Answer:
x^4 - mx^2 + n^2 = 0
Step-by-step explanation:
We can use algebraic manipulation to solve for m and n. First, we can square the equation xy = n to get:
(x^2)(y^2) = n^2
Since we also have x^2 + y^2 = m, we can substitute y^2 with m - x^2 to get:
x^2(m - x^2) = n^2
Expanding the left side of the equation, we get:
mx^2 - x^4 = n^2
Multiplying both sides by 16, we get:
16mx^2 - 16x^4 = 16n^2
Adding 32xy to both sides, we get:
16mx^2 + 32xy - 16x^4 = 16n^2 + 32xy
Substituting n for xy, we get:
16mx^2 + 32n - 16x^4 = 16n^2 + 32n
Rearranging the equation, we get:
16mx^2 - 16x^4 - 16n^2 = 0
Dividing both sides by -16, we get:
x^4 - mx^2 + n^2 = 0
Answer:
(4x+4y)²
Step-by-step explanation:
Given x²+y² = m ,xy=n.
Now 16m+32n = 16(m+2n)
= 16(x²+y²+2xy) = 4²(x+y)²[ x²+y²+2xy= (x+y)²]
(4x+4y)².
If Heidi makes 15.85 an hour and she works 47.50 hours this week what is her overtime pay ?
Answer: $178.31
Step-by-step explanation:
To calculate Heidi's overtime pay, we first need to find out how many hours she worked overtime and then multiply those hours by her overtime pay rate. The standard workweek in the United States consists of 40 hours, and any hours worked beyond 40 hours are considered overtime.
Step 1: Calculate the number of overtime hours:
Total hours worked = 47.50 hours
Standard workweek = 40 hours
Overtime hours = Total hours worked - Standard workweek = 47.50 - 40 = 7.50 hours
Step 2: Calculate Heidi's overtime pay rate:
Hourly wage = $15.85
Overtime pay rate = Hourly wage * 1.5 (overtime is typically paid at 1.5 times the regular hourly rate) = $15.85 * 1.5 = $23.775
Step 3: Calculate Heidi's overtime pay:
Overtime pay = Overtime hours * Overtime pay rate = 7.50 hours * $23.775 = $178.31 (rounded to 2 decimal places)
Heidi's overtime pay for the week is $178.31.
please answer fast will give brainliest ANSWER EVERYTHING
The given points can only be represented by an exponential function.
What is a linear function?
A linear function has the following form = y = f(x) = a bx
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
a is a constant term or y-intercept. This is the value of the dependent variable when x = 0.
b is the coefficient of the independent variable. It is also called the slope and gives the rate of change of the dependent variable.
We can determine the type of function that can represent the given points by looking at the pattern of y values corresponding to the x values.
Linear Function: A linear function has a constant slope, which means that the difference between any two consecutive values of y must be the same as the difference between two consecutive values of x. The difference between two consecutive y values is 9/8, which is not the same as the difference between two consecutive x values (which is 1). Therefore, the given points cannot be represented by a linear function. Exponential function: an exponential function has a constant ratio between two consecutive y-values, meaning that the ratio of any two consecutive y-values must be the same as the ratio of any two consecutive x-values.
The ratio of two consecutive y values is 2, which is the same as the ratio of two consecutive x values (which is 1/2). Therefore, the given scores can be represented by an exponential function. Quadratic function: A quadratic function has a quadratic term, which means that the y-values should show an increasing or decreasing pattern of differences between successive x-values. The differences between successive y values are 9/8, 3/8, 1/2, and 9. There is no pattern of increasing or decreasing differences between successive x values, so the given points cannot be represented by a square. function
Therefore, the given scores can only be represented by an exponential function.
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a particular fruit's weights are normally distributed, with a mean of 443 grams and a standard deviation of 34 grams. if you pick 2 fruit at random, what is the probability that their mean weight will be between 360 grams and 491 grams
The probability that the mean weight of two fruits picked at random falls between 360 grams and 491 grams is approximately 0.9554 or 95.54%.
