Answer:
She ate 8 donuts the first day, 14 on the second, 20 on the third, 26 on the fourth, and 32 on the fifth day
Step-by-step explanation:
Over the course of 5 days, she ate 100 donuts, each day eating 6 more than the day before. Let n be the number of donuts she ate on the first day, then she ate...
Day 1: n donuts
Day 2: n + 6 donuts
Day 3: n + 12 donuts
Day 4: n + 18 donuts
Day 5: n + 24 donuts
Add the days together and get the equation...
n + (n + 6) + (n + 12) + (n + 18) + (n + 24) = 100
Now combine like terms and solve for n...
5n + 60 = 100
5n = 40
n = 8
She ate 8 donuts the first day, 14 on the second, 20 on the third, 26 on the fourth, and 32 on the fifth day
The school principal spent $2,000 to buy some new computer equipment.Of this money $120 was used to buy some new keyboards.What percent of the money was spent on keyboard
Answer:
6%
Step-by-step explanation:
120/2000= 60/1000= 6/100= 6%
6% of the money was spent on keyboard
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that school principal spent $2,000 to buy some new computer equipment.
Out of $2000 , $120 was used to buy some new keyboards
We need to find what percent of the money was spent on keyboard.
We need to find what is $120 of $2000
Let x/100 is the percent of amount spent for keyboard
x/100×2000=120
20x=120
Divide both sides by 20
x=6
Hence, 6% of the money was spent on keyboard
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A potter works 4 days a week, makes 14 pots per day on average, and charges $24 a pot. Money per 4-day workweek?
The owner of a bike shop sells unicycles and bicycles and keeps inventory by counting seats and wheels . one day , she counts 15 seats and 22 wheels. The equation repesenting the total number of seats is u + b = 15 where u is the number of unicycles and b is the number of bicycles
Answer:
Step-by-step explanation:
U+b=15
7+8=15
Chuck's starting balance on his credit card was $268.23, and he made purchases of $125 and $98 during the month. He also made a payment of $100. If the finance charge is 1.4% per month on the unpaid balance, find the new balance at the end of the month.
Answer:
25.95
Step-by-step explanation:
Answer:
Roughly $396.71
Step-by-step explanation:
Chuck starts the month with $268.23 balance on his card
He makes a $125 and $98 purchase, add those two together to get $223, and then add that to the total starting balance of $268.23 to get $491.23.
At the end of the month, he made a $100 payment, subtracting $100 from the balance to get $391.23. $391.23 times 1.014 (Adding 1.4% converted into decimal form, to convert a percent into decimal form move the decimal left two places) equals $396.71
A helicopter flying 1600 feet above ground spots an airplane flying above. If the horizontal distance between the helicopter and airplane is 3,055 feet and angle of elevation is 71 degrees, find the airplane’s altitude.
Answer: 10,472.36 feet
Step-by-step explanation:
- Observe the diagram attached (It is not drawn to scale).
- Calculate the height between helicopter and airplane (h), as following:
[tex]tan\alpha=\frac{opposite}{adjacent}\\\\tan(71\°)=\frac{h}{3,055}[/tex]
Solve for h:
[tex]h=(3,055)(tan(71\°))\\h=8,872.36ft[/tex]
- Therefore, the altitude of the plane is:
[tex]altitude=1,600ft+8,872.36ft\\altitude=10,472.36ft[/tex]
You can use the tangent ratio to find the airplane's altitude.
The altitude of the airplane in the given condition is 10,471.72 ft
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
What is tangent ratio?In a right angled triangle(triangle with one of the angles as right angle which is 90 degrees), seeing from perspective of an angle, the tangent ratio is the ratio of the side opposite to that angle and the side which is perpendicular to that opposite side.
How to find the airplane's altitude if angle of elevation is given?Refer to the attached figure.
The altitude of the plane is the length of the line segment CE.
We have the rectangle ABDE, thus, AD = BE in terms of length.
(remember that |AB| means length of line segment AB).
