Answer: 729
Step-by-step explanation:
3^2 is the same has 3 to the power of 2
9^2 is the same as 9 to the power of 2
When you see an expression like 3^2 x 9^2, it means you must raise 3 and 9 to the power of 2, multiply those numbers, and then do it again.
3 raised to the power of 2, often known as 3 times itself or 3 x 3, equals 9.
9 raised to the power of 2, often known as 9 times itself (9 x 9), equals 81.
As a result, when we change these values in the original expression, we obtain:
3^2 x 9^2 = 9 x 81
Now that we have these two integers, we can easily multiply them to obtain the result:
9 x 81 = 729
Therefore, 729 is the answer to the equation 3^2 x 9^2.
Hope that was helpful.a textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced. a. what is the probability of exactly two flaws in a 50-yard piece of material? b. what is the probability of no more than two flaws in a 50-yard piece of material? c. what is the probability of no flaws in a 25-yard piece of material?
a. The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.
b. The probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.
c. The probability of no flaws in a 25-yard piece of material is approximately 0.3679.
To find the probability of exactly two flaws in a 50-yard piece of material, we can use the Poisson distribution. Let λ be the average number of flaws per 50 yards of material, which is 2. Then, the probability of exactly k flaws occurring in a 50-yard piece of material is given by
P(k flaws) = (e^(-λ) × λ^k) / k!
So, for k=2, we have
P(2 flaws) = (e^(-2) × 2^2) / 2! ≈ 0.2707
Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2707.
b. To find the probability of no more than two flaws in a 50-yard piece of material, we need to sum the probabilities of having 0, 1, or 2 flaws. So, we have
P(no more than 2 flaws) = P(0 flaws) + P(1 flaw) + P(2 flaws)
We already know P(2 flaws) from part (a). To find P(1 flaw), we can use the same formula as before with λ=2 and k=1
P(1 flaw) = (e^(-2) × 2^1) / 1! ≈ 0.2707
To find P(0 flaws), we use the same formula with λ=2 and k=0
P(0 flaws) = (e^(-2) × 2^0) / 0! ≈ 0.1353
Therefore, we have:
P(no more than 2 flaws) = 0.2707 + 0.2707 + 0.1353 ≈ 0.6767
So, the probability of no more than two flaws in a 50-yard piece of material is approximately 0.6767.
c. To find the probability of no flaws in a 25-yard piece of material, we can again use the Poisson distribution, but with a different value of λ. Since the average number of flaws per 50 yards is 2, the average number of flaws per 25 yards is 1. So, we have:
P(0 flaws) = (e^(-1) × 1^0) / 0! ≈ 0.3679
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Which quadratic inequality best describes the graph?
Answer: parabolic curve
Step-by-step explanation:
Answer: parabolic curve
Step-by-step explanation:
I NEED HELP ON THIS ASAP!!!
1. The numeric values of the function are given as follows:
x = -4, y = 1/16.x = -3, y = 1/8.x = -2, y = 1/4.x = -1, y = 1/2.x = 0, y = 1.2. As x approaches negative infinity, y approaches zero.
How to calculate the numeric value of a function or of an expression?To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.
The numeric values for this problem are given as follows:
x = -4, y = 1/16, as 2^(-4) = 1/2^4 = 1/16.x = -3, y = 1/8, as 2^(-3) = 1/2^3 = 1/18.x = -2, y = 1/4, as 2^(-2) = 1/2^2 = 1/4.x = -1, y = 1/2, as 2^(-1) = 1/2^1 = 1/2.x = 0, y = 1, as 2^(0) = 1/2^0 = 1.Increasing the negative exponent, the number gets closer to zero.
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I just need the perimeter
Example #2 - Coordinate Perimeter/Area Calculate the area and perimeter of the shape shown. Determine the: Perimeter Area
Using composite figures, we can find that the area of the shape is 18unit² and the perimeter of the shape is 20 + √8 units.
Define composite figures?A composite shape is a shape that is made by connecting a few polygons to form a different shape. These shapes or figures can be formed from a variety of shapes, including triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.
In essence, a composite shape is a combination of fundamental shapes. It goes by the name's "composite" or "complex" shapes.
In this composite figure,
We have 2 rectangles and a triangle.
Dimension of rectangle:
Base = 2units
Height = 2 units.
Hypotenuse = √ (2² + 2²)
= √8
Area of the triangle = 1/2 × b × h
= 1/2 × 2 × 2
= 2unit².
