Since speckled chickens have both b and w feathers, they must inherit one allele for w feathers and one allele for b feathers. Therefore, to produce the greatest percentage of speckled chickens, the breeder should cross a w chicken with a b chicken.
The Punnett square for this cross would be:
| F F
A | A F A F
A | A F A F
This shows that all offspring (100%) will be heterozygous for both white and b feathers (genotype: AFAF), which is the genotype for speckled feathers. Therefore, the percentage of speckled offspring that will result from this cross is 100%.
Putting the alleles for the hen and rooster in the blank boxes outside the Punnett square would look like this:
| F F
A | A F A F
A | A F A F
Hen Rooster
the graph shows a population of butterflies, t weeks since their migration began.
c. Write an equation for the
population, q, after t weeks.
Answer:
q = 250,000·(0.6^t)
Step-by-step explanation:
You want an equation that models the graph of an exponential function that has an initial value of 250,000 and a value of 150,000 after 1 week.
Exponential functionAn exponential function has the form ...
q = a·b^t
where 'a' is the initial value, and 'b' is the decay factor over a period of one time unit of t.
ApplicationThe graph with this problem shows the initial value (for t=0) to be a=250,000. The decay factor will be ...
b = 150,000/250,000 = 3/5 = 0.6
Then the exponential function can be written as ...
q = 250000·(0.6^t) . . . . . . where t is in weeks
PLEASE HELP! THIS IS MY LAST QUESTION, BUT I DON'T KNOW HOW TO DO IT!
The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases continuously at a relative rate of 7% per day. Find the mass of the sample after six days if there were 552 grams of the substance present at the beginning of the study.
Do not round any intermediate computations, and round your answer to the nearest tenth.
Also, may you please explain how you got the answer, it would be very helpful because I don't understand how to solve this. Thank you!
Answer:
864.3
Step-by-step explanation:
Since the substance is increasing continuously at a relative rate of 7% per day, we can use the continuous exponential growth formula:
P(t) = P(0) * e^(rt)
where:
P(t) is the mass of the substance after "t" days
P(0) is the initial mass of the substance (552 grams in this case)
e is the mathematical constant e (approximately equal to 2.71828)
r is the relative growth rate (0.07 per day in this case)
Substituting the given values, we get:
P(t) = 552 * e^(0.07t)
To find the mass after 6 days, we can substitute t = 6:
P(6) = 552 * e^(0.07*6)
Using a calculator, we get:
P(6) ≈ 864.3 grams
Therefore, the mass of the substance after 6 days is approximately 864.3 grams rounded to the nearest tenth.
Annual dues for the Mathematical Association of America were $3 in 1916. They were $175 in 2023.
a) Based on the inflation rate, how much would the $3 dues in 1916 be in 2023 dollars?
Round to the nearest dollar. (Hint: The answer isn’t $175)
b) In 2023, after adjusting for inflation (your answer to part a), what was the absolute change for the dues compared with the actual price?
Note: the answer is not $175-$3 = $172
c) In 2023 (your answer to part a), what was the relative change for the dues compared with the actual price? Round to the nearest percent.
Note: the answer is not ($175-$3)/$3=57.33 = 5733%
d) In your opinion, which measure of change is most meaningful, and why?
a) Based on the inflation rate, the $3 dues in 1916 would be worth $57.39 in 2023 dollars.
b) In 2023, after adjusting for inflation, the absolute change for the dues was $117.61.
c) In 2023, after adjusting for inflation, the relative change for the dues was 204.84%, rounded to the nearest percent.
d) The relative change is most meaningful, as it is the easiest to interpret. It shows the percentage of the dues increase over the time period, which gives a clear indication of the rate of inflation.
a) To find the value of the $3 dues in 1916 in 2023 dollars, we need to use the formula for inflation:
FV = PV(1 + r)^t
where FV is the future value, PV is the present value, r is the inflation rate, and t is the number of years.