Thus,
|CE| = |CB| + |BE| = |CB| + 1600 ft
Using the tangent ratio for triangle ABC from angle A, we get:
[tex]tan(A) = \dfrac{|CB|}{|AB|} = \dfrac{|CB|}{3055}\\\\tan(71) \approx 2.904 = \dfrac{|CB|}{3055}\\\\|CB| = 3055 \times 2.904 = 8.871.72 \: \rm ft[/tex]
Thus,
|CE| = |CB| + 1600 = 8871.72 + 1600 = 10,471.72 ft.
Thus,
The altitude of the airplane in the given condition is 10,471.72 ft
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Fill in the blanks to complete the following statements. Bold left parenthesis a right parenthesis For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1minusp)greater than or equals______. Bold left parenthesis b right parenthesis Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals______. (This is a reading assessment question. Be certain of your answer because you only get one attempt on this question.)
Answer:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np (1 -p ) greater than or equals 10.
Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals0.35.
Step-by-step explanation:
Normal distribution is the shape data takes as a symmetrical bell shaped curve. Normal approximation can only be taken when np or np(1-p) greater than 10.
Fill in the blanks to complete the following statements:
For the shape of the distribution of the sample proportion to be approximately normal, it is required that np(1 - p)greater than or equals__10____. Suppose the proportion of a population that has a certain characteristic is 0.35. The mean of the sampling distribution of ModifyingAbove p with caret from this population is mu Subscript ModifyingAbove p with caretequals__0.35____.The first blank should be filled with '5' as per the npq rule for approximation using normal distribution and the second statement's blank is filled with '0.35', which is the population proportion.
Explanation:To complete your statements:
np(1-p) greater than or equals 5 - This is a common guideline when checking if we can use a normal distribution to approximate a binomial distribution, also referred to as the 'npq rule'. The mean of the sampling distribution with a population proportion of 0.35 (p) is 0.35. This is true based on the formula for the mean of a sampling distribution for proportions, which equals the population proportion (p).
It's essential to remember that in hypothesis testing of a single population proportion, the binomial distribution's shape needs to be similar to a normal distribution. The terms 'np' and 'nq' refer to the conditions for this binomial distribution. Here 'n' is the number of trials, 'p' is the probability of success, and 'q=1-p' is the probability of failure, both must be more significant than five for the approximation to be acceptable.
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Factor completely, then place the factors in the proper location on the grid. 2a 2 + 2b 2 - 5ab
Answer:
[tex](2a-b)(a-2b) = 0[/tex]
Step-by-step explanation:
We can use the quadratic formula to factor this expression
For a quadratic function of the form:
[tex]na ^ 2 + ma + c[/tex]
Whe have:
[tex]2a^2 + 2b^2 - 5ab[/tex]
Then:
[tex]n = 2\\\\m = -5b\\\\c = 2b^2[/tex]
The quadratic formula is:
[tex]a =\frac{-m\±\sqrt{m^2-4nc}}{2n}[/tex]
Then the solutions are:
[tex]a= \frac{-(-5b)\±\sqrt{(-5b)^2 -4(2)(2b^2)}}{2(2)}\\\\a = \frac{5b\±\sqrt{25b^2-16b^2}}{4}\\\\a = \frac{5b\±3b}{4}\\\\a_1=2b\\\\a_2 =\frac{b}{2}[/tex]
Finally The factored expression is:
[tex]a-\frac{b}{2} = 0\\\\2a -b = 0\\\\[/tex]
and
[tex]a-2b= 0[/tex]
Then
[tex]2a^2 + 2b^2 - 5ab = (2a-b)(a-2b) = 0[/tex]
Which equation is an identity?