To solve this problem, we need to use the formula for the sampling distribution of the sample mean:
x' = μ/√n
where x' is the sample mean, μ is the population mean, and n is the sample size.
Given that the population mean is 443 grams and the standard deviation is 34 grams, we can calculate the standard error of the sample mean:
SE = σ/√n
= 34/√2
≈ 24.04 grams
Now we need to standardize the sample mean to a standard normal distribution using the z-score formula:
z = (x' - μ)/SE
The probability that the sample mean falls between 360 grams and 491 grams is equivalent to the probability that the z-score falls between:
z = (360 - 443)/24.04 ≈ -3.45 and z = (491 - 443)/24.04 ≈ 1.99
Using a standard normal table or calculator, we can find the probability that the z-score falls between -3.45 and 1.99, which is approximately 0.9554.
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which of the following is true of primary data? multiple choice primary data collection methods are unaffected by biases of the respondent. primary data are relatively less expensive than secondary data. primary data consists of two types: exploratory and descriptive. primary data are collected exclusively from academic journals. primary data are collected specifically for the research problem at hand.
The following is true of primary data collection: primary data are collected specifically for the research problem at hand.Primary data collection refers to the process of collecting new data or original data that have not been collected before. Primary data are the first-hand data gathered by researchers from original sources.
The following is true of primary data: primary data are collected specifically for the research problem at hand. Primary data are collected to meet specific research objectives and to provide solutions to research problems.Primary data collection methods are affected by the biases of the respondent.
This is because the collection of primary data requires direct contact between the researcher and the respondents or participants. It is important to note that primary data collection methods are relatively more expensive than secondary data. Therefore, researchers should consider the cost implications of primary data collection methods before using them.
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suppose that three students are randomly selected from the student body. what is the probability that all three will possess a gpa in excess of 3.0?
The probability that at least three out of five randomly selected students will possess a GPA in excess of 3.0 is approximately 0.1772.
To solve this problem, we need to use the binomial distribution with n = 5 and the probability of success p = P(GPA > 3.0), which can be found using the normal distribution table:
P(GPA > 3.0) = P(Z > (3.0 - 2.7)/0.7) = P(Z > 0.43) = 1 - P(Z < 0.43) = 1 - 0.6664 = 0.3336
Now we can use the binomial distribution to find the probability that at least three students out of five have a GPA greater than 3.0:
P(X ≥ 3) = P(X = 3) + P(X = 4) + P(X = 5)
Using the binomial formula and the probabilities of success and failure:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
we get:
P(X = 3) = (5 choose 3) * 0.3336^3 * 0.6664^2 = 0.1311
P(X = 4) = (5 choose 4) * 0.3336^4 * 0.6664^1 = 0.0421
P(X = 5) = (5 choose 5) * 0.3336^5 * 0.6664^0 = 0.0040
Therefore:
P(X ≥ 3) = 0.1311 + 0.0421 + 0.0040 = 0.1772
So the probability that at least three out of five students have a GPA greater than 3.0 is approximately 0.1772.
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--The given question is incomplete, the complete question is given
" The grade point averages (GPAs) of a large population of college students are approximately normally distributed with mean 2.7 and standard deviation 0.7. Suppose that five students are randomly selected from the student body. What is the probability that at least three will possess a GPA in excess of 3.0? "--
Plssssss!!!! Help SOLVE FOR Y!!!!!!
Answer:
y = 23 degrees
Step-by-step explanation:
115° and 5y° are equal because they are alternate exterior angles
115 = 5y
Divide by 5 to isolate the y
23 = y
so y is 23°
Arianna ate 0.45 of the grapes and Alex at 35% of them if there were 18 grapes left how many were in the container at first
There were 90 grapes in the container at first.
What is the percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
Let's assume that there were x grapes in the container at first.