Assuming an average inflation rate of 3% per year, we can plug in the values and solve for FV:
FV = 3(1 + 0.03)^(2023-1916)
FV = 3(1.03)^107
FV = 3(19.13)
FV = $57.39
So, the $3 dues in 1916 would be worth $57.39 in 2023 dollars.
b) To find the absolute change for the dues compared with the actual price, we need to subtract the value of the dues in 1916 in 2023 dollars from the actual price in 2023:
Absolute change = $175 - $57.39 = $117.61
c) To find the relative change for the dues compared with the actual price, we need to divide the absolute change by the value of the dues in 1916 in 2023 dollars and multiply by 100 to get a percentage:
Relative change = ($117.61/$57.39) * 100 = 204.84%
d) In my opinion, the relative change is the most meaningful measure of change because it takes into account the value of the dues in 1916 in 2023 dollars and shows how much the dues have increased relative to their original value. The absolute change only shows the difference in dollar amounts, but does not account for the effects of inflation.
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i need help with this questchin (image attach)
Answer:
scalene triangle
Step-by-step explanation:
in a scalene triangle, all the sides are not equal
IH is not equal to HJ and also is not equal to JI
1.State domain and range
2.Is it a function
3.Is it a one to one function
1. domain: All real numbers. range: [2,4]
2. It is a function.
3. Not one to one function.
What is function?
A function is a relationship or expression involving one or more variables. It has a set of input and outputs
1. domain of the given function would be, real numbers.
range of the function is [2,4].
2. Yes. It is a function.
3. No it is not one to one function. It is many to one function?
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Is (2,1) a solution to this system of equations?
8x+7y=11
x+y=3
(2,1) is a solution to the system of equations 8x+7y=11 and x+y=3.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To check if (2,1) is a solution to the system of equations:
8x + 7y = 11
x + y = 3
We substitute x = 2 and y = 1 into both equations:
For the first equation: 8(2) + 7(1) = 16 + 7 = 23
For the second equation: 2 + 1 = 3
Hence, we can see that both equations are true when x = 2 and y = 1.
Therefore, (2,1) is a solution to the system of equations.
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Suppose {x1,x2,..., xn} and {y1, y2, ..., yn} are two independent samples from population N (µ1, δ^2 1) and N (µ2, δ^2 2), respectively. We wish to test H0 : µ1 = µ2 vs. HA: µ1 > µ2. Assume δ = δ2 = δ = 1. a) Find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 and the sample size is 100. Use a significance level of 0.05. Hint: x -y ~ N (µ1 - µ2, 2δ^2/n). b) Suppose a research wishes to detect µ1 - µ2 = 1 with power at least 80%, how large should the sample size be? Show the key steps.
The sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.
The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we wish to find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 when the sample size is 100 and the significance level is 0.05.
a) First, we need to find the critical value for the z-test at a significance level of 0.05. This can be found using a z-table or a calculator. The critical value is 1.645.
Next, we need to find the standardized difference between the two means, which is (δ1 - δ2)/√(2δ^2/n) = (0.1)/√(2(1)^2/100) = 0.1/√(0.02) = 0.7071.
Finally, we can find the power of the test by subtracting the standardized difference from the critical value and finding the corresponding probability from a z-table or calculator. The power is 1 - P(Z < 1.645 - 0.7071) = 1 - P(Z < 0.9379) = 1 - 0.8264 = 0.1736.
Therefore, the power of the z-test to detect a difference of δ1 - δ2 = 0.1 with a sample size of 100 and a significance level of 0.05 is 0.1736.
b) To find the sample size needed to detect µ1 - µ2 = 1 with power at least 80%, we can use the formula for power:
Power = 1 - P(Z < (critical value - standardized difference))
We can rearrange this formula to solve for the sample size:
Standardized difference = (critical value - Z value corresponding to power)/√(2δ^2/n)
n = (2δ^2(critical value - Z value corresponding to power)^2)/(standardized difference)^2
Plugging in the values for critical value (1.645), Z value corresponding to power (0.8416), and standardized difference (1), we get:
n = (2(1)^2(1.645 - 0.8416)^2)/(1)^2 = 322.69
Therefore, the sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.
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A certain number is multiplied by 7 and
11 is added to the product. The total is
67. What is the number?
Answer:
the answer is 8
Step-by-step explanation:
subtract 11
67 - 11 = 56
Divide 7 to find the answer
56/7 = 8
what equivalent expression for (32 • 54)3?