Now, the rectangles are equal in shape and size.
Dimensions are:
Length = 4 units
Breadth = 2 units.
Area = l × b
= 4 × 2
= 8unit².
We have 2 rectangles so total area = 2 × 8
= 16unit².
Total area of the shape = area of triangle + area of 2 rectangles
= 2 + 16
= 18unit²
Now coming to the perimeter of the shape, we have to find the sum of the measure of the sides of the shape:
So, we have
2 + 4 + 2 + 6 + 6 + √8
= 20 + √8 units.
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y=3-x 3y+x=5 solve by substitution method
Answer:
x = 2
y = 1
Step-by-step explanation:
3y + x = 5 y = 3 - x
3(3 - x) + x = 5
9 - 3x + x = 5
9 - 2x = 5
-2x = -4
x = 2
Now put 2 in for x and solve for y
3y + x = 5
3y + 2 = 5
3y = 3
y = 1
Let's Check
1 = 3 - 2
1 = 1
So, x = 2 and y = 1 is the correct answer.
wo random samples of earnings of professional golfers were selected. one sample was taken from the professional golfers association, and the other was taken from the ladies professional golfers association. at , is there a difference in the means? the data are in thousands of dollars. use the critical value method with tables. pga lpga
in general, to perform a hypothesis test comparing the means of two independent samples using the critical value method, you would follow these steps:
State the null and alternative hypotheses. For example, the null hypothesis could be that there is no difference in means between the two populations (i.e., H0: µ1 - µ2 = 0), and the alternative hypothesis could be that there is a significant difference in means (i.e., Ha: µ1 - µ2 ≠ 0).
Determine the level of significance, α, which represents the probability of rejecting the null hypothesis when it is actually true. For example, if α = 0.05, then there is a 5% chance of making a Type I error (rejecting the null hypothesis when it is true).
Calculate the test statistic. The most common test statistic for comparing the means of two independent samples is the t-test. The formula for the t-test is:
t = (x1 - x2) / [s^2pooled/n1 + s^2pooled/n2]^0.5
where x1 and x2 are the sample means, s^2pooled is the pooled variance (calculated using the two sample variances and sample sizes), and n1 and n2 are the sample sizes.
Determine the critical value(s) from the t-distribution table based on the degrees of freedom (df) and level of significance (α). The degrees of freedom for a two-sample t-test is calculated as:
df = n1 + n2 - 2
Compare the test statistic to the critical value(s). If the absolute value of the test statistic is greater than the critical value(s), then reject the null hypothesis; otherwise, fail to reject the null hypothesis.
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5. Find the perimeter and area
*Triangle- based prism*
Step-by-step explanation:
for the perimeter you have to say two brackets live plus height plus with plastic
What is the area of a right triangle with a height of ten and one-half feet and a base of 33 feet?
twenty-one and three-fourths ft2
forty-three and one-half ft2
one hundred seventy-three and one-fourth ft2
three hundred forty-six and one-half ft2
The area of the right triangle is 173.25 square feet.
What is the area of the right triangle?The formula for the area of a right triangle is:
A = (1/2)bh
where A is the area, b is the base, and h is the height.
We are given that the height of the right triangle is ten and one-half feet (10.5 ft) and the base is 33 feet.
Substituting the given values into the formula, we get:
A = (1/2)(33)(10.5)
Simplifying the expression on the right side, we get:
A = 173.25
Therefore, the area of the right triangle is 173.25 square feet.
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A number line going from negative 2 to positive 1. What is the correct order of the fractions from least to greatest? Point A: −11 3 Point B: −2 3 Point C: 1 3 Point D: −12 3 The correct order for the fractions is .
Answer:
D, A, B, C
Step-by-step explanation:
-12/3, or -4, is lowest
-11/3, or -3.6, is 0.3 more, therefore closer to 0.
-2/3, or -0.6, is much closer to 0, precisely 3 units closer.
1/3, or 0.3, is the only positive number, so it is the most amount.
A salesman's commission varies directly as his sales.If the commission is $10 for $100 in sales, find the commission for $150 in sales.
a. $12 b. $20 c. $15 d. $25
The commission for $150 in sales is $15. This corresponds to option (c) in the given answer choices.