Arianna ate 0.45 of the grapes, which means she ate 0.45x grapes.
Alex ate 35% of the grapes, which means he ate 0.35x grapes.
The total number of grapes eaten is the sum of what Arianna and Alex ate:
0.45x + 0.35x = 0.8x
This means that 0.8x grapes were eaten, and the number of grapes left is x - 0.8x = 0.2x.
We know that there were 18 grapes left, so we can set up an equation:
0.2x = 18
Solving for x, we get:
x = 90
Therefore, there were 90 grapes in the container at first.
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Leslie has received 10 more instant messages than Anita, and Anita has received 2 more than Sondra. Together, these three individuals have received 83 instant messages (and that's just in one evening). How many instant messages has Sondra received?
Step-by-step explanation:
A = S + 2
L = A + 10 = S+2 + 10 = S + 12
S = S
Summed , they equal 83
S+2 + S+12 + S = 83
3S = 69
S = 23 messages
Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich
Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
Preparing food for a day at the beach can be a fun and fulfilling experience. Charlie decided to make sandwiches for his family to snack on when they get hungry. In this case, each sandwich contains 3 slices of turkey and 3 slices of ham.
The first step in making the sandwiches is to gather all the necessary ingredients. Charlie will need bread, turkey slices, ham slices, and any other desired condiments such as mayonnaise, mustard, lettuce, or tomato. He can choose any type of bread, but a sturdy bread such as a ciabatta, sourdough, or French bread would be ideal for a day at the beach.
To assemble the sandwiches, Charlie can follow these simple steps:
1. Lay out the bread slices. Charlie can choose to use one slice of bread per sandwich or two slices for a heartier sandwich.
2. Add a layer of mayonnaise or mustard if desired. Charlie can choose to spread the condiment on one or both slices of bread.
3. Add a layer of lettuce or tomato if desired. This can add some crunch and freshness to the sandwich.
4. Add 3 slices of turkey on one slice of bread, making sure they are evenly distributed. Charlie can choose to overlap the slices or lay them flat.
5. Add 3 slices of ham on top of the turkey slices, again making sure they are evenly distributed.
6. Top the sandwich with the other slice of bread, condiment-side down.
7. If desired, cut the sandwich in half or quarters for easy sharing and eating.
Charlie can repeat these steps for as many sandwiches as needed for his family. He can also customize the sandwiches by adding or subtracting ingredients, such as cheese, bacon, avocado, or pickles.
In terms of nutritional value, the sandwiches provide a good source of protein from the turkey and ham. The bread provides carbohydrates for energy, while the lettuce and tomato provide vitamins and minerals. The mayonnaise or mustard provides some fat and flavor, but can be skipped if desired.
Overall, making sandwiches for a day at the beach is a simple and convenient way to provide nourishing and satisfying food for the family. By following these steps, Charlie can ensure that each sandwich contains 3 slices of turkey and 3 slices of ham, and can adjust the recipe as needed to suit his family's tastes and preferences.
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Charlie's family is going to relax at the beach all day! In preparation, Charlie made s sandwiches for them to eat when they get hungry. Charlie put 3 slices of turkey and 3 slices of ham on each sandwich how does he adjust the situation ?
COMPARING METHODS In Exercises 27-32, tell whether you would use the Law of Sines, the Law of Cosines, or the Pythagorean Theorem (Theorem 9.1) and trigonometric ratios to solve the triangle with the given information. Explain your reasoning. Then solve the triangle.
what is the value of 16^1/2?
A. 2
B. 4
C. 8
D. 32
Answer: 8
Step-by-step explanation:
Jamie was given the problem, "Find the result when the factors of 65 x 2 + 212 x − 313 65x 2 +212x−313 are multiplied together." Before she could answer, her sister, Lauren, said, "I know the answer without factoring or multiplying!" What was Lauren's answer and how did she know?