Answer:
5,184 from my knowledge
Please HELP! I'll DO ANYTHING!!!!
If you could provide me more details, including the dimensions of the two triangle ' angles and sides, I might be able to evaluate whether or not they are comparable.
What precisely is a triangle?A triangle is a polygon because it includes four or so additional parts. It features a simple rectangular shape. A rectangle having edges A, B, and C is referred to as a triangle. When the sides are actually not collinear, Euclidean geometry yields a single plane and cube. If a triangle contains three parts and three angles, it is a polygon. The intersections of a triangle's three sides are referred to as its corners. The sum of a triangle's sides is 180 degrees.
Two polygons must have congruent corresponding angles and proportionate corresponding sides in order to be considered comparable.
If you could provide me more details, including the dimensions of the two polygons' angles and sides, I might be able to evaluate whether or not they are comparable.
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The price of stock a at 9 AM was 12.58 and the price has been increasing at a rate of 0.09 each hour at noon the price of stock B what is 13.08 it begins to decrease at the rate of 0.12 each hour if the rate continues in how many hours will the prices of the two stalks me the same
Practice math quadratic equation
4a^2+6=0
The given quadratic equation does not have a real solution.
What are Quadratic Equations?Quadratic equations are polynomial equations of second degree.
The general form of a quadratic equation is ax² + b x + c = 0.
The given quadratic equation is,
4a² + 6 = 0
We have to find the solution of the quadratic equation.
Subtracting both sides by 6,
4a² + 6 - 6 = 0 - 6
4a² = -6
a² = -6/4
a² = -3/2
Taking square root on both sides,
a = √(-3/2), which implies that the given quadratic equation does not have a real solution.
Hence there are no real solution for the given equation.
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explain how 2 2/3 compares to another mixed numbers
Answer:
To compare 2 2/3 to another mixed number, you need to convert both mixed numbers to improper fractions.
To convert 2 2/3 to an improper fraction, you need to multiply the whole number (2) by the denominator of the fraction (3), and then add the numerator (2). This gives you:
2 2/3 = (2 x 3) + 2/3 = 6 + 2/3 = 20/3
Now that you have the improper fraction for 2 2/3, you can compare it to the improper fraction of another mixed number.
For example, if you want to compare 2 2/3 to 4 1/2, you would convert 4 1/2 to an improper fraction:
4 1/2 = (4 x 2) + 1/2 = 8 + 1/2 = 17/2
Now that you have both mixed numbers as improper fractions, you can compare them by finding a common denominator and then comparing the numerators. In this case, the common denominator is 6, so you need to multiply 17/2 by 3/3 to get:
17/2 = (17 x 3)/(2 x 3) = 51/6
Now you can compare 20/3 and 51/6 by looking at their numerators:
20/3 = 6.666...
51/6 = 8.5
So 2 2/3 is less than 4 1/2.
Factor. 144p2−9q2 a. 9(p−q)2 b. (12p+3q)(12p−3q) C. (12p+3q)2 d. (12p−3q)2
The complete factorization of the expression 144p² - 9q² is (12p + 3q)(12p − 3q). The correct answer is B.
To factor 144p² - 9q², we can use the difference of squares formula, which states that:
a² - b² = (a + b)(a - b)
We can see that 144p² is a perfect square, as it is the square of 12p. Similarly, 9q² is a perfect square, as it is the square of 3q. So we can write:
144p² - 9q² = (12p)² - (3q)²
Now we can use the difference of squares formula to factor:
(12p)² - (3q)² = (12p + 3q)(12p - 3q)
Simplifying, we can also write this as:
144p² - 9q² = 3²(16p² - q²)
So, the factored form of 144p² - 9q² is:
144p² - 9q² = 3²(16p² - q²) = (12p + 3q)(12p - 3q)
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Find the null space of \( A \). a. \( A=\left[\begin{array}{ccc}1 & -2 & 0 \\ 1 & 0 & 2\end{array}\right] \) b. \( B=\left[\begin{array}{cccc}1 & 3 & 4 & 0 \\ 0 & 2 & 4 & 4 \\ 1 & 1 & 0 & -4\end{array
The null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
To find the null space of a matrix, we need to solve the equation \( Ax=0 \), where \( x \) is a vector in the null space.
