The fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) following from the laws of indices is; 8x³ y² / 7.
What is the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² )?It follows from the task content that the fully simplified form of the given expression 16x⁵y⁴ / ( 14x²y² ) is to be determined.
Since the given expression is; 16x⁵y⁴ / ( 14x²y² ).
As evident in the task content; same base terms are present in the numerator and denominator; we therefore have that;
The expression can be simplified as follows using the laws of indices as follows;
[tex] \frac{16 {x}^{5} {y}^{4} }{14 {x}^{2} {y}^{2} } [/tex]
It follows from the quotient of exponents law of indices; we have that;
[tex] \frac{8}{7} {x}^{5 - 2} {y}^{4 - 2} [/tex]
= 8x³ y² / 7
Therefore, the fully simplified form of the given expression using the laws of indices is; 8x³ y² / 7.
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A wire is first bent into the shape of a rectangle with width 5cm and length 16 cm . Then the wire is unbent and reshaped into a triangle. If each side of the triangle has equal length, what is this length?
Hello,
I hope you and your family are doing well!
To find the length of each side of the triangle, we can use the formula for the perimeter of a rectangle: perimeter = 2 * (width + length). In this case, the perimeter of the rectangle is 2 * (5cm + 16cm) = 42 cm. Since each side of the triangle has the same length, and the perimeter of the triangle is equal to the perimeter of the rectangle, the length of each side of the triangle is 42cm / 3 = 14 cm.
Therefore, the length of each side of the triangle is 14 cm.
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An observer whose eye level is 5 ft is observing the top of an object with a mirror on the
ground. The mirror is 3 feet from the observer and 12 feet from the object. Calculate the
height of the object.
The height of the object is 20 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
An observer whose eye level is 5 ft is observing the top of an object with a mirror on the ground.
The mirror is 3 feet from the observer and 12 feet from the object.
Using proportion
5/ 3= x/ 12
60= 3x
x = 20 feet
hence, the height of the object is 20 feet.
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Suppose that the functions g and h are defined for all real numbers x as follows.
g(x)=x-6
h(x)=4 x+3
By using the concept of function, it can be calculated that-
(h.g)(x) = 4x - 21
(h + g)(x) = 5x - 3
(h - g)(-1) = 6
What is a function?
A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.
There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.
Here,
a) The given functions are
g(x)= x - 6
h(x) = 4x + 3
(h.g)(x) = h(g(x)) = 4(x - 6) + 3 = 4x - 21
(h + g)(x) = h(x) + g(x) = 4x + 3 + x - 6 = 5x - 3
(h - g)(x) = h(x) - g(x) = 4x + 3 - x + 6 = 3x + 9
(h - g)(-1) = 3 [tex]\times[/tex] (-1) + 9 = 6
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Describe how the values of r, x, and y relate to each of sinø, cosø and tanø
the values of r, x, and y are related to the sine, cosine, and tangent of angle ø as:
sin ø = y / r
cos ø = x / r
tan ø = y / x
What is trigonometry?
Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
In a right triangle, the sides are typically labeled as follows:
The side opposite the angle ø is called the "opposite side" and is labeled "y".
The side adjacent to angle ø is called the "adjacent side" and is labeled "x".
The hypotenuse is the side opposite the right angle and is labeled "r".
The values of r, x, and y can be used to calculate the sine, cosine, and tangent of angle ø. These trigonometric functions are defined as follows:
Sine (sin ø): sin ø = y / r
Cosine (cos ø): cos ø = x / r
Tangent (tan ø): tan ø = y / x
Hence, the values of r, x, and y are related to the sine, cosine, and tangent of angle ø through the above equations.
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Cindy bought 7/8 yard of ribbion at the craft store. Jacob bought 4/5 the length of ribbon as Cindy. How many yards of ribbon did jacob buy?
If the lengths of two sides of a triangle are represented by 2x + 5 and 3x + 7 (in which x is positive), describe in terms of x the possible lengths of the third side whose
length is represented by y.
