The more accurate forward finite divided difference estimates for the derivatives are
f₁'(x₁) = 0
f₂'(x₂) = 0
f₃'(x₃) = 0
To make it easier to work with, let's rearrange the equations in terms of the variables:
4x₁ + 2x₂ + x₃ = 1
2x₁ + x₂ + x₃ = 4
2x₁ + 2x₂ + x₃ = 3
The truncated formula for estimating the derivative using the forward finite divided difference is given by:
f'(x) ≈ (f(x + ht) - f(x)) / ht
Here, f(x) represents the function we want to differentiate, and ht is the step size.
Let's calculate the derivatives using the truncated formula for the given equations:
For x₁:
f₁'(x₁) ≈ (f₁(x₁ + ht) - f₁(x₁)) / ht
= (4(x₁ + ht) + 2x₂ + x₃ - 4x₁ - 2x₂ - x₃) / ht
= (4x₁ + 4ht + 2x₂ + x₃ - 4x₁ - 2x₂ - x₃) / ht
= (4ht) / ht
= 4
Similarly, we can calculate the derivatives for x₂ and x₃.
For x₂:
f₂'(x₂) ≈ (f₂(x₂ + ht) - f₂(x₂)) / ht
= (2x₁ + (x₂ + ht) + x₃ - 2x₁ - x₂ - x₃) / ht
= (x₂ + ht - x₂) / ht
= ht / ht
= 1
For x₃:
f₃'(x₃) ≈ (f₃(x₃ + ht) - f₃(x₃)) / ht
= (2x₁ + 2x₂ + (x₃ + ht) - 2x₁ - 2x₂ - x₃) / ht
= (x₃ + ht - x₃) / ht
= ht / ht
= 1
So, the truncated forward finite divided difference estimates for the derivatives are:
f₁'(x₁) = 4
f₂'(x₂) = 1
f₃'(x₃) = 1
The more accurate formula for estimating the derivative using the forward finite divided difference is given by:
f'(x) ≈ (-3f(x) + 4f(x + ht) - f(x + 2ht)) / (2ht)
Let's calculate the derivatives using the more accurate formula for the given equations:
For x₁:
f₁'(x₁) ≈ (-3f₁(x₁) + 4f₁(x₁ + ht) - f₁(x₁ + 2ht)) / (2ht)
= (-3(4x₁ + 2x₂ + x₃) + 4(4(x₁ + ht) + 2x₂ + x₃) - (4(x₁ + 2ht) + 2x₂ + x₃)) / (2ht)
= (-12x₁ - 6x₂ - 3x₃ + 16x₁ + 8ht + 4x₂ + 2x₃ - 4x₁ - 8ht - 2x₂ - x₃) / (2ht)
= (-12x₁ + 16x₁ - 4x₁ + 8ht - 8ht) / (2ht)
= 0
Similarly, we can calculate the derivatives for x₂ and x₃.
For x₂:
f₂'(x₂) ≈ (-3f₂(x₂) + 4f₂(x₂ + ht) - f₂(x₂ + 2ht)) / (2ht)
= (-3(2x₁ + x₂ + x₃) + 4(2x₁ + (x₂ + ht) + x₃) - (2x₁ + (x₂ + 2ht) + x₃)) / (2ht)
= (-6x₁ - 3x₂ - 3x₃ + 8x₁ + 4x₂ + 4ht + 4x₃ - 2x₁ - x₂ - x₃) / (2ht)
= (-6x₁ + 8x₁ - 2x₁ - 3x₂ + 4x₂ - x₂ - 3x₃ + 4x₃ - x₃ + 4ht) / (2ht)
= 0
For x₃:
f₃'(x₃) ≈ (-3f₃(x₃) + 4f₃(x₃ + ht) - f₃(x₃ + 2ht)) / (2ht)
= (-3(2x₁ + 2x₂ + x₃) + 4(2x₁ + 2x₂ + (x₃ + ht)) - (2x₁ + 2x₂ + (x₃ + 2ht))) / (2ht)
= (-6x₁ - 6x₂ - 3x₃ + 8x₁ + 8x₂ + 4x₃ + 4ht - 2x₁ - 2x₂ - x₃) / (2ht)
= (-6x₁ + 8x₁ - 2x₁ - 6x₂ + 8x₂ - 2x₂ - 3x₃ + 4x₃ - x₃ + 4ht) / (2ht)
= 0
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A particular type of mouse's weights are normally distributed, with a mean of 409 grams and a standard deviation of 24 grams. If you pick one mouse at random, find the following: (round all probabilities to four decimal places) a) What is the probability that the mouse weighs less than 332 grams? b) What is the probability that the mouse weighs more than 480 grams? c) What is the probability that the mouse weighs between 332 and 480 grams? d) Is it unlikely that a randomly chosen mouse would weigh less than 332 grams? No, the likelihood exceeds 5% Yes, the likelihood is less than 50% Yes, the likelihood is less than 5% No, the likelihood exceeds 50% e) What is the cutoff for the heaviest 6% of this type of mouse? grams (round to the nearest whole gram).