For matrix \( A \), we can set up the following system of equations:
\begin{align*}
x-2y &= 0 \\
x+2z &= 0
\end{align*}
Solving for \( x \) and \( y \) in terms of \( z \) gives us:
\begin{align*}
x &= -2z \\
y &= -z
\end{align*}
So the null space of \( A \) is the set of all vectors of the form \( \left[\begin{array}{c}-2z \\ -z \\ z\end{array}\right] \), where \( z \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right] \), so the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \).
For matrix \( B \), we can set up the following system of equations:
\begin{align*}
x+3y+4z &= 0 \\
2y+4z+4w &= 0 \\
x+y-4w &= 0
\end{align*}
Solving for \( x \), \( y \), and \( z \) in terms of \( w \) gives us:
\begin{align*}
x &= 4w \\
y &= -2w \\
z &= w
\end{align*}
So the null space of \( B \) is the set of all vectors of the form \( \left[\begin{array}{c}4w \\ -2w \\ w \\ w\end{array}\right] \), where \( w \) is any scalar. This can also be written as the span of the vector \( \left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right] \), so the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
Therefore, the null space of \( A \) is \( \text{span}\left\{\left[\begin{array}{c}-2 \\ -1 \\ 1\end{array}\right]\right\} \) and the null space of \( B \) is \( \text{span}\left\{\left[\begin{array}{c}4 \\ -2 \\ 1 \\ 1\end{array}\right]\right\} \).
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Orange juice drinks were to be distributed to the schools in the District of Nueva Valencia South. 950 packs were given to La Paz Elementary School, 785 to Igdarapdap Elementary School, 1, 370 to Cabalaynan Elementary School. If there are 5, 000 packs of juice drinks, how many were distributed to different schools? How many packs were not given?
3. First Solution: ______________
4. Second Solution: ______________
By those 2 ways of solution, a total of 3,105 packs of juice drinks were distributed to different schools.
How to find out the numberFirst Solution:To find out how many packs of juice drinks were distributed to different schools, we need to add the number of packs given to each school.
950 (La Paz Elementary School) + 785 (Igdarapdap Elementary School) + 1,370 (Cabalaynan Elementary School) = 3,105 packs of juice drinks
So, a total of 3,105 packs of juice drinks were distributed to different schools.
Second Solution:To find out how many packs of juice drinks were not given, we need to subtract the number of packs distributed to different schools from the total number of packs available.
5,000 (total number of packs) - 3,105 (number of packs distributed to different schools) = 1,895 packs of juice drinks
So, a total of 1,895 packs of juice drinks were not given.
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The value of y varies directly with x. When y = 1.5, x = 5. What is the value of y when x is 30?
variables y = 1.5, x = 5, hence, the value of y is 9 when x is 30
How are linear equations solved?Two variables, such as x and y, are proportional to one another and their ratio is constant when they vary directly. In other words, if y and x vary directly, their relationship can be written as y = kx, where k is the proportionality constant. With the knowledge that y = 1.5 when x = 5 as provided, we can utilise this information to find the value of y when x equals 30:
1.5 = k(5) \sk = 1.5/5 \sk = 0.3
We can use the equation y = kx to get the value of y for x = 30 now that we know the value of k:
y = 0.3(30) \sy = 9
Hence, the value of y is 9 when x is 30.
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please this is the last thing I have to do and need help
Answer:you have to think but maybe you can put de answer is y =(1.2)x
Step-by-step explanation:
the circumference of a circle is 23r cm. what is exact the area of the circle?
As a result, the circle's precise size is (529/4)π³ square centimetres.
Explain what a circle is?A circle is a closed, two-dimensional shape where every point in the surface is equally spaced from a central point. The line of mirror symmetry is formed by all lines that traverse the circle. Additionally, every point has circular symmetry around the centre.