Answer:
x + 2 < y < 5x + 12
Step-by-step explanation:
given 2 sides of a triangle then the third side y is within the limits
difference of 2 sides < y < sum of 2 sides
3x + 7 - (2x + 5) < y < 3x + 7 + 2x + 5
3x + 7 - 2x - 5 < y < 5x + 12
x + 2 < y < 5x + 12
2. Determine the theoretical probability of rolling a two with one standard die. Write this probability in three equivalent forms: as a fraction, a decimal (rounded to three places), and a percentage (rounded to one decimal place).
The theoretical probability of rolling a two with one standard die in three equivalent form is 1/6, 0.167 and 16.7%
How to determine the theoretical probability?From the question, we have the following parameters that can be used in our computation:
The rolling of a standard die
In this case, we assume that the standard die is a fair die
i.e. the faces have equal chance of appearing
This means that the sample space of the die is
Sample space = {1. 2. 3. 4. 5. 6}
In this sample space, we have
Number of occurrence of 2 = 1
Number of items in the sample space = 6
The theoretical probability of 2 is then calculated as
Probability = Number of occurrence of 2/Number of items in the sample space
Substitute the known values in the above equation, so, we have the following representation
Probability = 1/6 --- in fraction
Evaluate the quotient
Probability = 0.167 -- in decimal
Express as percentage
Probability = 16.7%
Hence, the probability is 16.7%
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Solve the equation for w.
w divided by 1.1 minus 3.9 equals 10.5
6
7.26
13
15.84
W will be 15.84.
What is an equation?The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.
We know that w divided by 1.1 minus 3.9 equals 10.5
That will be W/1.1 - 3.9 = 10.5
W/1.1 = 10.5 + 3.9
W/1.1 = 14.4
W = 14.4* 1.1
W = 15.84
W will thus equal 15.84.
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Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.
A sample of 72 stocks traded on the NYSE that day showed that 29 went up.
You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of a = 0.02.
What is the test statistic for this sample?
Use p rounded to 4 decimal places. (Report answer accurate to 4
decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to 4 decimal places.)
p-value =
The p-value is either less than (or equal to) or
greater than?
This p-value leads to a decision to...
reject the null or accept the null or fail to reject the null?
As such, the final conclusion is that... (select a letter)
A) There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went
up is is more than 0.3.
B) There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that
went up is is more than 0.3.
C) There is sufficient evidence to support the claim that the proportion of stocks that went up is is more
than 0.3.
D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
The test statistic and the p-value of the research are respectively z = 1.9072 and p-value = 0.0283 and the conclusion is that; D) There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is more than 0.3.
How to find the p-value from the research?Let us first of all define the hypotheses;
Null Hypothesis; H₀: p ≤ 0.3
Alternative Hypothesis; Hₐ: p > 0.3
Sample proportion is;
p^ = 29/72 = 0.403
The formula for the test statistic is;
z = (p^ - p)/(√(p(1 - p)/n))
Plugging in the relevant values gives;
z = (0.403 - 0.3)/(√(0.3(1 - 0.3)/72))
z = 1.9072
From p-value from z-score calculator, we have that;
p-value = 0.0283
p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that There is not sufficient sample evidence to support the claim that the proportion of stocks that went up
is is more than 0.3.
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Mario makes 6 throw shots out of his first 10 attempts
Ok⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
Answer: 4
Step-by-step explanation: If you are trying to see how many Mario missed that would be 4
5 + w - 9 = 8
How do I solve this equation? Please explain step by step
Answer:
w=12
Step-by-step explanation:
w+5-9=8
w-4=8
w=12
Answer:
w = 12
Step-by-step explanation:
Subtract the numbers.
5 + w - 9 = 8
-4 + w = 8
Rearrange terms
-4 + w = 8
w - 4 = 8
Add 4 to both sides
w - 4 = 8
w - 4 + 4 = 8 + 4
Add
w - 4 + 4 = 8 + 4
w = 8 + 4
Add
w = 8 + 4
w = 12
Multiply by using the Distributive Property. (x2 + 3)(x − 4) =
The expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
What is distributive property?The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b) in the form of (ac+bc).