We are told that the salesman's commission varies directly with his sales. This means that if the sales increase by a certain percentage, then the commission will also increase by the same percentage. We can set up a proportion to solve for the commission:
Commission/Sales = Commission Rate
We are given that the commission rate is $10 for every $100 in sales. We can use this information to set up a proportion:
Commission/150 = 10/100
To solve for the commission, we can cross-multiply and simplify:
Commission = (150 x 10)/100 = $15
In general, if we let x represent the sales amount, and c represent the commission, then we can use the formula:
c = (x/100) * 10
where 10 represents the commission rate of $10 per $100 in sales. We can use this formula to calculate the commission for any given sales amount.
Therefore, Correct option is C.
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17. Corina makes $27 for every 2 hours that she works. If she worked 36
hours this week, how much money did she make?
If she worked 36 hours this week, then Corina made $486 this week.
From the question, we have the following parameters that can be used in our computation:
Corina makes $27 for every 2 hours that she works.
So she makes:
27/2 = $13.50 per hour
If she worked 36 hours this week, she would make:
36 hours x $13.50 per hour = $486
Therefore, Corina made $486 this week.
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PLEASE HELP I'LL GIVE THE BRAINLIEST!
Answer:
Box A: 2 × 4.5 × 6 = 54 cubic inches
Box B: 6 × 2.5 × 3 = 45 cubic inches
Box C: 5 × 4.5 × 2.25 =
50.625 cubic inches
Box D: 2.5 × 2.25 × 3 = 16.875 cubic inches
From least to greatest, the order of the boxes' volumes is D, B, C, A.
The vertices of a figure are given. Rotate the figure as described. Find the coordinates of the image.
E(−4, 1), F(−3, 3), G(−2, 3), H(−1, 1)
180°
about the origin
Mr ade plans to spend his monthly salary as fellow
food-20%
children-25%
parents-20%
car-10%
entertainment-10%
saving-2½
miscellenceous-2½
if the amount of saving kept for saving is Ghc 250.00. calculate his
a) monthly salary
b) total amount spent on his parent
a) His monthly salary is, 555.6
b) Total amount spent on his parent is, 111.1
Given that;
Mr. Ade plans to spend his monthly salary as follows
food-20%
children-25%
parents-20%
car-10%
entertainment-10%
saving-2½
miscellenceous-2½
And, the amount of saving kept for saving is Ghc 250.00.
Hence, We get;
Monthly salary is,
Since, We have;
Percent of savings = 100% - 20% - 10% - 10% - 12.5% - 2.5%
= 45%
Hence, We get;
45% of salary = 250
45/100 x salary = 250
Monthly salary = 25000 / 45
Monthly salary = 555.6
And, Money spent on parents;
20% of 555.6
20/100 x 555.6
111.1
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Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. a. (2xy2 − 3xy3)(2xy2 + 3xy3) b. (2xy2 − 3xy3)(2xy2 − 3xy3) c. (4xy2 + 9xy3)(xy2 − xy3) d. (4xy2 − 9xy3)(xy2 − xy3)
Given the polynomial 4x2y4 − 9x2y6, rewrite as a product of polynomials. (2xy2 − 3xy3)(2xy2 + 3xy3). So, correct answer is A.
To multiply two binomials, we use the FOIL method which stands for First, Outer, Inner, Last. For option A, using the FOIL method, we get
(2xy² - 3xy³)(2xy² + 3xy³) = (2xy²)² - (3xy³)² = 4x²y⁴ - 9x²y⁶
This is the given polynomial, so option A is correct.
For other option, we have two identical binomials multiplied together, which would give us a trinomial with three terms, so it cannot be a product of two binomials.
Option C is also incorrect because when we multiply the two binomials, we do not get the given polynomial. Option D is incorrect as well because the signs are incorrect and we would get a different polynomial when we multiply the two binomials.
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--The given question is incomplete, the complete question is given
" Given the polynomial 4x²y⁴ − 9x²y⁶, rewrite as a product of polynomials. a. (2xy² − 3xy³)(2xy² + 3xy³) b. (2xy² − 3xy³)(2xy² − 3xy³) c. (4xy² + 9xy³)(xy² − xy³) d. (4xy² − 9xy³)(xy² − xy³)"--
what is the number of permutations of the letters in the word indis- tinguishable such that the strings git, tin, and nab do not appear in the permutation?
The number of permutations of the letters in the word indistinguishable such that the strings git, tin, and nab do not appear in the permutation is
3,172,973,824,000
Let A be the set of stages that contain the string "git",
B be the set of changes that contain the string "tin", and
C be the set of stages that contain the string "nab".
