From the given information provided, the number of people having brown eyes in town is 180.
If the probability that a person in the town has brown eyes is 2/5, then we can expect that 2 out of every 5 people have brown eyes.
To find the number of people in the survey who would be expected to have brown eyes, we can use the following proportion:
(2/5) = (x/450)
where x is the number of people expected to have brown eyes.
Solving for x, we can cross-multiply:
5x = 2 × 450
5x = 900
x = 180
Therefore, the expected number of people in the survey who would have brown eyes is 180.
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Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.
To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.
Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:
30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches
The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.
The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.
Now, we can calculate the volume of the box by multiplying its length, width, and height:
Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.
In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.
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Can some one solve this and show their work please
Answer:
m = 2n = 7Step-by-step explanation:
we solve with two equations between the corresponding sides
9m = 7m + 4
9m - 7m = 4
2m = 4
m = 2
----------------------------------
check
9 x 2 = 7 x 2 + 4
18 = 18
this answer is good
n + 6 = 2n - 1
n + 7 = 2n
7 = n
-----------------------------------
7 + 6 = 2 x 7 - 1
13 = 13
this answer is good
A function is shown in the box. What is the value of this function for f(-8)?
(Write the answer as an improper fraction in lowest terms.)
Answer:
f(x) = (5/6)x - (1/4)
f(-8) = (5/6)(-8) - (1/4)
f(-8) = (5/3)(-4) - (1/4)
f(-8) = (-20/3) - (1/4)
f(-8) = (-80-3)/12
f(-8) = -83/12
Which of the following are equations of straight lines? Select all that apply. Please keep in mind that for questions like this where there are one or more correct answers, Canvas will deduct points for incorrect selections. yhat = 23 + 4w yhat = 2c +34 yhat = 2h yhat= d2 + 3 yhat = 23r+ 4 yhat=2s + 3t yhat= 3
The equations of straight lines are \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t. Option(A),(B) and (F) are correct.
A line in the coordinate plane can be described with the help of a linear equation, that is, an equation that has a first-degree expression, like y = 2x – 3.
There are many ways to put the equation of a line in the form y = mx + b,
where m is the slope and
b is the y-intercept,
but they all require the use of algebraic properties of equations, such as addition, subtraction, multiplication, division, and substitution.
The equations of straight lines among the following are: \hat{y} = 2h, \hat{y} = 23r + 4 and \hat{y}= 2s + 3t
Hence, the correct options are:Option A: \hat{y} = 2h , Option B: \hat{y} = 23r + 4 and Option F: \hat{y}= 2s + 3t.
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Seven bags of cement weighs 3kg 52g what Is the weight of the each?
Answer:
436g
Step-by-step explanation:
1kg=1000g
3kg=3000g
3000+52=3052
3052÷7=436
50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
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If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?
As the demand for tobacco is inelastic so the consumers are the group who are less responsive to a higher price as an outcome of it the consumers will have to bear the largest share of the tobacco tax.
This inelasticity of demand will lead to only a small decline in the quantity demanded after the tax have been leived , therefore the deadloss weight will be in really small degree. the percentage increase in price of any amount will overcome a smaller decline in the quantity which eventually would lead to a rise in the tax revenue collection.
Inelasticity of demand refers to the degree to which the quantity demanded of a particular good or service changes in response to a change in its price. When demand is inelastic, a change in price will result in a proportionally smaller change in quantity demanded. This is typically the case for goods or services that are considered necessities or have few substitutes available.
For example, if the price of insulin, a life-saving medication for diabetics, increases by 10%, it is unlikely that the quantity demanded will decrease by 10%. People with diabetes require insulin to manage their condition, and there are few substitutes available, so they are willing to pay a higher price to maintain their health.
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Complete Question: -
Suppose the supply of tobacco is elastic and the demand for tobacco is inelastic. If an excise tax is levied on the suppliers of tobacco, will the incidence fall mostly on consumers or mostly on producers? Will there be a large amount or small amount of deadweight loss? Will tax revenue from the tobacco tax fall or rise?