It is given that, the expression is (x² + 3)(x − 4)
The expression is simplified using the distributive property as,
=(x² + 3)(x − 4)
=x²(x − 4)+3(x − 4)
=x³-4x²+3x-12
Thus, the expression is obtained by simplifying it by the distributive Property is x³-4x²+3x-12.
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The multiplication of the term (x² + 3)(x - 4) using distributive property is x³ - 4x² + 3x - 12.
Distributive property explains to us how to solve expressions in the form of a(b + c).
After apply distributive property, this term converts as ab+ac
The given expression is,
(x² + 3)(x - 4)
Solve by using distributive property formula (a+b)(c+d)= a(c+d) + b(c+d),
x²(x - 4) + 3(x - 4)
Now further simplify by using formula a(b+c) = ab+ac,
x³ - 4x² + 3x - 12.
The required multiplication of the given terms is x³ - 4x² + 3x - 12.
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X
Y
If L=4, Y=30 and Z=14. Solve for X. (round to 2 decimal places)
L
N
Answer:
Y+Z/Z = X/L
X= (44/14)4 = 12.57(nearest 2 decimal
At the school fair, students used a scatter plot to compare the number of T-shirts sold
with the number of jars of jam sold. What can you conclude about the relationship
between the sales of the T-shirts and the jars of jam?
Answer: The jars of jam sales and the T-shirt sales have a positive correlation, but neither may cause the other.
Step-by-step explanation:
The correlation is a positive slope but selling T-Shirts and Jam shouldn't correlate to each other.
A rectangular solar panel has a length that is 11 inches shorter than 4 times it’s width. If the perimeter of the panel is 178 inches, what are the dimensions of the panel?
The width of the panel is *blank* inches.
Answer:
The width of the panel is 20 inches----------------------
Let the width be x, then the length is 4x - 11.
The perimeter of the rectangle is:
2(x + 4x - 11) = 178Solve it for x:
2(5x - 11) = 1785x - 11 = 895x = 100x = 20Anita Jacobs could deposit R600 every 3 months in her credit union which pays 12% interest compounded quarterly. How much more would she have in her account at the END of 4 years if she deposited the R600 at the BEGINNING of each quarter rather than at the END of each quarter?
Answer: 1890
Step-by-step explanation:
The number of bacteria in a certain population increases Accor to a continuous growth model,with a growth parameter of 9.6% per hour. How many hours does it take for the size of the sample to double
The required number of hours does it take for the size of the sample to double is 11 hours.
What is percentage?Percentages are basically divisions where the denominator is 100. To show that a number is a percent, we utilize the percent image (%) close to the number. For instance, in the event that you got 75 inquiries right out of 100 on a test (75/100), you would have scored 75%.
According to question:Let initial population be x.
As question says number of bacteria increases by 9.6% per hours.
9.6% of x takes 1 hours,
So, in 11 hours size of sample become 105.6%, means almost double of initial size.
Thus, 11 hours will be taken to make size double.
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We want to determine if [u, v, w is linearly independent. To do that we write the vectors as columns of a matrix A and row reduce that matrix To check this we add We then add We then add We conclude that times the first row to the second. times the first row to the third. times the new second row to the new third row. OA. The set [u, v, w} is linearly dependent. O B. The set {u, v, w] is linearly independent. C. We cannot tell if the set [u, v, w] is linearly independent or not.
Option C, If your row reduces the matrix A and obtains a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly dependent.
This is because the row of all zeros except for a 1 in the rightmost column indicates that one of the vectors in the set can be expressed as a linear combination of the other vectors.
On the other hand, if your row reduces the matrix A and does not obtain a row of all zeros except for a single 1 in the rightmost column, then the set {u, v, w} is linearly independent. This is because the absence of such a row indicates that none of the vectors in the set can be expressed as a linear combination of the other vectors.