We need to discover the number of stages that don't contain any of these strings, which is the same as finding the measure of the set (A∪B∪C)'.
Utilizing the guideline of inclusion-exclusion, we have:
|A∪B∪C| = |A| + |B| + |C| - |A∩B| - |A∩C| - |B∩C| + |A∩B∩C|
We need to discover |(A∪B∪C)'|, which is the complement of the set A∪B∪C. In this manner:
|(A∪B∪C)'| = n! - |A∪B∪C|
Now we have to discover the measure of the sets A, B, and C, and their convergences.
For set A, able to settle the string "git" in its put in 3! ways, and after that permute the remaining 14 letters in 14! ways. In this manner, |A| = 3!×14!.
Essentially, we will discover |B| = 3!×14! and |C| = 3!×14!.
For the convergences, we are able to settle the comparing strings in their places and permute the remaining 11 letters in 11! ways. In this manner,
|A∩B| = 2!×11!,
|A∩C| = 2!×11!,
and |B∩C| = 2!×11!.
At long last, we have |A∩B∩C| = 1!×11! since we are able to settle all three strings in their places and permute the remaining 11 letters in 11! ways.
Substituting these values into the inclusion-exclusion equation, we get:
|A∪B∪C| = 3(3!×14!) - 3(2!×11!) + 1!×11!
|A∪B∪C| = 13608000
Subsequently:
|(A∪B∪C)'| = 17! - 13608000
|(A∪B∪C)'| = 3172973824000
So there are 3,172,973,824,000 permutations of the letters within the word "indistinguishable" such that the strings "git", "tin", and "nab" don't show up within the stage.
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7z + 7> - 2z -4 solve the following for inequality for z simplest form
Answer:
z > - [tex]\frac{11}{9}[/tex]
Step-by-step explanation:
7z + 7 > - 2z - 4
9z + 7 > - 4
9z > -11
z > - [tex]\frac{11}{9}[/tex]
Answer: Just turn it into an equation! Replace the > with a =.
Step-by-step explanation:
Subtract 7 from both sides (bc you’re doing the opposite of +7) So 7z +7-7 cancels out so you just have 7z. 7z = -2z -4 -7, so 7z = -2z -11
Add 2z to both sides (bc your doing the opposite again) to get 9z = -11
Divide both sides by the number of the of the term with both a number and variable, in this case 9z, the number is 9. So 9z/9= -11/9 so simplified, z= -11/9
Final answer = -11/9
Hope this helps :D
4.a) Increase £75 by 5%
Please help me and explain this to me.
Answer:
£78.75
Step-by-step explanation:
An easy way step but longer way to do this is
10% of 75 is 7.5 ((75/10= 7.5))
divide by 2 on both sides
5% = 3.75
then just add it, its increasing 75 by 5%
so 75 + 3.75 = 78.75
DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS
Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.
2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.
3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.
4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.
The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.
What is Proportion?Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.
The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.
Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.
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can someone help me pls!!!! Imma give u brainliest
Answer:
sin0= 9/15
cos0= 12/15
tan0 = 9/12
A salesman and 30% commission on all merchandise that he sells last month. He sold $700 worth of merchandise how much commission in dollars did he earn last month
11. Phyllis ran in a 5-kilometer race to help raise money for the school. How many meters long is the race?
Answer:5000 meters
Step-by-step explanation:1km=1000m
What is the volume of the composite shape?
Write an expression for the apparent nth term an of the sequence. (Assume that n begins with 1.) 4, 5/3, 6/5, 1, 8/9
The nth term of the sequence as: an = { 4 (n - 1) if n is odd
1 if n is even and n ≠ 4 8/2n when n = 4
What is arithmetic progression and its formula ?
An arithmetic progression is a list of numbers where each term is obtained by adding a specific number to the previous term, except for the first term. The following formulas help solve arithmetic progression problems: AP common difference: d = an - an-1. AP nth term: an = a (n -1)d
Sum of n terms of AP: Sn = n/2 (2a (n - 1)d)
The given sequence is 4, 5/3, 6/5, 1, 8/9.
To find the expression for the nth term, we must observe the pattern of the sequence. We see that the numerators of the series fractions increase by 1 for each term, while the denominators increase by 2 for each term except the fourth term, which is 1. Therefore, we can write the nth term of the sequence as:
an = { 4 (n - 1) if n is odd
1 if n is even and n ≠ 4
8/2n when n = 4
where n is a positive integer representing the position of the term in the sequence.
