Please show all your work! Thankyou for your time!1. Use a local linear approximation to estimate (you should not need to use a calculator): 24.73
Answers
Using the local linear approximation, we estimate the square root of 24.73 to be approximately 4.973.
To estimate the square root of 24.73 using a local linear approximation, we will use the following steps:
1. Choose a value close to 24.73 for which the square root is easy to compute (e.g., 25, since the square root of 25 is 5).
2. Find the derivative of the square root function, f(x) = sqrt(x), which is f'(x) = 1/(2*sqrt(x)).
3. Use the linear approximation formula: L(x) = f(a) + f'(a) * (x - a), where a is the chosen value (25 in this case), and x is the value we want to estimate (24.73).
Now, let's apply these steps:
1. We have chosen a = 25, and we know that f(a) = sqrt(25) = 5.
2. Compute the derivative at a: f'(25) = 1/(2*sqrt(25)) = 1/(2*5) = 1/10.
3. Apply the linear approximation formula: L(24.73) = 5 + (1/10) * (24.73 - 25) = 5 - (1/10) * 0.27 = 5 - 0.027 = 4.973.
So, using the local linear approximation, we estimate the square root of 24.73 to be approximately 4.973.
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Related Questions
Frank ate half of his jellybeans and then bought a package with 16 more. If he now has 20 remaining jellybeans, how many did he have in the beginning?
Answers
Answer:
8
Step-by-step explanation:
20-16=4 4*2=8
help me nowwww show work thank you
Answers
Answer:
Step-by-step explanation:
I assume the triangle is right angled
A card will be picked at random from a standard deck of 52 cards. What is the probability that the card is a king and a diamond? Enter your answer as a fraction.
Answers
Solution:
Given:
\(\begin{gathered} total\text{ cards}=52 \\ number\text{ of kings = 4} \\ number\text{ of diamonds = 13} \end{gathered}\)From the numbers, the number of king and diamond cards = 1
Hence, the probability that the card is a king and a diamond is;
\(P(King\text{ and diamond\rparen}=\frac{1}{52}\)How to add scientific notation with different exponents.
Answers
To add scientific notation with different exponents, you need to adjust the exponents so that they are equal. Once the exponents are aligned, you can add or subtract the corresponding coefficients.
First, identify the numbers in scientific notation that you want to add. Let's say you have two numbers, A and B, expressed in scientific notation as A x 10^n and B x 10^m, where n and m are the exponents.
To add these numbers, you need to adjust one of them so that the exponents are the same.
Choose the number with the smaller exponent and multiply both its coefficient and exponent by the appropriate power of 10 to match the exponent of the other number.
For example, if n < m, you would multiply number A by \(10^{m-n}\), which means multiplying the coefficient of A by \(10^{m-n}\) and keeping the exponent of 10 as n.
Once the exponents are aligned, you can add or subtract the coefficients of the adjusted numbers.
This will give you the final result in scientific notation.
It's important to note that if the exponents are significantly different, adjusting the exponents may involve multiplying or dividing by large powers of 10, which can affect the precision of the final result.
Therefore, it's advisable to retain the appropriate number of significant figures in your calculations.
In summary, to add scientific notation with different exponents, you adjust one of the numbers by multiplying its coefficient and exponent by an appropriate power of 10 to match the exponent of the other number.
Then, you can add or subtract the coefficients and express the result in scientific notation.
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If one cookie needs 1/6 cup(s) of oil, how much vegetable oil will 4 cookies need?
Answers
Answer:
2/3 cups.
Step-by-step explanation:
1/6 + 1/6 + 1/6 + 1/6 is 4/6
Then simplify
2/3
find the equation of the ellipsoid passing through the points (±8,0,0),(0,±6,0) and (0,0,±5)
Answers
To find the equation of the ellipsoid passing through these three points, we can use the general equation of an ellipsoid:
((x-h)^2/a^2) + ((y-k)^2/b^2) + ((z-l)^2/c^2) = 1
where (h,k,l) is the center of the ellipsoid, and a, b, and c are the lengths of the semi-axes along the x, y, and z directions, respectively.