The circumference of a circle is given by the formula:
C = 2πr
where r is the radius of the circle. We can rearrange this formula to solve for the radius:
r = C / 2π
When we substitute the circumference's specified number, we obtain:
r = (23r) / (2π)
Simplifying:
r = (23/2)π
Now that we know the radius, we can use the formula for the area of a circle:
A = πr²
Substituting the value we found for the radius, we get:
A = π[(23/2)π]²
Simplifying:
A = π(529/4)π²
A = (529/4)π³
Therefore, the exact area of the circle is (529/4)π³ square cm.
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3 halves of a cupcake for my family plus some extra for my 2 friends. They will each want a quarter of a cupcake.
15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
5 halves of a cupcake for your family, which is equivalent to 2.5 cupcakes.
To divide this evenly among your two friends who each want a quarter of a cupcake, we can start by converting the amount of cupcakes you have to quarters:
2.5 cupcakes × 4 quarters/cupcake = 10 quarters of a cupcake
Now we can divide the 10 quarters of a cupcake equally between your two friends:
10 quarters of a cupcake / 2 friends = 5 quarters of a cupcake per friend
Hence, a total of 5 + 5 + 5 = 15 quarters of a cupcake, which is equivalent to 3.75 cupcakes in total.
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Which function is equivalent to y=3(x−2)2+6?
By answering the above question, we may state that As a result, y = function 3(x2)2+6 is identical to the function y = 3x212x+18.
what is function?Mathematicians research numbers, their variants, equations, forms, and related structures, as well as possible locations for these things. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a function. Every input contributes to a single, distinct output in a connection between inputs and outputs known as a function. A domain, codomain, or scope is assigned to each function. Often, functions are denoted with the letter f. (x). The key is an x. There are four main categories of accessible functions: on functions, one-to-one capabilities, so many capabilities, in capabilities, and on functions.
The vertex of the function y = 3(x2)2+6 lies at (2, 6), and the coefficient 3 denotes that the parabola widens upwards.
This function needs to be expanded and simplified in order to be written in standard form:
y = 3(x−2)2+6 y = 3(x−2)(x−2)
6 y equals 3 (x24x+4) + 6 y equals 3 (x212x+18)
As a result, y = 3(x2)2+6 is identical to the function y = 3x212x+18.
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-5i - 3 = -43
Answer and work shown
Answer:
i = 8
Step-by-step explanation:
To solve this equation, we need to isolate the variable i on one side of the equation.
-5i - 3 = -43
First, we add 3 to both sides of the equation:
-5i - 3 + 3 = -43 + 3
Simplifying the left side:
-5i = -40
Now we divide both sides by -5:
-5i / -5 = -40 / -5
Simplifying:
i = 8
Therefore, the solution to the equation -5i - 3 = -43 is i = 8.
Students are making lemonade from a powdered lemon drink mix.
Wyatt mixes 2 cups of water and 1 cup of powdered lemon mix. Emma
mixes 12 cups of water and 7 cups of powdered lemon mix. Use Wyatt
and Emma's percent of water to determine whose mix will be more
watery.
Wyatt's mix will be more watery compared to Emma's mix.
What does it mean for a mixture to be "more watery"?
The percentage of water in a mix is an essential factor that determines its taste, texture, and consistency. A higher percentage of water in a lemonade mix will make it more watery and less concentrated. In contrast, a lower percentage of water will make the mix less watery and more concentrated. The right balance of water and lemon mix is crucial to make a perfect lemonade.
Calculation for percent of water in the lemon drink mix:
To find the percent of water in the lemonade mixes, we need to divide the amount of water by the total volume of the mix and then multiply by 100.
For Wyatt's mix:
Percent of water = (2 cups water / (2 cups water + 1 cup lemon mix)) x 100
Percent of water = 66.67%
For Emma's mix:
Percent of water = (12 cups water / (12 cups water + 7 cups lemon mix)) x 100
Percent of water = 63.16%
From the calculations, we can see that Wyatt's mix has a higher percentage of water than Emma's mix. Therefore, Emma's mix will be less watery compared to Wyatt's mix.
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Rachel and David were shopping for holiday gifts when they noticed a Thanksgiving sweater on the discount rack. Rachel really wanted the sweater, even though she wouldn’t be wearing it until Thanksgiving of 2021! .Rachel has a coupon for an additional 25% off the sale price of the sweater. If she pays for the shirt with a $10 bill, what will her change be?