a) To find the probability that the mouse weighs less than 332 grams is calculated using the z-score formula which is: z= (x-μ)/σ where, x=332μ=409σ=24z= (332−409)/24z=−3.21
Hence, P (x < 332) = P (z < -3.21)
The probability that the mouse weighs less than 332 grams is approximately equal to 0.0007. Therefore, the answer is 0.0007 (rounded to four decimal places).
b) To find the probability that the mouse weighs more than 480 grams is calculated using the z-score formula which is: z= (x-μ)/σwhere,x=480μ=409σ=24z= (480−409)/24z=2.96
Hence, P (x > 480) = P (z > 2.96)
The probability that the mouse weighs more than 480 grams is approximately equal to 0.0015. Therefore, the answer is 0.0015 (rounded to four decimal places).
c) To find the probability that the mouse weighs between 332 and 480 grams is calculated using the z-score formula which is: P (332 < x < 480) = P (-3.21 < z < 2.96)
Hence, the probability that the mouse weighs between 332 and 480 grams is approximately equal to 0.9980. Therefore, the answer is 0.9980 (rounded to four decimal places).
d) The probability of a randomly chosen mouse weighing less than 332 grams is found to be P (x < 332) = 0.0007 which is less than 5%. Therefore, it is unlikely that a randomly chosen mouse would weigh less than 332 grams. Hence, the answer is "Yes, the likelihood is less than 5%".
e) To find the cutoff for the heaviest 6% of this type of mouse can be done by using the Z-table, that gives the z-score for any given probability. For the heaviest 6%, we need to find the z-score corresponding to a probability of 0.94 (100% - 6%). Hence, the Z-score for 0.94 probability is 1.55. Cutoff weight = μ + Z-score * σ= 409 + 1.55 * 24 = 447.2 ≈ 447 (rounded to the nearest whole gram). Therefore, the answer is 447 (rounded to the nearest whole gram).
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write a equation of a line in slope-intercept form for slope: 5/6, y intercept: 8
Find the value of x.
Answer: 55
Step-by-step explanation:90-31= 59
59-4=55
The Lawrence family went out to dinner. The
total amount of dinner was $53.89, and they
decided to add an 18% tip. How much did the
waitress receive for a tip from the Lawrence
family?
Answer: 9.70$
Step-by-step explanation: The equation is 53.89 * 0.18 = 9.7002 but, If you round to the nearest hundred it is 9.70$. Hope this helped!!!
The amount of tip waitress get from the Lawrence family is $63.5902.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
The total amount of dinner was $53.89.
Tip= 18%
So, the tip amount will be
= 53.89 x 18/100
= 53.89 x 0.18
= 9.7002
And, the total amount to pay
= 53.89+ 9.7002
= $63.5902
Hence, the amount of tip waitress get is $63.5902.
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Solve for X if 8X = 40
Step-by-step explanation:
X=40/8
X=5 Answer
hope it helps
Answer:
X= 5
Step-by-step explanation:
NOTE: DIVIDE 8 IN BOTH SIDE
8X/8 = X
40/8 = 5
SO X = 5
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The length of title a is about 2.23607 inches which mark on the tape measure is closest to 2,23607 inches ?