We can plug in the given points to get a system of equations:
(±8-h)^2/a^2 + (-k)^2/b^2 + (-l)^2/c^2 = 1
(-h)^2/a^2 + (±6-k)^2/b^2 + (-l)^2/c^2 = 1
(-h)^2/a^2 + (-k)^2/b^2 + (±5-l)^2/c^2 = 1
Simplifying these equations, we get:
64/a^2 + k^2/b^2 + l^2/c^2 = (h±8)^2/a^2
h^2/a^2 + 36/b^2 + l^2/c^2 = (k±6)^2/b^2
h^2/a^2 + k^2/b^2 + 25/c^2 = (l±5)^2/c^2
We have three equations with four unknowns (h, k, l, and the scale factor λ), so we need one more equation to solve for all four variables. We can use the fact that the ellipsoid is symmetric about the x, y, and z axes, which gives us three more equations:
h = λh
k = λk
l = λl
Combining all these equations and eliminating λ, we get:
x^2/64 + y^2/36 + z^2/25 = 1
Therefore, the equation of the ellipsoid passing through the points (±8,0,0), (0,±6,0), and (0,0,±5) is:
x^2/64 + y^2/36 + z^2/25 = 1.
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Rectangle PQRS will be reflected over the y-axis. What will be the coordinates of Q'M
Answers
Answer:
Coordinates for Q' Option (A) : (-5, 2)
2. Tentukan modus dari data berikut:
Nilai Frekuensi
30-34 4
35-39 10
40-4416
45-49 7
50-54 3
Answers
Answer:
note:
Step-by-step explanation:
Construct an augmented matrix for this linear system: x − y − 4z = 5 2x 2z = 0 4x y z = 3.
Answers
The augmented matrix is,
\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)
We have given system of linear equation is,
\(x - y - 4z = 5,2x + 2z = 0 ,4x +y +z = 3.\)
What is the meaning of augmented matrix?In an augmented matrix, each row represents one equation in the system and each column represents coefficients (with signs) of variables or the constant terms.
So, the first row is
\(1\ -1\ -4\ 5\)
the second row is
\(2\ 0\ 2\ 0\)
and the third row is
\(4\ 1\ 1\ 3\)
Therefore the augmented matrix for this linear system is,
\(\left(\begin{array}{ccccc}1&-1&-4&|&5\\2&0&2&|&0\\4&1&1&|&3\end{array}\right)\)
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The augmented matrix for the given linear equations will be constructed as follows
\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)
What will be the augmented matrix of the given linear equations?The augmented matrix is generally a matrix form of the given linear equations and the coefficient of the variables are arranged in the form of a matrix.
The given equation has three variables so the matrix form will be of \(3\times3\)
The given linear equations are
\(x-y-4z=5\\2x+0y+2z=0\\4x+y+z=3\)
From the above equations, we will make an augmented matrix.
\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)
The first equation will be followed by the first row of the matrix and the rest will be followed the same.
Thus the augmented matrix for the given linear equations will be constructed as follows
\(\left[\begin{array}{ccc}1&-1&-4\\2&0&2\\4&1&1\end{array}\right] \left[\begin{array}{ccc}5&\\0\\3\end{array}\right]\)
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please answer all these for crown and separate them from each other ty ill give u a crown
Answers
The values of x for the different diagrams are given below.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
There are four diagrams.
Diagram 1:
By the alternate exterior angles,
8x + 19 = 139
8x = 120
x = 15
Diagram 2:
By the corresponding angles,
17x - 45 = 108
17x = 153
x = 9
Diagram 3:
By the alternate interior angles,
7x -1 = 13x - 43
6x = 42
x = 7
Diagram 4:
By the consecutive interior angles,
8x + 19 = 139
8x = 120
x = 15
Hence, the solutions for all the values are given above.
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4. Ashley claims that if she triples the side length of a square (s), the area of the square will also be tripled. Do you agree? Explain your thinking.
