) = 7 * 5.8 = 40.6
(d) loga (square root y) = (1/2) loga (y) = (1/2) * 5.8 = 2.9
Therefore, the answers are:
(a) loga (xy) = 8.9
(b) loga (x/z) = 2
(c) loga (y^7) = 40.6
(d) loga (square root y) = 2.9
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Graduate Management Admission Test (GMAT) is a computer adaptive test intended to assess certain analytical, writing, quantitative, verbal and reading skills in written English for use in admission to a graduate management program such as an MBA programme. GMAT scores are normally distributed with a mean of 550 and a standard deviation of 120. Suppose a random sample of 35 students is selected randomly. (a) Describe the shape of the sampling distribution of the sample means. State the theorem used and explain briefly. (b) Find the mean and the standard deviation of the sample means. (c) What is the probability that the average score of those 35 selected students is above 600? (d) A student, Ann, is randomly selected from the population, find the probability that her score is above 600?
The probability that Ann's score is above 600 is 1 - 0.6628 = 0.3372.
(a) The shape of the sampling distribution of the sample means will be approximately normal. This is because of the Central Limit Theorem, which states that the sampling distribution of the sample means will be approximately normal if the sample size is large enough, regardless of the shape of the population distribution. In this case, the sample size of 35 is large enough for the Central Limit Theorem to apply.
(b) The mean of the sampling distribution of the sample means will be equal to the mean of the population, which is 550. The standard deviation of the sampling distribution of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size, which is 120/√35 ≈ 20.28.
(c) To find the probability that the average score of the 35 selected students is above 600, we need to find the z-score for 600 using the mean and standard deviation of the sampling distribution of the sample means. The z-score is (600 - 550)/20.28 ≈ 2.47. Using a z-table, we can find the probability that the z-score is less than 2.47, which is 0.9932. Therefore, the probability that the average score of the 35 selected students is above 600 is 1 - 0.9932 = 0.0068.
(d) To find the probability that Ann's score is above 600, we need to find the z-score for 600 using the mean and standard deviation of the population. The z-score is (600 - 550)/120 ≈ 0.42. Using a z-table, we can find the probability that the z-score is less than 0.42, which is 0.6628.
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Hudson was making $9.00 per hour before his raise. He is now making $9.45 per hour. what is his increase pay ?
Answer:
$0.45
Step-by-step explanation:
Adina makes 53112 per year and is looking to find a new apartment rental in her city. She searched online and found an apartment for 1500 per month. The recommendation is to budget between 25% and 30% of your monthly income for rent. Can Adina afford this apartment based upon the recommended interval? Explain.
( i have to show my work )