Pls help! 100 points and im giving brainliest!! Plss help fast!!
Answer:
A. the first one is true because when x = 5, 4x - 1 equals 19. The second inequality doesn't allow for it to equal 19.
B. 9 is the value that makes the equation true. See below for work to show.
Step-by-step explanation:
4x -1 </= 19 is true because it's "less than or equal to" and when you change the x to 5, the answer is exactly 19. 4(5) - 1 = 19. The other sentence is "4x - 1 is less than 19", and that means it can't equal 19 for that sentence to be true.
Math + words = confusion sometimes. Does that make sense?
------------------------------------
Now let's solve
5x + 2 = 47
Subtract 2 from both sides
5x = 45
divide both sides by 5
x = 9
Please lmk if you have questions.
Lighthouse B is 9 miles west of lighthouse a a boat leaves a and sales 6 miles. At this time it is lighted from B. If the bearing of the boat from B is North 64° east how far from be is the boat?
Answer:
12.61 miles
Step-by-step explanation:
The distance of lighthouse B from lighthouse A, the distance from lighthouse A to the boat and the distance of lighthouse B from the boat all form a triangle. Since lighthouse B is west of lighthouse A, and at a distance of 9 miles form lighthouse A, light house A is at a bearing of North 90° East of lighthouse B. The distance from lighthouse A to the boat is 6 miles, and the bearing of the boat from lighthouse B is North 64° East.
So, the angle between the distance from lighthouse B to the boat and lighthouse B to lighthouse A is 90° - 64° = 26°
Since we have two sides and an angle, we use the sine rule
a/sinA = b/sinB where a = 6, A = 26°, b = 9, B = unknown
So, sinB = bsinA/a
= 9sin26/6
= 3(0.4384)/2
= 1.3151/2
= 0.6576
B = sin⁻¹(0.6576)
= 41.11°
≅ 41.1°
We now find the third angle in the triangle, C(the angle facing the distance from lighthouse B to the boat) from
26° + 41.1° + C = 180° (sum of angles in a triangle)
67.1° + C = 180°
C = 180° - 67.1° = 112.9°
Using the sine rule again to find the third side, c(the distance from lighthouse B to the boat), we have
a/sinA = c/sinC
c = asinC/sinA
= 6sin112.9°/sin26°
= 6(0.9212)/0.4384
= 5.5271/0.4384
= 12.61 miles
the polynomial x^2+bx+15 has a factor of x-3. what is the value of b ?
Answer:
b = -8
Step-by-step explanation:
Attachment.....added.
Hope it helps :)
Shade 3/4 on the grid
Lines need to be painted on the field at a football stadium. The painter estimated that one can of paint would last 11 yards. How many cans of paint will be needed to paint the length of the 100-yard field?
I've been stuck on this question for two days :,) the answers are A.8 B.10 C.12 D.14
Can someone please tell me the answer?
Answer:
area = pi*24^2/4 = 452 yd^2
so that means you will need 452/59 = 7.6 (or 8) gallons
What divided by 76 equals 127
Easy one please answer ASAP
Answer is : 9692
cxcvbnm
Use Polynomials to Find Perimeter & Area
Find the area of this rectangle.
Answer:
Area of rectangle =
[tex]l \times b[/tex]
= 5x *( 5x -4)
=
[tex] {25x}^{2} - 20x[/tex]
Perimeter of rectangle = 2(l + b)
=2(5x +5x -4)
= 2(10x - 4)
= 20x - 8
which answer choice correctly shows 0.3% as a decimal?
a.300
b.3
0c.0.03
d.0.003
d.0.003 choice correctly shows 0.3% as a decimal.
Here, we have,
given that,
the percent is: 0.3%
now, we know that,
percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. percentage.
now, we get,
0.3%
=0.3 ÷ 100
=0.003
now, we know, 0.003 is a decimal.
so, we get,
d.0.003 choice correctly shows 0.3% as a decimal.
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help pls and tyyy:)))
Ms. Keating’s class wants to compare the use of social media between the seventh-grade students and eighth-grade students at Valleydale School.The MAD (the average distance between each data value and the mean) for both data sets is approximately 14. What can you infer about the two sets of data?