Answers
Answer :-
Let the side of the square measure a cm, thus, according to the question,
New length = 3(a cm)We know that,
➭ Area ( Square ) = a²
Thus, the area of the square with normal length i.e. a cm, will be,
⤳ Area = a x a
⤳ Area = a²
Now, by taking the new length, the area will become,
⤳Area = 3a x 3a
⤳ Area = 9a²
Now,
We observe that, if we divide these, we get,
➤ 9a²/a²
( a² will get canceled since its common )
Thus, the ratio becomes,
➭ 9 : 1 = Area square with tripled length : Area of square
Thus, the area will increase by 9 times, and not 3.
Hence, Ashley's assumptions are wrong.
select the statement that correctly describes a type i and a type ii error in this context.
a. Type I error occurs when the null hypothesis is accepted when it is actually true, while Type II error occurs when the null hypothesis is rejected when it is actually false.
b. Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error occurs when the null hypothesis is accepted when it is actually false.
c. Type I error occurs when the alternative hypothesis is accepted when it is actually true, while Type II error occurs when the alternative hypothesis is rejected when it is actually false.
d. Type I error occurs when the alternative hypothesis is rejected when it is actually true, while Type II error occurs when the alternative hypothesis is accepted when it is actually false.
Answers
The correct statement that describes Type I and Type II errors in hypothesis testing is:
b. Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error occurs when the null hypothesis is accepted when it is actually false.
In hypothesis testing, Type I error refers to rejecting the null hypothesis when it is actually true. This error represents a false positive result, indicating that a significant effect or relationship is detected when it does not exist in reality. Type II error, on the other hand, occurs when the null hypothesis is accepted (not rejected) when it is actually false. This error represents a false negative result, indicating a failure to detect a significant effect or relationship that does exist. The correct understanding and interpretation of Type I and Type II errors are crucial in hypothesis testing to ensure accurate conclusions.
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Determine which set of side measurements could be used to form a right triangle. square root of 19 comma square root of 35 comma 54 square root of 15 comma 6 comma square root of 51 5, 8, 30 5, 6, 7
Answers
As per the concept of right angled triangle, the set of side measurements that could be used to form a right triangle is √15, 6, and √51
Right-angle triangle:
Right angle triangle means a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given,
√19, √35, 54
√15, 6, √51
5, 8, 30
5, 6, 7
Now, we have to determine which set of side measurements could be used to form a right triangle.
Here we know that, according to the Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
So, by using Pythagoras' theorem:
Option (2) √15, 6, √51
Makes the right angle triangle,
Because when we verify these by using the Pythagoras theorem,
(√15)² + (6)² = (√51)²
15 + 36 = 51
51 = 51
Therefore, the set of side measurements that could be used to form a right triangle is √15, 6, and √51 option (2) is correct.
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i am a number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44. what number am i?
Answers
The number less than 3,000.when you divide me by 32, my remainder is 30. when you divide me by 58, my remainder is 44 is one of this {798, 1726, 2654}.
There exists a, b∈N such as
N= 30+32a=44+58b
Therefore,
16a-29b= 22-15=7
Let us notice that 5×29-9×16=1
Therefore, 35×29-63×16=7
Hence, a= -63 is a non-fundamental solution to our equation.
We can show that the other solution are of the form a=-63+29k, with k∈Z
Therefore, the first positive solutions are
a= -63+3×29= 24
N= 798
a= -63+4×29= 53
N= 1726
a= -63+5×29=82
N= -63+6×29= 111
N= 3582
Therefore, the number is one of {798, 1726, 2654}.
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What is the equivalent exponential expression for the radical expression below? 5 A. 52 B. 5 C. 51/2 D. 2.5
Answers
Answer:B) 5
Step-by-step explanation:
Select true or false to tell whether the following conditional p q is true or false. Use the truth table if needed.
If 3+2 = 5, Then 5 + 5 = 10
True
False
Answers
Answer:
true
Step-by-step explanation:
Find the missing side lengths.
Can someone help me?
Answers
9514 1404 393
Answer:
m = n = 5√2
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you ...
Sin = Opposite/Hypotenuse
sin(45°) = m/10
m = 10·sin(45°) = 10·(√2)/2 = 5√2
The triangle is isosceles, so m = n.
n = m = 5√2
_____
The side ratios of an isosceles right triangle are 1 : 1 : √2. That is, the legs are 10/√2 = 5√2 in this triangle. It can be useful to remember these ratios for this "special" triangle.