8 – (6v + 7) = –6v – 1
5y + 5 = 5y – 6
3w + 8 – w = 4w – 2(w – 4)
6m – 6 = 7m + 9 – m
Answer:
Equation 3
Step-by-step explanation:
An identity is, simply put, an equation that is always true. 1 = 1, 2 = 2, and x = x are all examples of identities, as there's no case in which 1 ≠ 1, 2 ≠ 2, and x ≠ x. Essentially, if we can manipulate and equation so that we end up with the same value on either side, we've found an identity. Let's run through and try to solve each of these equations to see which one fulfills that condition:
8 - (6v + 7) = -6v - 1
8 - 6v - 7 = -6v - 1
1 - 6v = -6v - 1
1 = -1
This is clearly untrue. Moving on to the next equation:
5y + 5 = 5y - 6
5 = -6
Untrue again. Solving the third:
3w + 8 - w = 4w - 2(w - 4)
2w + 8 = 4w - 2w + 8
2w + 8 = 2w + 8
If we created a new variable z = 2w + 8, we could rewrite this equation as
z = z, which is always true. We can stop here, as we've now found that equation 3 is an identity.
The identity among the given equations is 3w + 8 - w = 4w - 2(w - 4), as it simplifies to a true statement 2w + 8 = 2w + 8 for all values of w.
Explanation:The student asked which equation is an identity. To find the identity, we simplify and solve each equation:
8 – (6v + 7) = –6v – 1: When we simplify, we get 8 - 6v - 7 = -6v - 1, which further simplifies to 1 - 6v = -6v - 1. Adding 6v to both sides, we have 1 = -1, which is not true, so it's not an identity.
5y + 5 = 5y – 6: Simplifying this we simply subtract 5y from both sides, and we are left with 5 = -6, which is not true, so this is not an identity either.
3w + 8 – w = 4w – 2(w – 4): Simplifying we get 2w + 8 = 4w - 2w + 8, which reduces to 2w + 8 = 2w + 8. This is true for all values of w, therefore, this is an identity.
6m – 6 = 7m + 9 – m: Simplifying gives us 6m - 6 = 6m + 9. Subtracting 6m from both sides, we get -6 = 9, which is not true and thus not an identity.
The identity is the equation 3w + 8 – w = 4w – 2(w – 4) because it simplifies to a true statement regardless of the value of w.
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At what value of x does the graph of the following function f(x) have a vertical asymptote?
F(x)= [tex]\frac{1}{x-6}[/tex]
A. -3
B. 0
C. 6
D. -6
Answer:maybe A.
but I'm not sure
Answer:
C.) 6
Step-by-step explanation:
x-6 = -6
Inververse Operation
-6=+6
(Honestly don't know if that is the right reasons but that is what I have been doing and I have got those answers right so maybe I'm doing it right...)
Complete the tables of values
The equations are shown in the top of the tables,
Replace x in the equations with the values of x given:
a = 4^-0 = 1
b = 4^-2 = 1/16
c = 4^-4 = 1/256
d = (2/3)^0 = 1
e = (2/3)^2 = 4/9
f = (2/3)^4 = 16/81
The value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
What is an exponential function?
It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a×
where a is a constant and a>1
We have:
y = 4⁻ˣ
x = 0
a = 4⁻⁰ = 1
x = 2
b = 4⁻² = 1/16
x = 4
c = 4⁻⁴ = 1/256
y = (2/3)ˣ
x = 0
d = (2/3)⁰ = 1
x = 2
e = (2/3)² = 4/9
x = 4
f = (2/3)⁴ = 16/81
Thus, the value of a, b, c, d, e, and f are 1, 1/16, 1/256, 1, 4/9, and 16/81 after plugging the values of x.
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Which expression is equivalent to 27 cubed ?
9^3
9
3^3
3
Answer:
your 3rd option because 3^3 is 27
I agree because when you do prime factorization you get 27 by doing it
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
95 % ; n=100; σ = unknown; population appears to be skewed
Choose the correct answer below.
A. tα/2 =2.626
B. zα/2 = 1.96
C. tα/2 =1.984
D. zα/2 = 2.575
E. Neither the normal nor the t distribution applies
To construct a confidence interval using the given confidence level, do whichever of the following is appropriate. (a) Find the critical value z Subscript alpha divided by zα/2, (b) find the critical value t Subscript alpha divided by tα/2, or (c) state that neither the normal nor the t distribution applies.?