The product of the factors of [tex]65x^2 + 212x - 313[/tex] is equal to the original expression. Lauren may have recognized the expression as a difference of squares and factored it accordingly.
We can first simplify the expression [tex]65x^2 + 212x - 313[/tex] by factoring it:
[tex]65x^2 + 212x - 313 = (13x - 1)(5x + 313)[/tex]
(13x - 1)(5x + 313) = [tex]65x^2 + 212x - 313[/tex]
Therefore, the product of the factors is equal to the original expression.
To see this, we can rewrite the expression as:
[tex]65x^2 - 313 - 212x = (5x)^2 - (2\cdot 5x \cdot 7) + 7^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 7^2 - 212x[/tex]
= [tex](5x - 7)^2 - 212x - 49[/tex]
= [tex](5x - 7)^2 - 1^2\cdot 49 - 212x[/tex]
= (5x - 7 - 7)(5x - 7 + 7) - 49 = (5x - 14)(5x) - 49
= 5x(5x - 14) - 49
= 5x(5(x - 2) - 9)
= 5x(5x - 29)
Therefore, the factors of the expression are (5x - 7) and (5x - 29).
Lauren may have recognized the expression as a difference of squares by noticing that the coefficient of the x term (212) is twice the product of the square roots of the first and last terms (sqrt(65) and sqrt(313)), which is a common characteristic of a difference of squares.
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Q8g Chengbo Sold for 180000 (3 yaun. the amount for which he Sold the house is 24% more than the amount hepaid. for the house -work out the house. Give your 3 significant figure answer
Step-by-step explanation:
he sold the house for 180000, which is 24% more than the amount he paid.
180000 = x + 0.24x
Simplifying this equation, we get:
1.24x = 180000
x = 180000 / 1.24
x ≈ 145161.29
Chengbo paid approximately 145161.29 yuan for the house.
Find the third partial sum of the series. (picture included!!!) please I'm in dire need of help cus my grades a D if I could get help ill be so so happy ill probably cry a little tear of joy
Consequently, 15 is the third partial total of the sequence.
What in mathematics is arithmetic?The area of mathematics known as arithmetic deals with the mathematical study of numbers and the numerous procedures that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical processes. The icons listed above stand in for these processes.
The given series is an arithmetic series with first term a1 = 2 and common difference d = 3.
To find the third partial sum, we need to add the first three terms of the series:
S₃ = 2 + 5 + 8
S₃ = 15
Therefore, the third partial sum of the series is 15.
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Solve problem 24 and explain how you solved it
Answer the questions below. Write your answers in simplest form.
Answer:
(a.) 8m
(b.) 12 cm
Step-by-step explanation:
a:
given: area of square = 64m²
formula of area of a square A = s²
We will reverse the formula to find the sum of the sides:
S = √A
S =√64
S = 8
b:
Given: perimeter of a square is 48 cm
formula for a perimeter of a square: P = 4 · s
We will reverse the formula to find the sum of the sides:
S = P ÷ 4
S = 48 ÷ 4
S = 12
complete the figure with 4-fold rotational symmetry. the point is the center of rotation.
By following these steps, we will have a figure with 4-fold rotational symmetry around the given center point.
To complete the figure with 4-fold rotational symmetry around the center point, follow these steps:
1. Identify the center of rotation:
As mentioned, the given point is the center of rotation.
2. Determine the existing shape or pattern:
Observe the figure and identify the existing shape or pattern to replicate.
3. Divide the circle around the center point into four equal sections (quadrants):
This can be done by drawing two lines that intersect at the center point, dividing the area around it into four equal parts (90 degrees each).
4. Replicate the existing shape or pattern in each quadrant:
Copy the shape or pattern in the first quadrant to the other three quadrants, keeping them equidistant from the center point.
5. Check for symmetry:
Ensure that when you rotate the figure 90 degrees, 180 degrees, or 270 degrees around the center point, it remains identical in appearance.