Answer:
Need to add picture
Step-by-step explanation:
What amount paid on September 19 is equivalent to $1,900 paid on the following December 1 if money can earn 5.9%? (Use 365 days a year. Do not round intermediate calculations and round your final answer to 2 decimal places.)
The amount paid on September 19 that is equivalent to $1,900 paid on December 1, with an interest rate of 5.9% compounded daily, is approximately $1,930.53.
How to calculate equivalent payment amount?To determine the amount paid on September 19 that is equivalent to $1,900 paid on December 1, we can use the concept of compound interest.
The formula to calculate compound interest is:
A = P(1 + r/n)^(nt)
Where:
A = final amount
P = principal amount (initial payment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = time in years
In this case, we need to find the equivalent amount on September 19. The time between September 19 and December 1 is approximately 74 days.
Using the formula, we can calculate the equivalent amount as follows:
A = 1900(1 + 0.059/365)^(365/74)
Calculating this expression will give us the equivalent amount on September 19. Let me calculate that for you.
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Determine if each of the following DEQs is homogeneous: A) X^2 + y^2 + 7xy y' = 0. B) X^2 + y^2 + 5x y' = 0. C) x - y - 8x y' = 0. D) 2x + y = y y'. Enter (1) if homogeneous, or enter (0) if not homogeneous.
A) The DEQ x² + y² + 7xyy' = 0 is not homogeneous.
B) The DEQ x² + y² + 5xy' = 0 is homogeneous.
C) The DEQ x - y - 8xy' = 0 is not homogeneous.
D) The DEQ 2x + y = yy' is not homogeneous.
How to classify the functionsTo determine if each of the given differential equations (DEQs) is homogeneous, we need to check if they satisfy the property of homogeneity, which states that all terms in the equation must have the same total degree.
A) The DEQ x² + y² + 7xyy' = 0:
The term x² has a degree of 2.
The term y² has a degree of 2.
The term 7xyy' has a degree of 2 + 1 + 1 = 4.
DEQ A is not homogeneous.
B) The DEQ x² + y² + 5xy' = 0:
The term x² has a degree of 2.
The term y² has a degree of 2.
The term 5xy' has a degree of 1 + 1 = 2.
DEQ B is homogeneous.
C) The DEQ x - y - 8xy' = 0:
The term x has a degree of 1.
The term -y has a degree of 1.
The term -8xy' has a degree of 1 + 1 = 2.
DEQ C is not homogeneous.
D) The DEQ 2x + y = yy':
The term 2x has a degree of 1.
The term y has a degree of 1.
The term yy' has a degree of 1 + 1 = 2.
DEQ D is not homogeneous.
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This large cube sculpture at the University of Michigan is made of steel. Even though it is extremely heavy, students can walk by and spin the cube very easily. Each side of the cube measures 15 feet across.
If this cube was a perfect cube and filled with sand, how much sand would be needed to completely fill it?
We would need 337,500 pounds of sand to completely fill the cube with sides measuring 15 feet across if it were a perfect cube.
The volume of a cube is calculated by taking the length of one side and raising it to the power of 3. In this case, the cube has sides that measure 15 feet each, so the volume can be calculated as:
Volume of cube = (Length of one side)^3 = (15 feet)^3 = 3,375 cubic feet
To fill the cube with sand, we would need to add enough sand to completely fill this volume. The weight of the sand we need can be calculated using its density. The density of sand varies depending on the type of sand, but a common density for dry sand is around 100 pounds per cubic foot.
Therefore, the weight of sand needed to fill the cube would be:
Weight of sand = (Volume of cube) x (Density of sand) = 3,375 cubic feet x 100 pounds per cubic foot = 337,500 pounds
It is worth noting that the real cube sculpture at the University of Michigan is not a perfect cube and is not filled with sand.
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Plz help me out again thanks!!
Answer:
303.2 cubic inches
Step-by-step explanation:
20.6in × 3.8in ×2.9in + 3.7in × 7.1in × 2.9in
= answer
3 Jazmin is mailing two packages. One package weighs 3 pounds, and the other package weighs 20 ounces. What is the total weight of both packages? (1 pound = 16 ounces)
Answer:
68oz
Step-by-step explanation:
1) 3lbs x 16oz = 48
Now we know 3lbs is 48oz. since one pound is 16 ounces, 3 pounds is 48 ounces.