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
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In the morning 134 books were checked out from the library.in the afternoon 254 books were checked out and 188 books were checked out in the evening.how many books were checked out in the library that day?
Answer:
576 books.
Step-by-step explanation:
134+254+188=576 books in total.
Hopefully this helps!
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
cindy and tom, working together, can rake the yard in 8 hours. working alone, tom takes twice as long as cindy. how many hours does it take cindy to rake the yard alone?
Cindy and tom, working together, can rake the yard in 8 hours. Working alone, Tom takes twice as long as Cindy, it takes Cindy to rake the yard 2 hours
How do we calculate the time it takes Cindy?To find the time it takes Cindy to rake the yard alone, let's use the following steps:Let x be the time taken by Cindy to rake the yard alone . Then the time taken by Tom to rake the yard alone will be 2xIt is given that Cindy and Tom can rake the yard in 8 hours when they work together.
Using the formula for working together, we get:[tex]\[\frac{1}{x} + \frac{1}{2x} = \frac{1}{8}\][/tex] Multiplying the equation by the least common multiple of the denominators, we get:[tex]\[16 + 8 = 2x\][/tex] Simplifying, we get:[tex]\[2x = 24\][/tex]Dividing both sides by 2, we get:[tex]\[x = 12\][/tex]Therefore, it takes Cindy 12 hours to rake the yard alone.
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What are the zeros of g(x) = x3 + 6x2 − 9x − 54?
Answer:
Solution: Given, the equation is x3 + 6x2 - 9x - 54. We have to find the real zeroes of the given equation. Therefore, the roots of the equation are +3, -3 and -6.
4) Ella drives 60 miles per hour. How far will she drive in 2% hours?
Answer: 1.2 miles
Step-by-step explanation:
1 hour = 60 min
60 x 0.02 = 1.2 1 minute and 20 seconds has elapsed
60 miles/ every 60 minutes or 1 mile a minute
1 x 1.2 = 1.2
she has traveled 1.2 miles
Answer: The answer is 120 mph (miles per hour)
Step-by-step explanation:
The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.
So, you need to do 60 x 2, and you will get the answer 120.
And there's your answer!
Given that m∠A=(16x)°, m∠C=(8x+20)°, and m∠D=128°, what is m∠B
The value of m∠B is 212 - 24x.
How did we get the value?The totality of the angles in a quadrilateral is always amount to 360°. This is a primary property of all quadrilaterals, irrespective of their shape or size.
As a result, irrespective of the shape say if you are dealing with a square, rectangle, parallelogram, trapezoid, or any other type of quadrilateral, the totality of the angles will always be sum to 360°.
To determine the value of m∠B, one can employ the notion that the sum of the angles in a quadrilateral is 360°.
Thus,
m∠A + m∠B + m∠C + m∠D = 360
Substituting the given values, we get:
(16x)° + m∠B + (8x+20)° + 128° = 360
Simplifying and solving for m∠B, we get:
m∠B = 360 - (16x)° - (8x+20)° - 128°
m∠B = 212 - 24x
Therefore, the value of m∠B is 212 - 24x.
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Compute the value of the expression without using a calculator
Answer:
Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:
7^(log_7(12)) = 12
Therefore, the value of the expression is 12.
Find the following percentiles for the standard normal distribution. Interpolate where appropriate. (Round your answers to two decimal places.)a. 81stb. 19thc. 76thd. 24the. 10 th
The percentiles for the standard normal distribution
a. 0.93
b. -0.88
c. 0.67
d. -0.65
e. -1.28
To determine the percentiles for the standard normal distribution, use the standard normal distribution table. Percentiles for standard normal distribution are given by the standard normal distribution table.
The standard normal distribution is a special type of normal distribution with a mean of 0 and a variance of 1.
Step 1: Write down the given percentiles as a decimal and round to two decimal places.
For example, for the 81st percentile, 0.81 will be used.
Step 2: Use the standard normal distribution table to find the corresponding z-score.