98 % ; n= 19; σ = 21.4; population appears to be normally distributed
A. zα/2 = 2.33
B. tα/2 = 2.214
C. zα/2 = 2.552
D. zα/2 = 2.055
E. Neither normal nor t distribution applies
Answer:
1: z = 1.96
2: t = 2.552
Step-by-step explanation:
1: When you don't know the population standard deviation and the sample size is large, you can still use a z test because many large samples are relatively normally distributed. A 95% confidence interval uses a z-score of 1.96
2. We are told that n < 30, so we use t distribution. Use the degrees of freedom, which is one less than the population, and the column that has 0.02 in the area of 2 tails.
In constructing a confidence interval, if the standard deviation is unknown and the population appears skewed, we typically use the t-distribution. However, without enough information given, the answer to the first problem tends towards 'Neither normal nor t distribution applies'. For the second problem, the standard deviation is given and the population appears normally distributed, hence answer is 'zα/2 = 2.33' from the z-table.
Explanation:The relevant subject matter here is Statistics, specifically, confidence intervals. The construction of a confidence interval depends on the knowledge of the standard deviation and whether the population is normally distributed or not.
For the first problem, since the standard deviation (σ) is unknown and the population appears to be skewed, student's t-distribution applies here. This would involve using tα/2 with degree of freedom (n-1) in place of the unavailable standard deviation. However, without enough data provided in the question, it is difficult to correctly compute tα/2. The answer therefore likely tends towards option E: 'Neither the normal nor the t distribution applies'.
For the second problem, the standard deviation (σ) is given and the population appears to be normally distributed. This suggests the normal distribution applies, hence you would compute zα/2, the critical value for the z-score at a 98% confidence level. Referring to a standard z-table at a 98% confidence level gives a z-score of approximately 2.33. So, the answer for this scenario is A: zα/2 = 2.33.
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If 4 dice are rolled, what is the number of ways in which at least 1 die shows 3?
I think the number of ways is 671?
Yadira's mom is buying hot dogs and hot dog buns for the family barbecue. Hot dogs come in packs of 1 and hot dog buns come in packs of 9. The store does not sell parts of a pack and Yadira's mom wants the same number of hot dogs as hot dog buns. What is the smallest total number of hot dogs that Yadira's mom can purchase?
Answer:
Nine
Step-by-step explanation:
The smallest number of buns is one pack or 9 buns.
If there is one hot dog per bun, the smallest number of hot dogs is nine.
Answer:
36 hotdogs
Step-by-step explanation:
Mathematically, we say that 36 is the least common multiple of 12 and 9. In math notation this looks like:
lcm of 9 and 12 is 36
The smallest total number of hot dogs that Yadira's mom can purchase is , 36.
Which is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8yWhich is the equation of a parabola with vertex (0, 0), that opens to the right and has a focal width of 8? a.y^2=8x b.y^2=-8x c. x^2=8y d. x^2=-8y
Answer:
the first answer is A y^2=8x
Step-by-step explanation:
The equation of a parabola that opens to the right with vertex at the origin (0,0) and has a focal width of 8 is y^2 = 8x. This follows from the equation of a parabola in standard form, y^2 = 4ax, where 4a equals the focal width.
Explanation:The equation of a parabola in standard form is either y^2=4ax or x^2=4ay, depending on its orientation. The vertex is at the origin (0,0). A parabola that opens to the right or left has the form y^2 = 4ax, and one that opens upward or downward has the form x^2 = 4ay. Given that your parabola opens to the right and has a focal width of 8, it would utilize the first form. The focal width is the absolute value of 4a. Thus, for your parabola, 4a is equal to the focal width, which is 8. Therefore, a = 8/4 = 2. Hence, the equation of the parabola with vertex at the origin that opens to the right and has a focal width of 8 is y^2 = 8x.
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What is the value after 7 years of a 2014 ford mustang that originally costs $25,000.00 if it depreciates at a rate of 8% per year round your answer to the nearest dollar
Answer:
After 7 years it will have a value of $13.946 to the nearest dollar.
Step-by-step explanation:
As it depreciates by 8% (0.08) a year the value of the car after each year is
1 - 0.08 = 0.92 of the previous year's value.
So we have the formula:
Value = 25,000(0.92)^7
= $13,946.17 (answer).
