Answer:
The solution is w ≤ 18
A Statistics Primer A researcher is interested in handedness in ants. (Here, handedness refers to the propensity of individuals to turn more often in one direction than another.) He hypothesizes that if ants show handedness they should be more likely to turn into the right or left arms of a T-maze. He plans to place 20 ants into a maze and use a binomial test to evaluate this hypothesis. When the 20 ants were placed into the maze he observed that 16 of the ants walked into the right arm and that three ants walked into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). (1 point) 5. What is the probability that exactly 16 of the ants enter the right arm when the null hypothesis is true? (1 point) 6. What outcomes are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true? (Example of a more extraordinary outcome: The outcome in which all 19 ants turn into the right arm and no ants turn into the left arm (19R, OL) is more extraordinary than the outcome he observed.] (1 point) 7. What are the probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true? (Probability for example given in Problem 6: 1 (1 point) 8. What is the probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true? Be sure to include the observed outcome in this calculation! (This is the P value for the binomial test.) (1 point) 9. Does the observed outcome indicate that the null hypothesis should be rejected at a rejection criterion of 0.05? What do you conclude?
The observed data indicates that the null hypothesis should be rejected at a rejection criterion of 0.05. This means that the data supports the researcher's hypothesis that ants show handedness, and that they are more likely to turn into the right or left arms of a T-maze.
The researcher is interested in determining if ants show handedness.
The researcher is hypothesizing that if ants show handedness, they will be more likely to turn into the right or left arms of a T-maze.The researcher placed 20 ants into the maze and observed that 16 of the ants walked into the right arm and 3 into the left arm (one ant managed to crawl over the edge of the maze before it went down either of the arms). The probability that exactly 16 of the ants enter the right arm when the null hypothesis is true is 0.368. This is calculated using the binomial formula, P(x=16) = (20 choose 16) * (0.5)^16 * (0.5)^4, where 0.5 is the probability of each ant turning into either arm.Outcomes that are equally extraordinary or more extraordinary than the outcome observed under conditions in which the null hypothesis is true include: 17R, 3L; 18R, 2L; 19R, 1L; and 19R, OL.The probabilities associated with the outcomes identified in Problem 5 under conditions in which the null hypothesis is true are: 0.246 for 17R, 3L; 0.127 for 18R, 2L; 0.052 for 19R, 1L; and 0.026 for 19R, OL.The probability that an outcome as extraordinary or more extraordinary than the outcome observed would occur when the null hypothesis is true is 0.451. This is calculated by adding up the probabilities associated with each of the outcomes identified in Problem 5 (0.368 for 16R, 4L, 0.246 for 17R, 3L, 0.127 for 18R, 2L, 0.052 for 19R, 1L, and 0.026 for 19R, OL).
The observed outcome does not indicate that the null hypothesis should be rejected at a rejection criterion of 0.05 since the P value for the binomial test (0.451) is greater than 0.05. Therefore, we cannot reject the null hypothesis and conclude that ants do not show handedness.
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What is the sum of the first 20 multiples of five?
Answer:
1050
Step-by-step explanation:
Answer:
the answer is: 1050
Step-by-step explanation:
hope it helped you mark brainliest
2. În triunghiul ABC, AB=3√7 cm, BC = sqrt(17) cm şi AC= 4√5 cm. Verificați dacă triunghiul este dreptunghic cu catetele AB şi BC.
Answer: it’s b
Step-by-step explanation:
your welcome
#13
Points (1,-1), (3, 2), and (7, -3) are three vertices of a
parallelogram. How many parallelograms can be created using
these three vertices?
O One
O Two
O Three
O Four
Identify the coordinates of each point that could be the fourth
vertex. Select all that apply.
(9,-2)
(-3,2)
(5,4)
(9,0)
(-3, 4)
(5, -6)
(5,-4)
(3,2)
Answer:
Two parallelograms can be created using these three vertices. The fourth vertex of the first parallelogram would have the coordinates (9,-2), and the fourth vertex of the second parallelogram would have the coordinates (-3,4). The other coordinates given are not valid for the fourth vertex of a parallelogram.
Answer:
three
(5,-6)
(9,0)
(-3,4)
d is inversely proportional to r.
d = 7 when r = = 8
a) Use the information above to write an
equation for d in terms of r.
b) What is the value of d when r =
Give any decimal answers to 1 d.p.