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The hypotenuse of a right triangle measures 16 cm and one of its legs measures 9 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
What is the value of the quadratic equation: y=4x^2+8x+7
The value of quadratic equation with the help of hit and trial method is 39
what is quadratic equation ?A quadratic equation is a polynomial equation of degree 2, which means that the highest power of the variable (usually x) in the equation is 2. It is in the form:
ax^2 + bx + c = 0
where a, b, and c are constants and a is not equal to zero.
According to given informationthe value of given quadratic equation is
given
y=4x²+8x+7
using hit and trial method:
The value of the quadratic equation y = 4x² + 8x + 7 depends on the value of x.
To find the value of y for a specific value of x, simply substitute that value of x into the equation and solve for y.
For example, if x = 2, then:
y = 4(2)² + 8(2) + 7
y = 16 + 16 + 7
y = 39
So the value of the quadratic equation y = 4x^2 + 8x + 7 when x = 2 is 39.
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What number should be written in the penultimate line of the script instead of -1 for the function f to be linear? justify
For the function f to be linear, the number that should be written in the penultimate line of the script should be 0 because a linear function has a constant slope and no term with a power higher than 1.
In the general form of a linear function
y = mx + b
where m is the slope and b is the y-intercept.
Since the function f is defined as
f(x) = x² + mx + b
we can see that it is a quadratic function.
Therefore, to make it linear, we need to eliminate the x² term.
To eliminate the x² term, we can set the coefficient of x² to 0. Since the coefficient of x² is 1, we can subtract x² from both sides of the equation
f(x) = x² + mx + b
f(x) - x² = mx + b
Now, we have a linear function since the term with x² has been eliminated. Thus, the number that should be written in the penultimate line of the script is 0, which will make the coefficient of x² equal to 0 and eliminate the quadratic term.
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Help on both problems pls
Answer:
DE = √21
x = 10
Step-by-step explanation:
4)
AC is bisected by BX
AC/2 = 8/2 = 4 = AB
BX² + AB² = AX²
3² + 4² = AX²
AX = 5 = radius of the circle
DE² = DX² - EX²
DE² = 5² - 2² = 25 - 4 = 21
DE = √21
6)
x² = (11-5)² + 8² = 36 + 64 = 100
x = √100 = 10
x = 10
What is the area of this figure? 10 mi 17 mi 3 mi 4 mi 4 mi 6 mi 4 mi 18 mi
The area of the figure is 197 square miles
How to find the area of the figure.To find the area of the figure, we need to first identify the shape of the figure. From the given dimensions, it appears to be an irregular quadrilateral with a triangle on top.
We can divide the figure into two parts: a rectangle with dimensions 17 mi by 10 mi, and a triangle with base 18 mi and height 3 mi.
The area of the rectangle is:
Area of rectangle = length x width = 17 mi x 10 mi = 170 mi^2
The area of the triangle is:
Area of triangle = (base x height) / 2 = (18 mi x 3 mi) / 2 = 27 mi^2
Therefore, the total area of the figure is the sum of the areas of the rectangle and triangle:
Total area = 170 mi^2 + 27 mi^2 = 197 mi^2
So the area of the figure is 197 square miles.
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Como se resuelve esto
2x²-11x=-14
Mediante factorizacion
The solutions to the equation are x = 7/2 or x = 2. This is because if either of the factors (2x - 7) or (x - 2) equals zero, then the whole expression will equal zero.
To solve the quadratic equation 2x²-11x=-14 by factorization, we need to rearrange the equation to bring all terms to one side so that it is in the form ax² + bx + c = 0.
First, we add 14 to both sides of the equation, which gives us:
2x² - 11x + 14 = 0
To factorize this quadratic equation, we need to find two numbers that multiply to give the constant term (14) and add to give the coefficient of the middle term (-11). In this case, the two numbers are -2 and -7, as (-2) x (-7) = 14 and (-2) + (-7) = -9.
Using these two numbers, we can rewrite the middle term as -2x - 7x, which gives us:
2x² - 2x - 7x + 14 = 0
We can then factorize the first two terms and the last two terms separately, which gives us:
2x(x - 1) - 7(x - 2) = 0
We can then use the distributive property to simplify the equation:
2x² - 2x - 7x + 14 = 0
2x(x - 1) - 7(x - 2) = 0
(2x - 7)(x - 2) = 0
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