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need help with this question, im stuck on it
Answer:
120° and 60°
Step-by-step explanation:
5x - 10 + 3x - 18 = 180
8x = 180 + 10 + 18
8x = 208 / : 8
x = 26
.
(5x - 10)° = (5 × 26 - 10)° = 120°
(3x - 18)° = (3 × 26 - 18)° = 60°
The diameter of a circle is 10 centimeters. What is the angle measure of an arc bounding a sector with area 10 square centimeters?
Answer:
72 degrees
Step-by-step explanation:
the same answer 3 Question. I think by of a number multiply. and add 7. I if I multiply the number by 4 and subtract 12. find the number? Solve this in equation
The value of the number is 19
What are algebraic expressions?Algebraic expressions are defined as those expressions that are composed of terms, constants, variables, coefficients and factors.
These expressions are also made up of certain mathematical operation, such as;
SubtractionDivisionAdditionMultiplicationBracketParenthesesFrom the information given, we have;
Let the number be x
Then,
3x + 7
4x - 12
Equate the expressions
3x + 7 = 4x - 12
collect the like terms
7 + 12 = 4x - 3x
add or subtract the values
x = 19
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Use the discriminant to describe the roots of each equation. Then select the best description. 2x2 + 7x + 6 = 0
real and irrational roots
real and rational roots
double root
non-real roots
Answer:
real and rational roots
Step-by-step explanation:
The discriminant of the given equation is [tex]7^2-4(2)(6)=1[/tex].
Since the discriminant is a perfect square, the equation has real and rational roots.
a) determine an equation for the family of quartic functions with zeroes -5/2, -1, 7/2, 3.
b) write equations for two functions that belong to this family
c) determine an equation for the member of the family whose graph passes through the point (-2,25)
a. A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3), b) Two examples of functions that belong to this family are: f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3) and the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x.
a) A quartic function with zeroes -5/2, -1, 7/2, and 3 can be written as the product of linear factors with those zeroes:
f(x) = a(x + 5/2)(x + 1)(x - 7/2)(x - 3)
where "a" is a constant that determines the overall scaling of the function.
b) Two examples of functions that belong to this family are:
f1(x) = 2(x + 5/2)(x + 1)(x - 7/2)(x - 3)
f2(x) = -0.5(x + 5/2)(x + 1)(x - 7/2)(x - 3)
Note that these functions differ only in the value of the constant "a".
c) To find the value of "a" that makes the graph of the function pass through the point (-2,25), we can substitute x = -2 and y = 25 into the equation for f(x):
25 = a(-2 + 5/2)(-2 + 1)(-2 - 7/2)(-2 - 3)
Simplifying this expression:
25 = a(5/2)(-1)(-11/2)(-5)
25 = a(6875/4)
a = 100/6875 = 4/275
Therefore, the equation for the member of the family that passes through the point (-2,25) is:
f(x) = (4/275)(x + 5/2)(x + 1)(x - 7/2)(x - 3)
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A Cap is discounted at 25% off. The original price is $60.
What is the sales price?
O $40
O $50
O $45
O $30
Answer:
It's 45.
Step-by-step explanation:
Same as the last question :)
Ms. Angelino made 2 pans of lasagna and
cut each pan into twelfths. Her family ate
112 pans of lasagna for dinner. How many
pans of lasagna were left? (Lesson 6.7)
A. 11/12
B.1 11/12
C.2 1/12
D.3 1/12
Find the value of x. *
43⁰
99°
2x°
A.28
B22.5
C.19
D.71
a box contains a combination of solid-colored tickets: 1/10 of the tickets are green, 1/2 are red , 1/4 are blue, and the remaining 30 tickets are white. how many blue tickets are in the box?
There were 50 blue box at total in the box.
What is combination?In mathematics, a cοmbinatiοn is a way οf selecting items frοm a cοllectiοn where the οrder οf selectiοn dοes nοt matter. Suppοse we have a set οf three numbers P, Q and R. Then in hοw many ways we can select twο numbers frοm each set, is defined by cοmbinatiοn.