= 5?
Answer: 11.2
Step-by-step explanation:
a) d= k/r
=> 7= k/8
=> k= 7x8
therefore, k=56
b) d=k/r
=> d=56/ 5
so, d= 11.2
The value of d is 7 when r = 5.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
d is inversely proportional to r.
This can be written as,
d ∝ 1/r
d = k/r
Now,
d = 7 when r = = 8
This means.
7 = k/8
k = 56
Now,
Substituting r = 8.
d = 56/8
d = 7
Thus,
d = 7.
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consider a game of nim with four piles, of sizes 9, 10, 11, 12. (a) is this position a win for the next player or the previous player (assuming optimal play)? describe the winning first move. (b) consider the same initial position, but suppose that each player is allowed to remove at most 9 chips in a single move (other rules of nim remain in force). is this an n- or p-position?
This is a position a win for the next player; the first player's winning move is to remove 2 chips from the pile with size 11, and if each player is allowed to remove at most 9 chips in a single move, then this is a P-position, and the previous player has won.
(a) The outcome of a game of Nim depends on the XOR (exclusive or) of the sizes of the piles. The XOR of 9, 10, 11, and 12 is 2, which means that this is a P-position (i.e., the previous player has won).
To determine the winning first move, we must find a combination of pile sizes that results in a new XOR of 0. One way to do this is to remove 2 chips from the pile with size 11, resulting in 9, 10, 9, and 12. The XOR of these new pile sizes is 0, which means that this is an N-position (i.e., the next player will win).
The first player's winning move is to remove 2 chips from the pile with size 11.
(b) The maximum number of chips that can be removed in a single move is 9, so the players are restricted in the amount they can remove. However, the outcome of the game still depends on the XOR of the pile sizes. In this case, the XOR of 9, 10, 11, and 12 is 2, which means that this is still a P-position and the previous player has won.
The winning first move, as described above, would still be to remove 2 chips from the pile with size 11.
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What is the area of rhombus KLMN? Rhombus 467.4 in 387.6 in 289 in 287.3 in
The area of rhombus KLMN is 287.3 in²
What are rhombuses?A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.
Given:
Since, the diagonals of a rhombus bisects each other at a right angle,
Let they bisect at O,
so, KM = 2MO = 2KO = 2×11.4 = 22.8 in
Thus, Δ KON is a right triangle,
Using Pythagoras theorem,
KN² = KO² + ON²
ON = √17²-11.4²
ON = 12.611 in
LN = 2×12.611
LN = 25.22 in
Then, Area of a rhombus = 1/2 × diagonal 1 × diagonal 2
Area = 1/2 × 25.22 × 22.8
= 287.3 in²
Hence, the area of rhombus KLMN is 287.3 in²
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Evaluate the expression and write your answer in the form a+bi.
√−25
The express in the form of a + bi would be 0 + 5i.
What is meant by Complex numbers?Complex numbers are those expressed as a + ib, where a, b are real numbers and 'i' is a fictitious number called a "iota." i is equal to (√-1). A pair of real and imaginary numbers combined in the form a + bi.
When a and b are real numbers, a complex number is one with the formula a + bi. The complex number has two parts: real component (a) and imaginary part (b). If both the real and imaginary components of two complex numbers are identical, only then are the two complex numbers equal.
Let the given expression be [tex]$\sqrt{-25}$$[/tex].
We have to evaluate the expression.
[tex]$$\begin{aligned}\sqrt{-25} & =\sqrt{-1 \cdot 25} \\& =\sqrt{-1} \sqrt{25} \\& =i(5) \\& =5 i\end{aligned}$$[/tex]
The express in the form of a + bi = 0 + 5i.
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Suppose the demand curve for pencils is QD = 200 - 4P. What is the exact own price elasticity of demand at P-$30?A. -0.67B. -10.67C. -0.09D. -1.5
The exact own price elasticity of demand is (A) -0.67.
The own price elasticity of demand measures the responsiveness of the quantity demanded to changes in price. It can be calculated using the formula:
epsilon = (dQ/dP) * (P/Q)
where dQ/dP is the derivative of the demand curve with respect to price and P/Q is the price elasticity of demand.
In this case, the demand curve is QD = 200 - 4P, so dQ/dP = -4. When P=$30, Q = 200 - 4 * 30 = 140. So,
epsilon = (-4) * (30/140) = -0.67
Hence, the exact own price elasticity of demand at P=$30 is -0.67, so the answer is A. -0.67.