Step 3: Round off the obtained answer to two decimal places.
a) 81st percentile:
The area to the left of the z-score is 0.81.
The corresponding z-score is 0.93.
Hence, the 81st percentile for the standard normal distribution is 0.93.
b) 19th percentile:
The area to the left of the z-score is 0.19.
The corresponding z-score is -0.88.
Hence, the 19th percentile for the standard normal distribution is -0.88.
c) 76th percentile:
The area to the left of the z-score is 0.76.
The corresponding z-score is 0.67.
Hence, the 76th percentile for the standard normal distribution is 0.67.
d) 24th percentile:
The area to the left of the z-score is 0.24.
The corresponding z-score is -0.65.
Hence, the 24th percentile for the standard normal distribution is -0.65.
e) 10th percentile:
The area to the left of the z-score is 0.10.
The corresponding z-score is -1.28.
Hence, the 10th percentile for the standard normal distribution is -1.28.
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Your monthly take-home pay is $900. Your monthly credit card payments are about $135. What percent of your take-home pay is used for your credit card payments?
i came up with $765
Answer:15 percent
Step-by-step explanation:
question if all other factors are held constant, which of the following results in an increase in the probability of a type ii error? responses the true parameter is farther from the value of the null hypothesis. the true parameter is farther from the value of the null hypothesis. the sample size is increased. the sample size is increased. the significance level is decreased. the significance level is decreased. the standard error is decreased. the standard error is decreased. the probability of a type ii error cannot be increased, only decreased.
If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.
What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.
A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.
What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.
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the picture pls answer my picture.
Answer:
$63 more in tax
Step-by-step explanation:
Takis is 5.25 in tax
PlayStation is 68.25
well, we know the tax is 10.5% so let's get them for both.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{10.5\% of 49.99}}{\left( \cfrac{10.5}{100} \right)49.99} ~~ \approx ~~ 5.25[/tex]
[tex]\stackrel{\textit{10.5\% of 649.99}}{\left( \cfrac{10.5}{100} \right)649.99} ~~ \approx ~~ 68.25\hspace{9em}\underset{ \textit{taxes' difference} }{\stackrel{ 68.25~~ - ~~5.25 }{\approx\text{\LARGE 63}}}[/tex]
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is______. A) 0.24 B) 0.34 C) 0.41 D) 0.66
The percentage of customers who do not purchase clubs or balls is 0.66 or 66%.
Ten percent of customers who walk into a golf store purchase a golf club and 30% of customers purchase golf balls. Six percent of customers purchase both clubs and balls. The percentage of customers who do not purchase clubs or balls is 0.66.
Given that, The percentage of customers who purchase golf clubs = 10%The percentage of customers who purchase golf balls = 30%The percentage of customers who purchase both clubs and balls = 6%To find out the percentage of customers who do not purchase clubs or balls, we have to subtract the percentage of customers who purchase either clubs or balls or both from 100%.
Percentage of customers who purchase either clubs or balls or both = 10% + 30% - 6% = 34% Percentage of customers who do not purchase clubs or balls = 100% - 34% = 66%.
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When a homeowner has a 25-year variable-rate mortgage loan, the monthly payment R is a function of the amount of the loan A and the current interest rate i (as a percent); that is, R = f(A). Interpret each of the following. (a) R140,000, 7) - 776.89 For a loan of $140,000 at 7% interest, the monthly payment is $776.89. For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan. For a loan of $140,000 at 7.7689% interest, the monthly payment is $700.
The monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89 is the correct statement(A).
The statement given is describing a function that relates the monthly payment R of a 25-year variable-rate mortgage loan to the loan amount A and the current interest rate i.
The given values are R = $776.89 and A = $140,000, with an interest rate of 7%. This means that the monthly payment required to pay off a loan of $140,000 at 7% interest would be $776.89.
However, the other statements are incorrect interpretations. For instance, the statement "For a loan of $140,000 at 7.7689% interest, 700 monthly payments would be required to pay off the loan" is incorrect.
This is because the number of payments required to pay off a loan depends not only on the loan amount and interest rate, but also on the term of the loan.