Answer:
The rounded answer is equal to 14000
Step-by-step explanation:
1. the domain set of C = {( 2, 5), (2, 6), (2, 7)} {2} 2. the range set of E = {(3, 3), (4, 4), (5, 5), (6, 6)} domain = range = {all real numbers} 3. the range and domain of F = {(x, y ) | x + y =10} domain = {all real numbers}: range = {y: y = 3} 4. the range and domain of P = {(x, y ) | y = 3} {3, 4, 5, 6}
For the given sets, the domain of set C is {2}, and its range is {5, 6, 7}. Set E has both domain and range as {3, 4, 5, 6}.
A set of ordered pairs is defined as a relation. The domain of a relation is the set of all the first elements of the ordered pairs, and the range is the set of all the second elements. Let's look at the listed sets and determine their domains and ranges.
For set C = {( 2, 5), (2, 6), (2, 7)}, the domain is {2}, because 2 is the only first element in all the pairs. The range for set C is {5, 6, 7} since those are all the second elements in the pairs.The range of set E = {(3, 3), (4, 4), (5, 5), (6, 6)} is the set of y-values or second elements of the ordered pairs, which is {3, 4, 5, 6}. Since each pair has the same x and y values, the domain of E is also {3, 4, 5, 6}.For the relation F = {(x, y) | x + y = 10}, if the domain is all real numbers, then the range must also include all real numbers that can be paired with a number from the domain to sum up to 10.For relation P = {(x, y ) | y = 3}, regardless of the x values, if y is always 3, then the range is {3}. The domain can include any real number as x, but the specific domain provided is {3, 4, 5, 6}.A function is a special type of relation where each element of the domain is associated with exactly one element in the range. This condition is also known as the vertical line test when graphing the relation on a coordinate plane.
Ummm Hey,I don't know the answer for this question,when I solve the problem my answer always 6 but the real answer is 2 so I need help right now.
umm ok then its 2...
I’ll give brainliest!! Help!! Paige has $213.84 deducted from her paycheck for her 401(k). Her gross paycheck amount is $1944. What percent of her gross paycheck amount does she have deducted for her 401(k)
9%
11%
13%
Answer:
11 %
Step-by-step explanation:
Percent = Amount deducted/original amount × 100 %
= 213.84/1944 × 100 %
= 11.00 %
Paige has 11.00 % of her paycheck deducted for her 401(k).
Answer:
11%
Step-by-step explanation:
Which system of linear inequalities is graphed?
Answer:
Should be the first one again
The dotted line is a vertical line at x -2, so we know the first equation is X<-2
The solid line means the equation has to be less than or equal to and since it crosses the dotted line at -2
the second equation would be y <=-x-2
The first choice is correct.
let g(x)=3x+2 and f(x)= x-2/3
find the value
1.) f(g(0))
2.) g(f(2))
3.) g(g((0))
To find the values of f(g(0)), g(f(2)), and g(g(0)), substitute the given values into the functions step-by-step.
Explanation:1.) To find the value of f(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function f(x): f(2) = rac{2-2}{3} = 0.
2.) To find the value of g(f(2)), we first substitute 2 into the function f(x): f(2) = rac{2-2}{3} = 0. Then, substitute the value obtained into the function g(x): g(0) = 3(0) + 2 = 2.
3.) To find the value of g(g(0)), we first substitute 0 into the function g(x): g(0) = 3(0) + 2 = 2. Then, substitute the value obtained into the function g(x) again: g(2) = 3(2) + 2 = 8.
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To find the value of f(g(0)), substitute 0 into g(x) to get g(0) = 2 and then substitute this value into f(x) to get f(g(0)) = 4/3. To find the value of g(f(2)), substitute 2 into f(x) to get f(2) = 4/3 and then substitute this value into g(x) to get g(f(2)) = 8. To find the value of g(g(0)), calculate g(0) = 2 and then substitute this value into g(x) to get g(g(0)) = 8.
Explanation:To find the value of f(g(0)), we need to substitute the value of 0 into the function g(x) to get g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function f(x) to get f(2) = 2 - 2/3 = 4/3.