If you are unable to row reduce the matrix A for any reason, then it is not possible to determine if the set {u, v, w} is linearly independent or not.
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Fill in the diagram based on the following information
30% of the total is 12 grams
in this given question 30% of 12 will be 3.6.
What is the percentage?
A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.
30% of the total is 12 grams
So the given 30% of 12 will be
12*30/100
=3.6
Hence, in this given question 30% of 12 will be 3.6.
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Fully simplify. -15xy(15x^5y^3)
Answer:
−225x^6y^4
Step-by-step explanation:
Consider the piecewise function shown on the graph, which is composed of polynomial, constant, and exponential pieces.
10
-10-8-6-4-2 02 4
O
2
D. (-00, 4)
-2.
-6-
-8
-10-
Over which interval of the domain is the function increasing?
A. (1,4)
OB. (-00, 1)
OC. (-00,-4)
10
4
"Increasing" means the y-values are increasing as x-values increase. Or visually, if you were walking along the graph, from left-to-right, where would you be walking uphill?
The uphill portion is from (-infty, -4). Once you get to an x-value of -4, then it levels off (so it's "constant") until you get to x = 1, when it goes downhill (the function is decreasing).
The interval of the domain in which the function is increasing is(-∞, -4). so option C is correct.
What is a piecewise function?A function that is composed of several smaller functions, each with a distinct domain, is said to be piecewise. The term "piecewise" refers to the way in which these sub-functions are defined in terms of various intervals or "pieces" of the function's overall domain.
Given that,
The piecewise function which is discontinuous at x =1
In the interval
(-∞, -4) the value of the function is increasing.
[-4, 1) the value of the function is constant.
(1, ∞) the value of the function is decreasing.
Hence, the function is increasing in the domain (-∞, -4)
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Shelby and Aisha baked homemade dog treats to sell. They baked 116 dog treats in all.
Shelby baked 3 times as many treats as Aisha.
4) How many dog treats did Aisha bake?
Answer:
87
Step-by-step explanation:
If Shelby and Aisha baked a total of 116 dog treats to sell, and Shelby baked 3 times as many dog treats that Aisha, then we need to figure out what 3/4 of 116 dog treats is.
116 ÷ 4 = 29
29 × 3 = 87
Shelby baked 87 dog treats.
Simplify: 3/8(4a-5)-5/12(3a-4)=1/6
Answer:
Step-by-step explanation:
3/8(4a-5)-5/12(3a-4)=
9/24(4a-5)-10/24(3a-4)=1/6 | x24
9*(4a-5)-10(3a-4)=4
36a-45-30a+40=4
6a=9
a=3/2
A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one-half gallon of water is needed, and for every 6 scoops of mix, one and one-half gallons of water are needed. Part A: Find the constant of proportionality. Show every step of your work. (4 points) Part B: Write an equation that represents the relationship. Show every step of your work. (2 points) Part C: Describe how you would graph the relationship. Use complete sentences. (4 points) Part D: How many gallons of water are needed for 10 scoops of drink mix? (2 points)
a) The constant of proportionality of the given problem is; 4
b) An equation that represents the relationship is; y = 4x
c) The graph is as attached.
d) The gallons of water that are needed for 10 scoops of drink mix is; 2.5 gallons
How to find the proportional relationship?The general equation for the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope of line which tells us the unit rate of change of y with respect to x
c is the y - intercept
Now, it is pertinent to note that y = mx also represents direct proportionality. Making m the subject gives;
m = y/x
Thus, with proportion, we can say;
y₁/x₁ = y₂/x₂
The proportional relationship will be written as;
y = kx
where k is constant of proportionality
From the question, we can say that;
2 scoops require 0.5 gallon of water
6 scoops require 1.5 gallon of water
a) Thus;
k = 2/0.5
k = 2/(1/2)
k = 2 * 2 = 4
b) Equation that represents the relationship can be written as;
y = 4x + c
Since 2 scoops require 0.5 gallon of water, then;
2 = (4 * 1/2) + c
2 = 2 + c
c = 0
The equation will be; y = 4x.
c) Graph of y = 4x is attached at the end.
d) For 10 scoops of water;
10 = 4x
x = 2.5 gallons of water required.