Pythagorean Theorem
In a right triangle, the square of the _____ equals the sun of the squares of the ______.
Answers
Answer: In a right triangle, the square of the Hypotenuse equals the sun of the squares of the other two sides.
Step-by-step explanation: a^2+b^2=c^2
Answer: the Pythagoras theorem states that in a right angled triangle, the square of THE HYPOTENUSE is equal to the sum of the squares of the OTHER TWO SIDES.
Step-by-step explanation: :)
sally works in a factory that produces 1,000 televisions each day. when 40 televisions were sampled, it was found that 6 were defective. estimate how many defective televisions are made each day
Answers
An estimate of the number of defective televisions that are made each day is 150.
How many defective televisions are made each day?The first step is to determine the ratio of the televisions sampled to the total number of televisions produced each day.
1000 / 40 = 25
The second step is to multiply, 25 by 6: 25 x 6 = 150
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1) A wallet is full of $5 and $10 bills. He has a total of 25 bills and a total of $230. How many of each bill do you have?
Answers
Answer:
6 $5 dollar bills, and 20 $10 dollar bills
Step-by-step explanation:
Which of the following events below will have an equally likely chance of happening?
A
If an event has a 5%5\%5% chance of happening
B
If an event has a 50%50\%50% chance of happening
C
If an event has a 100%100\%100% chance of happening
D
If an event has a 0%0\%0% chance of happening
Answers
Answer:
B
Step-by-step explanation:
Think of it like a quarter you got a half and half shot if getting heads or tails. meaning a 50/50 chance.
2/3, 0.67, 3.1, 3 1/3, 2/5
least to greatest
Answers
The numbers are written in an ordered list according to their values when they are arranged from least to greatest. The smallest number should be written on the left, followed immediately by the next smallest number.
What is the order from least to greatest?Ascending order refers to the arrangement of numbers in which the smallest number comes before the largest. The numbers are listed in this fashion in ascending order. It is ideal for the first number to be less than the second. Descending order refers to arranging the integers from largest to least value.
When two fractions have the identical denominators, they are ranked according to the size of their numerators, with the smaller fraction being the smallest. The largest fraction is the one with the largest numerator. Both ascending and descending orders of fractions are possible.
Hence, when we arrange least to greatest the order will be
2/5,2/3,0.67,3.1,31/3
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When we arrange least to greatest the order will be 2/5,2/3,0.67,3.1,31/3
What is the order from least to greatest?Ascending order refers to the arrangement of numbers in which the smallest number comes before the largest. The numbers are listed in this fashion in ascending order. It is ideal for the first number to be less than the second. Descending order refers to arranging the integers from largest to least value.When two fractions have the identical denominators, they are ranked according to the size of their numerators, with the smaller fraction being the smallest. The largest fraction is the one with the largest numerator. Both ascending and descending orders of fractions are possible.Hence, when we arrange least to greatest the order will be
2/5,2/3,0.67,3.1,31/3
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Eff’ mom ak him to water the gra before he leave at 9:50 a. M. For wim practice. There are five location that require different prinkler etting, and each location require 25 minute of water. Jeff aume it will take him no more than 2 minute to change the prinkler, which mut be done for 4 location. What i the latet time that Jeff can tart watering and till be ready to leave for wim practice at 9:50 a. M. ?
Answers
Jeff needs to start watering at 8:57 a.m. to be ready to leave for swim practice at 9:50 a.m.
Let's start by calculating the total watering time as follows -
5 locations * 25 minutes each = 125 minutes of watering time
4 locations * 2 minutes each for changing the sprinkler = 8 minutes for changing the sprinkler.
Hence, total time = 125 minutes + 8 minutes = 133 minutes
So, Jeff needs 133 minutes for watering the garden. The latest time he should start is 9:50 a.m. - 133 minutes = 9:50 a.m. - 2 hrs 13 minutes = 8:57 a.m.
Therefore, Jeff needs to start watering around 8:57 a.m. to be ready to leave for swim practice at 9:50 a.m.