Similarly, the statement "For a loan of $140,000 at 7% interest, 776.89 monthly payments would be required to pay off the loan" is also incorrect, as the number of payments required would be determined by the term of the loan.
Finally, the statement "For a loan of $140,000 at 7.7689% interest, the monthly payment is $700" is also incorrect. This is because, for the given loan amount and interest rate, the monthly payment required would be $776.89, as calculated above.
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how can you convert a given number of fluid ounces to find equivalent number of cups explian
Step-by-step explanation:
There are 8 fluid ounces in a cup....
divide the number of ounces by 8 to find the number of cups
# ounces / 8 ounces/cup = cups
f of x is equals to 3 - 2 x and g of x is equals to X Minus x square + 1 where x is an element of I have set of numbers find the inverse of G and the value for X for which f of G is equals to g of f.
The inverse of the function g(x) is g⁻¹(x) = 0.5 + √(1.25 - x) and the value for x for which f(g(x)) = g(f(x)) is 1
Calculating the inverse of g(x)Given that
f(x) = 3 - 2x
Rewrite as
g(x) = -x² + x + 1
Express as vertex form
g(x) = -(x - 0.5)² + 1.25
Express as equation and swap x & y
x = -(y - 0.5)² + 1.25
Make y the subject
y = 0.5 + √(1.25 - x)
So, the inverse is
g⁻¹(x) = 0.5 + √(1.25 - x)
Calculating the value of xHere, we have
f(g(x)) = g(f(x))
This means that
f(g(x)) = 3 - 2(-x² + x + 1)
g(f(x)) = -(3 - 2x)² + (3 - 2x) + 1
Using a graphing tool, we have
f(g(x)) = g(f(x)) when x = 1
Hence, the value of x is 1
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Complete question
f(x) = 3 - 2x and g(x) = x - x² + 1 where x is an element of f have set of numbers
Find the inverse of G and the value for x for which f(g(x)) = g(f(x)).
Write the given third order linear equation as an equivalent system of first order equations with initial values. (t - 2t^2)y' - 4y'" = -2t with y(3) = -2, y'(3) = 2, y"(3) = -3 Use x_1 = y, x_2 = y', and x_3 = y". with initial values If you don't get this in 2 tries, you can get a hint.
The given third-order linear equation is (t - 2t^2)y' - 4y'' = -2t with y(3) = -2, y'(3) = 2, y''(3) = -3.
We can write this equation as a system of first-order linear equations with initial values by introducing three new variables x_1, x_2, and x_3 such that:
x_1 = y
x_2 = y'
x_3 = y''
with initial values x_1(3) = -2, x_2(3) = 2, x_3(3) = -3.
The resulting system of equations is:
x_1' = x_2
x_2' = x_3
x_3' = (2t^2 - t)x_2 - 4x_3 + 2t
This system can be solved numerically for the unknown functions x_1, x_2, and x_3 with the initial conditions given.
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A triangle has a side that is 5 inches long that is adjacent to an angle of 61. In addition, the side oppositethe 61 angle is 4,8 inches long. There are two triangles with these measurements. For each one,determine the other two angles of the triangle and the length of the third side..acute:(a) The triangle in which the angle opposite the 5-inch side-The angle between the two given sides measuresnearest tenth of a degree.)The third angle measuresThe remaining side is approximatelyan inch.)(b) The triangle in which the angle opposite the 5-inch side is obtuse:The angle between the two given sides measuresnearest tenth of andegree.)WThe third angle measuresThe remaining side is approximatelyan inch.)degrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)Ainches long. (Round to the nearest tenth ofdegrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)inches long. (Round to the nearest tenth of an inch
The two remaining angles are 58°, and the length of the third side of the triangle is 6.5 inch.