To find the value of g(f(2)), we need to substitute the value of 2 into the function f(x) to get f(2) = 2 - 2/3 = 4/3. Then, we substitute this value into the function g(x) to get g(4/3) = 3(4/3) + 2 = 6 + 2 = 8.
To find the value of g(g(0)), we need to calculate g(0) = 3(0) + 2 = 2. Then, we substitute this value into the function g(x) again to get g(2) = 3(2) + 2 = 8.
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If an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h = -16t^2+vt+s, where h is in feet. If the object is propelled from a height of 12 feet with an initial velocity of 64 feet per second, it's height h is given by the equation h = -16t^2+64t+12. After how many seconds is the height 72 feet?
Answer:
The object first reaches 72 feet after 1.5 seconds; it is this height again after 2.5 seconds.
Step-by-step explanation:
To find the amount of time it takes to reach 72 feet, we solve the equation
72 = -16t² + 64t + 12
To solve this, we will set it equal to 0 by subtracting 72 from each side:
72-72 = -16t² + 64t + 12 - 72
0 = -16t² + 64t - 60
Next we will use the quadratic formula to solve this:
By setting up and solving the required quadratic equation, it is determined that an object propelled from a height of 12 feet with an initial velocity of 64 feet per second will take 3.75 seconds to reach a height of 72 feet.
Explanation:The height h of the object is given by the equation h = -16t^2 + 64t + 12. We need to solve for time t, where the height h is 72 feet. By setting the equation equal to 72, we get 72 = -16t^2 + 64t + 12.
Moving -16t^2 and 64t to the other side, we get 16t^2 - 64t + (72 - 12) = 0. This simplifies to 16t^2 - 64t + 60 = 0. Divide every term in the equation by four to get: 4t^2 - 16t + 15 = 0. This equation must now be solved using the quadratic formula: t = [-b +/- sqrt(b^2 - 4ac)] / (2a).
Plugging in the values a=4, b=-16, and c=15, we get two possible solutions: t = 1 and t = 3.75 seconds. As the object is propelled up and comes down, we take the larger value, t=3.75 seconds, because that's the actual duration for the object to reach the height of 72 feet.
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A box of 6 golf balls cost 7.32. At the rate,how much will a box of 15 golf balls cost
Answer:
$18.30
Step-by-step explanation:
First, you can figure out the cost per golf ball by dividing the price by the number of golf balls. If 6 balls = 7.32, then 1 ball = 7.32/6, or 1.22. Now you can multiply this by the number of balls in the box to find out the price: 1.22 * 15 = 18.30.
Another way to solve this is to set up a ratio of balls / price:
(x is the unknown price)
[tex]\frac{6}{7.32} =\frac{15}{x}[/tex]
Now, cross-multiplying, you find that 6x = 7.32 * 15, or 6x = 109.8. Dividing both sides by 6, you get x=18.30.
Can someone please help me with this?
Answer:
23
Step-by-step explanation:
angles in a triangle add up to 180 so
124+33=157
180-157=23
x=23
y is 23 as well and z is 124
A quadrilateral has all sides the same length and no right angels.What is the name of the quadrilateral
I think it's possibly a rhombus
Determine if the function f is an exponential function. If so, identify the base. If not, why not? F(x)= x^ -3
Answer:
Not an exponential function. The exponent is a constant.
Step-by-step explanation:
An exponential function has the variable in the exponent. This function raises the variable to a fixed power, so it is not an exponential function.
The value of y varies directly with x, when x=1/4, y=25. What is the value of y when x= 2 1/3
The value of y, when x = 2 1/3 in a direct variation scenario where y = kx (k being the constant of variation), is approximately 233.3.
Explanation:In the given problem, the value of y varies directly with x. This means there's a constant of variation, k, such that y = kx. We can find k by plugging in the initial given values, x=1/4 and y=25, into this equation, which gives us k = y/x = 25/(1/4) = 100.