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Solve for x Round to the nearest tenth, if necessary.
Answer:
1.7
Step-by-step explanation:
tan30°=1/XX=1/tan30°X=1/0.57741.73191.7(to the nearest tenth)The sum of 7x^2+x+1 and -6x^2-8x-10
Answer:
Step-by-step explanation:
To find the sum of 7x^2+x+1 and -6x^2-8x-10, you can add the two expressions by combining like terms.
7x^2+x+1 + (-6x^2-8x-10)
= (7x^2 + -6x^2) + (x + -8x) + (1 + -10)
= x^2 + -7x + -9
Therefore, the sum of 7x^2+x+1 and -6x^2-8x-10 is x^2 - 7x - 9.
everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is 20%. What is the discount price? Please help me.
The discount price of the shirt will be $15.
How to calculate the price?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
From the information, the store offers a 25% discount and the regular price of a t-shirt is $20. Therefore, based on the information illustrated, the main points to note will be:
Discount = 25%
Regular price = $20.
In this case, the discount price will be the difference between the regular price and the discount.
The discount price will be:
= Regular price - Discount
= $20 - ($20 × 25%)
= $20 - $5
= $15
The price is $15.
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Complete question
everything at a store is on sale. The store offers a 25% discount. The regular price of a t-shirt is $20. What is the discount price? Please help me
Fill in the chart on paper,
then list the coefficient
of the "x" term.
4x
-10
3x²
-8x
+2
Enter
Answer:
2
Step-by-step explanation:
add 2 by 6 to get 02
Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.
Jonah runs 2 (19/20) laps more than the remaining two days
Adding Fractions:The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.
To make denominators as same we need to take the LCM of denominators of two fractions.
Here we have
Jonah ran 1(3)/(4) laps on Monday
=> 1 3/4 = 7/4 laps
On Tuesday he ran 2(3)/(10) laps
=> 2 3/10 = 23/10 laps
On Wednesday he ran 6(1)/(5) laps
=> 6 1/5 = 31/5 laps
The total number of laps ran combining Monday and Tuesday
= 7/4 laps + 23/10 laps
= (35 + 46)/20 [ take Lcm of 4, 10 i.e 20 ]
= 81/20
From the above calculations,
Jonah ran 81/20 laps on combining Monday and Tuesdays
The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps
= 31/5 - 81/20
= (140 - 81)/20 [ Take Lcm of 5, 20 i.e 20 ]
= 59/20
= 2 (19/20)
Therefore,
Jonah runs 2 (19/20) laps more than the remaining two days
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Complete Question:
Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.
Solve the following inequality and graph the solution:
(x-4)(x-5)<0
Choose test values and indicate whether the inequality is true or false in each region.
Enter the test values from smallest to largest.
Draw the solution above.
Write the solution as a compound inequality
4
The solution to the inequality (x - 4)(x - 5) < 0 is given as follows:
4 < x < 5.
The test values are given as follows:
x < 4 -> x = 3: false.4 < x < 5 -> x = 4.5: true.x > 5 -> x = 6: false.The graph of the inequality is given by the image shown at the end of the answer.
How to solve the inequality?The inequality in this problem is given as follows:
(x - 4)(x - 5) < 0
The inequality is a product, meaning that there is two cases for when it is negative, which are:
x - 4 > 0 and x - 5 < 0.x - 4 < 0 and x - 5 > 0.For the first case, the solution is given as follows:
x > 4 and x < 5 -> 4 < x < 5 (intersection).
For the second case, the solution is given as follows:
x < 4 and x > 5 (impossible).
Hence the compound inequality that gives the solution is of:
4 < x < 5.
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