2) 48 + 20 = 68oz
3) The total weight of both packages is 68 ounces.
Jesus loves ya, have a great day!
---------------------
John 8:12 - When Jesus spoke again to the people, he said, "I am the light of the world. Whoever follows me will never walk in darkness, but will have the light of life."
What is the surface area of the cylinder with height 5 mi and radius 2 mi? Round your
answer to the nearest thousandth.
Answer:
62.8319 mi²
Step-by-step explanation:
The volume formula here is V = (area of base)(height),
If we fill in the given measurements, we get:
V = π(2 mi)²(5 mi) = 62.8319 mi²
A group of researchers at UCLA are selecting existing multiple-item scales to measure depression. They found that in a previous study, "Depression Index of Diagnosis" had a Cronbach’s alpha of 0.93, "Adolescent’s Depression Scale" had a Cronbach’s alpha of 0.69. They decided to use "Depression Index of Diagnosis" because it has a higher _____ than the other and only when it is _________ it can be _________. Which is the answer A, B, C or D?
A. Reliability; valid; reliable
B. Validity; valid; reliable
C. Reliability; reliable; valid
D. Validity; reliable; valid
We can see here that option A. Reliability; valid; reliable completes the sentence.
Who is a researcher?A researcher is an individual who engages in the systematic investigation and study of a particular subject or topic to expand knowledge, gain insights, and contribute to the existing body of information in that field. Researchers can be found in various disciplines, such as science, social sciences, humanities, technology, and more.
Thus, it will be:
They decided to use "Depression Index of Diagnosis" because it has a higher reliability than the other and only when it is valid it can be reliable.
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Compute the following by using ancient Egyptian multiplication: (a) 74 X 64 (b) 129 X 413 (c) 58 X 692 (d) 4968 X 1234
Using Ancient Egyptian multiplication, the values are obtained as: (a) 74 × 64 = 2724: (b) 129 × 413 = 35405: (c) 58 × 692 = 30456: (d) 4968 × 1234 = 6148172.
Ancient Egyptian multiplication, also known as Egyptian multiplication or the method of multiplication through doubling and halving, is a method used by ancient Egyptians to multiply two numbers.
It involves breaking down one of the numbers into a sum of powers of two and then adding the corresponding multiples of the other number. Here's how you can compute the given multiplications using ancient Egyptian multiplication:
(a) 74 × 64:
We start with the number 1 and keep doubling it until we reach a number greater than or equal to 74. We then create a column for each power of 2 that was used, and write the corresponding multiple of 64 in each column. Finally, we add the numbers in the columns corresponding to the powers of 2 that make up 74.
1 × 64 = 64
2 × 64 = 128
4 × 64 = 256
8 × 64 = 512
16 × 64 = 1024
32 × 64 = 2048
Adding the numbers corresponding to powers of 2 that make up 74:
64 + 0 + 0 + 512 + 0 + 2048 = 2724
Therefore, 74 × 64 = 2724.
(b) 129 × 413:
1 × 413 = 413
2 × 413 = 826
4 × 413 = 1652
8 × 413 = 3304
16 × 413 = 6608
32 × 413 = 13216
64 × 413 = 26432
Adding the numbers corresponding to powers of 2 that make up 129:
413 + 0 + 1652 + 0 + 6608 + 0 + 26432 = 35405
Therefore, 129 × 413 = 35405.
(c) 58 × 692:
1 × 692 = 692
2 × 692 = 1384
4 × 692 = 2768
8 × 692 = 5536
16 × 692 = 11072
32 × 692 = 22144
Adding the numbers corresponding to powers of 2 that make up 58:
692 + 1384 + 0 + 5536 + 0 + 22144 = 30456
Therefore, 58 × 692 = 30456.