Now that we know k, we can calculate the value of y when x = 2 1/3 using the same equation. Here, y = kx = 100 * 2 1/3 = 100 * 7/3 = 700/3 = 233.3 recurring.
So, when x = 2 1/3, y is approximately 233.3.
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When [tex]\(x = \frac{1}{4}\), \(y = 25\)[/tex] in a direct variation relationship. The constant of variation[tex](\(k\))[/tex] is found to be 100. Thus, when[tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
If the value of [tex]\(y\)[/tex] varies directly with[tex]\(x\),[/tex] we can express this relationship using the formula [tex]\(y = kx\),[/tex] where [tex]\(k\)[/tex] is the constant of variation.
Given that when [tex]\(x = \frac{1}{4}\), \(y = 25\),[/tex] we can use this information to find [tex]\(k\)[/tex]:
[tex]\[25 = k \times \frac{1}{4}\][/tex]
Solving for [tex]\(k\):[/tex]
[tex]\[k = 25 \times 4 = 100\][/tex]
Now that we know [tex]\(k = 100\),[/tex] we can find the value of[tex]\(y\)[/tex] when[tex]\(x = 2 \frac{1}{3}\)\\[/tex]
[tex]\[y = 100 \times 2 \frac{1}{3} = 100 \times \frac{7}{3} = \frac{700}{3}\][/tex]
Therefore, when [tex]\(x = 2 \frac{1}{3}\), \(y = \frac{700}{3}\).[/tex]
Pentagon ABCDE Pentagon FGHIJ. Find BC for GH = 12, IJ = 15, and DE = 10.
NEED URGENTLY!!!
Answer:
BC = 8
Step-by-step explanation:
These are similar shapes, so they multiply out to the same ratio.
Seeing that 10 * 1.5 = 15, BC * 1.5 should equal 12.
All we do is divide 1.5 from both sides to get 8.
Then, plug it back into the equation to check and it works.
Answer: x = 8
Step-by-step explanation:
You can solve by setting up the proportions of the corresponding sides of the pentagon and then solve for x (the value of BC).
So, IJ/DE values are 15/10 and are set equal to GH/x (x represents the value of BC; the value you are solving for). Hint: It may be helpful for you to draw a diagram of the two pentagons and label them with the letters and values provided in the problem. This will help you to set up your proportion problem accurately.
To solve you can cross multiply to find the value of x.
15/10 = 12/x
15x = 12 * 10
15x = 120
x = 120/15
x = 8
WILL GIVE BRAINLIEST
Identify the factors of x2 + 16y2.
(x + 4y)(x + 4y)
(x + 4y)(x − 4y)
Prime
(x − 4y)(x − 4y)
Answer:
Prime
Step-by-step explanation:
Since none of the other answers work. Your answer is Prime.
Answer:
Prime
Step-by-step explanation:
(x + 4y)(x + 4y)
Appy FOIL method to multiply it
x^2 +4xy + 4xy +16y^2
x^2 + 8xy +16y^2
(x + 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy + 4xy -16y^2
x^2 - 16y^2
(x − 4y)(x − 4y)
Appy FOIL method to multiply it
x^2 -4xy - 4xy +16y^2
x^2 - 8xy +16y^2
the options does not gives us x^2 +16y^2
So it is not factorable , It is prime
If the heights of 4 family members is 153, 150, 151 and 152, find the mean height of the family.
Answer: 151.1
Step-by-step explanation:
First, you would add all the heights together (153+150+151+152=606)
Then you would divide 606 by the number of numbers in the data set in this case the number of family members which is (606 divided by 4= 151.1)
Answer:
151.5
Step-by-step explanation:
First of all, what is the mean in a set of numbers?
The mean is the average of all the numbers in the set. We can find this by finding the total value of all the terms and then dividing it by the number of terms. Let's just do a short example so we can make sure you understand.Let's look at this set of numbers:5, 3, 7, 4.To find the average of these numbers, we'll add all of the numbers and divide it by 4, the number of actual terms, in the set.
(5 + 3 + 7 + 4) / 4 = 19/4 which is also 4.75.Back to the actual problem.(153 + 150 + 151 + 152) / 4 = 151.5