Answer:
Unfortunately, the sale price of the sweater and the original price are not given in the problem, so we cannot calculate the exact change that Rachel will receive. We need more information to solve the problem.
In triangle ABC, angle B = 44°, IF AB =BC, SO find angle A and C
The value of angle A and C is 68° respectively
What is sum of angle in a triangle?The sum of angle In a triangle is 180°. This means that A+B+C = 180°.
An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as havingat least two sides of equal length.
Since AB = BC, then the triangle is an isosceles triangle.
The sum of angle in a triangle is 180. This means that A+B+C = 180
Since AB = BC , then angle A = angle C
therefore , substitute C for A
C +B + C = 180
2C + 44 = 180
2C = 180-44
2C = 136
divide both sides by 2
C = 136/2
C = 68°
then A= C = 68°
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Determine the LCM of the given polynomials: Leave your answer in factored form. \[ x^{2}+8 x+16 \text { and } x^{2}+11 x+28 \]
The LCM of the polynomials x² + 8x + 16 and x² + 11 x + 28 is (x + 4)(x + 4)(x + 7).
To determine the LCM of the given polynomials, we need to find the smallest polynomial that is a multiple of both x² + 8x + 16 and x² + 11 x + 28.
First, let's factor the given polynomials:
x² + 8x + 16 = (x + 4)(x + 4)
x² + 11 x + 28 = (x + 4)(x + 7)
Now, we can see that the LCM of these two polynomials is the product of the highest power of each factor:
LCM = (x + 4)(x + 4)(x + 7)
So, the LCM of the given polynomials in factored form is (x + 4)(x + 4)(x + 7).
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A jewlery shop sells 240 neaklesses in a month. 180 of the neaklesses were sold via he shops website, the rest were sold in a high street shop. Work out the ratios of online sales to shop sales, give your answer in its simplest form
The ratios of online sales to shop sales of A jewelery shop which sold 240 necklaces in a month is equals to the 3:1.
We have a jewelery shop and they sold there necklaces to the different shops.
Total number of sold necklaces in a month = 240
Number of online sold necklaces in a month = 180
Total online sales of jewelery shop = 180
and rest of necklaces were sold in a high street shop. So, the number of sold necklaces in high street shop during a month = total number of sold necklaces - online sold necklaces
= 240 - 180 = 60
Total shop sales jewelery shop = 60 necklaces
Ratio is used to determine the relationship between two or more things ( like size, quantity, etc.). It is represented by a/b or a : b ( read as a ratio b). Here, we have to calculate the ratios of online sales to shop sales. So, the ratio of online sales to shop sales = 180 : 60 or 180/60
Simplify the expression,
=> 180/60 = 3
Hence, required ratio is 3: 1.
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PLEASE HELP ME COMPLETE THIS ITS DUR TMR!!!
The total number of dimes in the container is 6 while the total number of quarters is 11.
How to solve the problemTo solve this problem, we will be using the simultaneous equation. The dimes and quarters will be assigned some figures:
First:
d + q = 17
10d + 25q = 335
This second equation is so because the value of the coins was converted to cents.
Where $1 = 100 cents
Next, we will resolve the figures to get the values for d and q as follows:
Multiply both sides of the first equation by -10
-10d - 10q = -170
Now, we shall minus the first equation from the second one to give:
15q = 165
q = 165/15
= 11
Substitute the value of q in the first equation:
d + 11 = 17
d = 17 - 11
d = 6
Substituting the values in the original equation will give the final sum of 335 for the coins.
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The estimated population, in thousands of people , of city A can be modeled by the function f(t)=15(1. 03) , where is the number of decades (10-year period) since 1980 the estimated population , in thousands of people , of city B can be modeled by the function g(t)=0. 4t+16, where t is the number of decades since 1980
Part A) Estimated Populations of Cities A and B are given.
Part B) City A's estimated population is increasing at a faster rate than City B's estimated population for each decade.