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The amusement park won't allow kids to ride
roller-coasters until they are a minimum of 48
inches tall. Michael is now 42 inches tall, and
grows about 1/2 inch every month. How many
months will it be until Michael can ride a roller-
coaster?
A. .5x+42 > 48 South
B .5x+42 > 48 East
C.5x+42 < 48 North
Answers
Answer:
c
Step-by-step explanation:
5. During the football game, Justin caught three passes. One was for a touchdown and went 52 yards. The other was for a first down and was for 17 yards. The other was on a screen pass that did not work so well and ended up a gain of -10 yards. What was the total yardage gained by Justin on the pass plays?
Answers
Answer: 59
Step-by-step explanation:
+52 + 17 - 10
= 69 - 10
= 59
\(\huge\boxed{Your\;answer\;is\;59!}\)
First, let's add \(52\) and \(17\).
\(52+17=69\).
Next, we subtract \(10\).
\(69-10=59\).
Therefore, our final answer is \(59\).
identify a pair of opposite rays.
Answers
Answer:
a and c are opposite hope it helps
what constant $c$ makes the expression a perfect square? \[49x^2-42x c\]
Answers
Answer:
Step-by-step explanation:
\(49x^2-42x+(\frac{42}{2})^2=49x^2-42x+(\frac{42}{2} )^2\) (completing the square)
\(49x^2-42x+441=49x^2-42x+21^2\)
\(=(7x-21)^2\)
So \(49x^2-42x+441=(7x-21)^2\)
Solution: The required constant is 441.
Remember: Completing the square IN \(ax^2+bx+c\) involves adding \((\frac{b}{2} )^2\) to both sides of the equation. THIS KEEPS IT BALANCED AND ALLOWS US TO MAKE A PERFECT SQUARE.
Suppose each of the apples weighs about 5 ounces. Can you buy 24 apples for $9? Explain
Answers
Yes You can buy 24 apples for $0.125 per pound. This price will not available except in festival or discounts sale.
what are ounces ?
An ounce is a unit of weight or mass commonly used in the United States and other countries. It is usually abbreviated as oz. One ounce is equal to 1/16th of a pound or approximately 28.35 grams. Ounces are often used to measure small quantities of food or ingredients in recipes, as well as for measuring the weight of small objects.
According to the question:
To determine whether you can buy 24 apples for $9, we need to find the cost per apple.
If 24 apples cost $9, then the cost per apple is:
$9 / 24 apples = $0.375 per apple
Since each apple weighs about 5 ounces, there are about 3 apples per pound:
16 ounces / 5 ounces per apple ≈ 3.2 apples per pound
Therefore, the cost per pound of apples is:
$0.375 per apple / 3 apples per pound = $0.125 per pound
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I picked the yellow one, was I correct?
Answers
Answer:
It seems like it.
Step-by-step explanation:
Have a good day!
Una mujer invierte un total de $20,000 en dos cuotas una paga 5% y la otra y la otra paga 8% de interes simple anual si recibe $1,180.00 cuanto invirtio a cada tasa
Answers
Answer:
For the 5% interest rate
she invested $14,000
For the 8% interest rate,
she invested $6,000
Step-by-step explanation:
Here, we want to know the amount the woman invested at each rate
Let the amounts at each rates be $x and $y respectively
She invested a total of $20,000
Thus;
x + y = 20,000 •••••••••(i)
let’s calculate interest on both investments
mathematically, the formula to use is;
I = PRT/100
for the $x investment, we have
I = x * 5 * 1/100 = 5x/100 = x/20
for the $y investment, we have
i = 8 * y * 1/100 = 8y/100 = 2y/25
adding both interests equal 1,180
x/20 + 2y/25 = 1,180
Multiply through by 100
5x + 8y = 118000 ••••••(ii)
we now solve both simultaneously
from i
x = 20,000-y
Put this into ii
5(20,000-y) + 8y = 118000
100,000 -5y + 8y = 118000
3y = 118000-100000
3y = 18,000
y = 18,000/3
y = $6,000
From i we know that
x = 20,000-y
x =
20,000 - 6000 = $14,000