In smaller cases, it is pοssible tο cοunt the number οf cοmbinatiοns, but fοr the cases which have a large number οf grοup οf elements οr sets, the pοssibility οf a set οf cοmbinatiοn is alsο higher.
The bοx will be represented as (x)
From the question, we form:
White tickets = (1 - 1/10 - 1/2 - 1/4)x = 30
Blue tickets = 3/20 x = 30
Blue tickets = = 30 x 20 / 3 = 200
Blue tickets = 1/4 x 200 = 50
Thus, There were 50 blue box at total in the box
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What is the area of a right triangle with a height of sixteen and three-fourths meters and a base of 45 meters?
The area of a right triangle is given by the formula:
Area = 1/2 * base * height
Substituting the values given in the problem:
Area = 1/2 * 45 meters * 16 and 3/4 meters
To simplify the computation, we convert the mixed fraction 16 and 3/4 to an improper fraction:
16 and 3/4 = (16 * 4 + 3) / 4 = 67/4 meters
Substituting this value, we get:
Area = 1/2 * 45 meters * 67/4 meters
Simplifying:
Area = 843.75 square meters
Therefore, the area of the right triangle is 843.75 square meters.
Answer: 376 7/8
Step-by-step explanation: if you multiply the base and the height you'll get 754 3/4 since this is a triangle we are talking about it would be halved which would make it 376 7/8.
and im doing the exam and its correct.
A bowl contains 3 apples, 5 bananas, 4 oranges. Mary randomly selects one piece of fruit from the bowl. What is the probability that she selects and apple out of the bowl? Give the answer in the form of a decimal.
Answer:
Step-by-step explanation:
You have a little unclear question with "selects and apple out of the bowl?" I only chose apples (there are 3 of them)
[tex]\frac{3}{12} =\frac{1}{4}[/tex] answer
Step-by-step explanation:
Given,
n(S) = 12
n(A)=3
We have,
P(A) = n(A)/n(S)
= 3 /12
= 1 /4
Lydia has a bag that contains orange chews, cherry chews, and peach chews. She performs an experiment. Lydia randomly removes a chew from the bag, records the result, and returns the chew to the bag. Lydia performs the experiment 62 times. The results are shown below:
A orange chew was selected 25 times.
A cherry chew was selected 24 times.
A peach chew was selected 13 times.
Based on these results, express the probability that the next chew Lydia removes from the bag will be orange or peach as a percent to the nearest whole number.
Answer:
The probability of selecting an orange chew is 25/62, and the probability of selecting a peach chew is 13/62. To find the probability that the next chew Lydia removes from the bag will be orange or peach, we add these probabilities:
P(orange or peach) = P(orange) + P(peach) = 25/62 + 13/62 = 38/62
To express this probability as a percent, we divide the numerator by the denominator, then multiply by 100:
P(orange or peach) = 38/62 = 0.6129...
0.6129... × 100 ≈ 61
Therefore, the probability that the next chew Lydia removes from the bag will be orange or peach, expressed as a percent to the nearest whole number, is 61%
PLEASE HELP DUE SOON
Answer:
output = -3n +1
Step-by-step explanation:
Given an input/output table for a linear function, you want an expression for the output when the input is n.
Arithmetic sequenceThe input values count up from 1, so we can consider the output values to be the terms of an arithmetic sequence.
The first term of the sequence is a1 = -2 (when n=1).
The common difference of the sequence is d = (-5 -(-2)) = -3.
The general (n-th) term of an arithmetic sequence is given by the formula ...
an = a1 +d(n -1)
For the known values of a1 and d, we find the n-th term to be ...
an = -2 +(-3)(n -1)
an = -2 -3n +3 . . . . . . . eliminate parentheses
an = -3n +1 . . . . . . . . collect terms
The term corresponding to an input value of n is ...
-3n +1