Part C) the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3)
Part D) The models may not realistically predict population growth over very long time scales, as they do not take into account other factors
Part A:
Estimated Populations of Cities A and B
Decades Since 1980 City A (in thousands) City B (in thousands)
0 15 16
1 19.5 16.4
2 25.2 17.8
3 32.7 19.2
4 42.4 20.6
Part B:
Population Increases from the previous Decade for Cities A and B
Decades Since 1980 City A (in hundreds) City B (in hundreds)
0 - -
1 450 40
2 570 140
3 750 140
4 970 140
Interpretation:
From the table, we can see that City A's estimated population is increasing at a faster rate than City B's estimated population for each decade. This indicates that City A is growing more rapidly than City B, and may continue to do so in the future.
Part C:
To find the start of the decade when the estimated population of City A first exceeds the estimated population of City B, we need to solve the equation:
15[tex](1.03)^t[/tex] > 0.4t + 16
where t is the number of decades since 1980.
One way to solve this is to use a graphing calculator to graph both functions and find their intersection point. Alternatively, we can use trial and error to test different values of t until we find the smallest one that satisfies the inequality.
Using a graphing calculator, we find that the estimated population of City A first exceeds the estimated population of City B at the start of the 4th decade (t = 3), when the estimated population of City A is approximately 32.7 thousand people, and the estimated population of City B is approximately 19.2 thousand people.
Part D:
The models may not realistically predict population growth over very long time scales, as they do not take into account factors such as changes in birth and death rates, migration patterns, and economic or environmental changes that may affect population growth. Additionally, the models assume that population growth will continue to follow a linear or exponential pattern, which may not be accurate in the long term. Therefore, while the models can provide useful estimates for short- to medium-term population trends, they should be used with caution when making long-term projections.
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The correct question should be:
The estimated population, in thousands of people, of city A can be modeled by the function SO) = 15(1.03), where is the number of decades (10-year period) since 1980 The estimated population, in thousands of people, of the city can be modeled by the function (1)-0.41 +16, where is the number of decades since 1980
Part A) Complete this table, showing both estimated population values, rounded to the nearest tenth for each city based on the number of decades since 1980 Estimated Populations of Cities A and B City Decades Since 1980 City B (thousands of people) (thousands of people) 0 . 2 3 4
Part B) Using the table in Part A, complete this table showing population increases, in hundreds of people, cach decade Population Increases from previous Decade for Cities A and B Decades Since 1980, Increase of City A Increase of City B (hundreds of people), (hundreds of people), fin)-(-1) g) -R-1) 2 3 4 Interpret the differences in the increases of the estimated populations of the two cities based on the functions that model cach city's population. Provide evidence to support your answer
Part C) At the start of which decade will the estimated population of city A first exceed the estimated population of city B? What will be the estimated populations of each city at the start of that decade? Provide evidence to support your answers.
Part D) Based on the behavior of the functions, do the models realistically predict population growth over very long time scales? Provide evidence to support your answer.
Determine the equation of the circle whose center is (-1, -1) and passes through the point (7, -7). a. (2 + 1)2 + (y + 1)2 = 100 b. (x + 1)2 + (y + 1)2 = 10 c. (+1)2 + (y+ 1)2 = √10 d. (2-7)2 + (y + 7)2 = √10
Answer:
its i think algebraic equation
The equation of the circle whose center is (-1, -1) and passes through the point (7, -7) is (x + 1)2 + (y + 1)2 = 100. This can be found using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is √((x2 - x1)2 + (y2 - y1)2). In this case, the distance between the center and the point on the circle is the radius of the circle. So, we can plug in the values for the center and the point on the circle to find the radius:√((7 - (-1))2 + (-7 - (-1))2) = √((7 + 1)2 + (-7 + 1)2) = √(82 + (-6)2) = √(64 + 36) = √100 = 10Therefore, the radius of the circle is 10. Now, we can use the general equation of a circle, (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius, to find the equation of the circle. Plugging in the values for the center and the radius, we get:(x - (-1))2 + (y - (-1))2 = 102(x + 1)2 + (y + 1)2 = 100So, the equation of the circle is (x + 1)2 + (y + 1)2 = 100, which is option a.
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