In order to determine the other two angles of each triangle as well as the length of the third side, we need to use the Cosine Rule. According to the Cosine Rule, for any triangle with sides of length a, b, and c, and angles of A, B, and C, the following equation holds:
[tex]c^2 = a^2 + b^2 - 2ab cos(C)[/tex]
For the first triangle, we are given that the side of length 5 is adjacent to an angle of 61°. Therefore, a = 5, C = 61°. Using the information provided, we can also determine that b = 4.8. Substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (5)^2 + (4.8)^2 - 2(5)(4.8) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the first triangle is 6.5. Additionally, we can use the Triangle Angle Sum theorem to determine the other two angles. According to this theorem, the sum of the three angles of a triangle is 180°. Therefore, for the first triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
For the second triangle, we use the same process, but with the given side lengths reversed. That is, we set a = 4.8, b = 5, and C = 61°. Again, substituting these values into the Cosine Rule equation, we get:
[tex]c^2 = (4.8)^2 + (5)^2 - 2(4.8)(5) cos(61°)[/tex]
We can solve this equation to get c = 6.5. Therefore, the length of the third side in the second triangle is also 6.5. We can use the Triangle Angle Sum theorem again to determine the other two angles. Again, for the second triangle, the two remaining angles are 180 - 61 - (180 - 61) = 58°.
In conclusion, for each triangle, the two remaining angles are 58°, and the length of the third side is 6.5 inch.
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What is the value of this expression when x = -6 and y=-1/2
The resultant value of the given expression 4(x²+3)-2y is 157 respectively.
What are expressions?The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values.
We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra.
Here, we refer to these letters as variables.
An expression is a group of words with operators between them.
The equation is the union of two expressions joined by the symbol "equal to" (=).
For instance, 3x-8. Ex: 3x-8 = 16.
So, the value would be:
4(x²+3)-2y
Insert values as follows:
=4((-6)²+3)-2(-1/2)
=4(36+3)+1=157
Therefore, the resultant value of the given expression 4(x²+3)-2y is 157 respectively.
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Complete question:
What is the value of this expression when x= -6 and y= -1/2? 4(x2+3)-2y
Hi help me with this question
Solve for X
30=5(X+5)
X=?
The solution for X in equation 30=5(X+5)X is X= 1.
To solve the equation, we can start by distributing the 5 on the right-hand side of the equation, which gives us:
30 = 5X + 25X
Combining like terms, we get:
30 = 30X
Dividing both sides by 30, we get:
X = 1
However, we need to check whether this value satisfies the original equation. Plugging X=1 into the equation gives us:
30 = 5(1+5)(1)
30 = 5(6)
30 = 30
Therefore, the only valid solution is X=1.
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Will give brainlest to first correct answer!!!
Evelyn has a bag that contains 3 red marbles and 2 blue marbles.
Evelyn randomly pulls a marble from the bag and then puts it back in the bag. She repeats this 20 times. How many times should she expect to draw a red marble from the bag?
Answer:
She will draw 120 times for a red marble
Step-by-step explanation:
What is the measure of ∠D? Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth. m∠D= ° A right triangle B C D. Angle C is marked as a right angle. Side B C is labeled as 25 feet. Side C D is labeled as 45 feet.
Therefore, the measure of ∠D is approximately 60.96 degrees.
What is measure?A measure is a function that assigns a number to each set in a given space, typically with the goal of describing the size or extent of the set. For example, the Lebesgue measure is a way of assigning a "volume" to sets in n-dimensional Euclidean space.
by the question.
To find the measure of ∠D in a right triangle with sides of 25 feet and 45 feet, we can use the inverse tangent function:
[tex]tan(∠D) = opposite/adjacent = CD/BC = 45/25[/tex]
Taking the inverse tangent of both sides, we get:
[tex]∠D = tan⁻¹(45/25) = 60.95 degrees[/tex]
Rounding this to the nearest hundredth, we get:
[tex]angleD = 60.95 degrees =60.96 degree.[/tex]
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Using the discriminant, how many real solutions does the following quadratic equation have? x^2 +8x+c= 0
The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:
[tex]b^2 - 4ac[/tex]
[tex]= 8^2 - 4(1)(c)[/tex]
[tex]= 64 - 4c[/tex]
Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).
In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.
Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
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