(d) 4968 × 1234:
1 × 1234 = 1234
2 × 1234 = 2468
4 × 1234 = 4936
8 × 1234 = 9868
16 × 1234 = 19668
32 × 1234 = 39468
64 × 1234 = 78936
128 × 1234 = 157872
256 × 1234 = 315744
512 × 1234 = 631488
1024 × 1234 = 1262976
Adding the numbers corresponding to powers of 2 that make up 4968:
1234 + 2468 + 4936 + 0 + 19668 + 39468 + 78936 + 157872 + 315744 + 0 + 1262976 = 6148172
Therefore, 4968 × 1234 = 6148172.
Using the ancient Egyptian multiplication method, we have computed the products for the given multiplications.
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give an estimated simple linear regression equation of = 46.2 589.2x with a coefficient of determination r2 of 0.7523, interpret the coefficient of determination for this equation.
The estimated simple linear regression equation is y = 46.2 + 589.2x, with a coefficient of determination (r^2) of 0.7523.
The coefficient of determination (r^2) measures the proportion of the total variation in the dependent variable (y) that can be explained by the independent variable (x) in a linear regression model. In this case, the coefficient of determination is 0.7523, indicating that approximately 75.23% of the variation in the dependent variable (y) can be explained by the independent variable (x) using the given regression equation. This means that the linear relationship between x and y accounts for 75.23% of the variability observed in y. The remaining 24.77% of the variation is attributed to other factors not included in the model. A higher value of r^2 indicates a stronger relationship between the variables.
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USA Today reported that the population mean life span of people who live in Hawaii is 77 years. A random sample of 20 obituary notices gave a sample mean life span of x= 71.4 years and a sample standard deviation s = 20.65 years. Assuming that the life span of people in Hawaii is normally distributed, does this indicate that the population mean life span is less than 77 years? Use a 5% level of significance. a.) What is a? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two tailed test?
α = ____
H_0: µ = _____
H_1: µ = _____
The test is a _______ test.
Yes, there is evidence to suggest that the population mean life span in Hawaii is less than 77 years.
How to find that is there statistical evidence that the mean life span in Hawaii is less than 77 years?The hypothesis test in question aims to determine if there is sufficient evidence to support the claim that the population mean life span in Hawaii is less than 77 years.
The null hypothesis (H₀) assumes that the mean life span is equal to 77 years, while the alternative hypothesis (H₁) suggests that the mean life span is less than 77 years.
To conduct the hypothesis test, a significance level (α) of 5% is chosen, which corresponds to a 95% confidence level.
Since the question asks whether the population mean is less than 77 years, this is a left-tailed test.
Using the given sample information, the test statistic can be calculated using the formula:
t = (x - µ) / (s / √n), where x is the sample mean (71.4), µ is the population mean (77), s is the sample standard deviation (20.65), and n is the sample size (20).
By plugging in the values, the test statistic is calculated to be t = (71.4 - 77) / (20.65 / √20) ≈ -1.64.
To determine whether the test statistic falls in the critical region, the critical value for a left-tailed test at α = 0.05 is obtained from the t-distribution table or calculator.
With 19 degrees of freedom, the critical value is approximately -1.73.
Since the test statistic (-1.64) is not less than the critical value (-1.73), we fail to reject the null hypothesis.
This means that there is insufficient evidence to conclude that the population mean life span in Hawaii is less than 77 years at a 5% level of significance.
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(+6) ÷ (+2) =
answer choices
+12
+8
+4
+3
-3
Answer:
+3
Step-by-step explanation:
(+6) ÷ (+2)
=6/2
Divide the numbers; 6/2=3
=3
Hope this helped!!!
What is another way to express 52 + 24?
8 (6 + 3)
4(13+6)
6 (9+4)
13 (4+2)
Done
Answer:
it's the 2nd one
Step-by-step explanation:
hoped I helped:)
is 0. overline 19 rational or irrational? Explain.
Answer:
19/99
Step-by-step explanation:
There are twenty books on a shelf. Ten of them are science books, two are social studies, seven are math, and one is reading. What is the probability of choosing a science book, replacing it and then choosing another science book?
Answer: 1/4
Step-by-step explanation: Probability is favorable outcomes/ all outcomes, to first choose a science book, the probability is 10/20, or one-half, and then to pick one again, is also 1/2, so you multiply them together to find the probability of both happening and you get 1/4!