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the radius of earth is 6371 km. how many times longer is the diameter of earth than the piece of wood's length? use scientific notation.
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
The radius of earth is 6371 km.
Let's say the length of the piece of wood is L.
The diameter of the Earth is 2 times its radius
The radius of our planet, The Earth, is the distance from the center of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km.
Radius of a circle is the distance from the center of the circle to any point on it's circumference. It is usually denoted by 'R' or 'r'. The area and circumference of a circle are also measured in terms of radius.The diameter of a circle is the length of the line starting from one point on a circle to another point and passing through the center of the circle. It is equal to twice the radius of the circle. It is usually denoted by ‘d’ or ‘D’.
Diameter = 2 x RadiusThe diameter of the Earth is 2 times its radius, or 2 x 6371 km = 12742 km.
The diameter of the Earth is 12742 km / L times longer than the length of the piece of wood.
In scientific notation, we can express this as:
12742 km / L = [tex]1.2742*10^4 km / L[/tex]
The [tex]1.2742*10^4 km / L[/tex] times longer is the diameter of earth than the piece of wood's length.
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Given that the econd term of a equence i 8 and the fourth term i 2, Franci wrote the explicit rule an = 4 · ( 1 4 )n − 1 for the equence. Complete the explanation of hi error
Francis made an error in writing the explicit formula. The correct formula should be an = 4 * (1/4)⁽ⁿ⁻¹⁾, not an = 4 * (1/4)ⁿ⁻¹. The exponent should be (n-1), not just n, to correctly represent the sequence where the second term is 8 and the fourth term is 2.
Explicit Formula Error CorrectionTo determine the error in Francis' formula, we need to apply it to the known terms of the sequence and see if it produces the correct values. For example, for the second term, n = 2, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)¹ = 4 * 1/4 = 1
But the second term of the sequence is 8, not 1. So the formula is incorrect.
Similarly, for the fourth term, n = 4, so using Francis' formula:
an = 4 * (1/4)⁽ⁿ⁻¹⁾ = 4 * (1/4)³ = 4 * 1/64 = 1/16
But the fourth term of the sequence is 2, not 1/16. So the formula is still incorrect.
Therefore, we can conclude that the formula written by Francis is not correct and needs to be corrected to accurately describe the sequence.
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evaluate the expression 4(3-2)^3+2(-8) and justify each step
Answer:-12
Step-by-step explanation: First you will have to deal with the things in parenthesis and the exponent. So after cubing the 3 and 2 the equation you will then multiply and then add them rest of the numbers to get -12
a soup can has a diameter of 278 inches and a height of 414 inches. how many square inches of metal are required to make the soup can?
Are required 482,972.60 in^2 of metal to make the soup can
What is the area?Is the measure of the space occupied by a body bounded by an environment called perimeter, the same is expressed in units of squared side. Example: ft^2, m^2
The formula and procedure to solve this geometry exercise is:
A= (2* π *r * h) + (2 * π * r²)
Where:
A = areah = height r = radiusProblem information:
d = 278 inh = 414 inA = ?Using the formula of the cylinder area we get:
A= (2* π *r * h) + (2 * π * r²)
A= [2* π *(278/2) * 414] + [2 * π * (278/2)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A= [2* π *(139) * 414] + [2 * π * (139)²]
A = 361575.18 in^2 + 121397.42 in^2
A = 482,972.60 in^2
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proms friend gives him a row of pascal’s triangle and asks which row it comes from. prom adds the numbers and obtains a sum of 65 536. which row do the numbers come from? 34 18 17 16
The correct answer is row number 16 since the sum is 65536 in
pascal's triangle which equals to the 2 power of 16 , that is 4th option.
Pascal's triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y)n. This triangle is the triangular array of numbers that begins with 1 on the top and with 1's running down the two sides of a triangle. In any row of Pascal's triangle, the sum of the first, third, fifth, … numbers is equal to the sum of the second, fourth, sixth numbers.
(1+x)n=(n0)+(n1)x+(n2)x2+⋯+(nr)xr+⋯+(nn−1)xn−1+(nn)xn.
We know that , 2^16 = 65536
Therefore, the numbers come from the row number.16
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0.800 in fraction form
Answer:8/
Step-by-step explanation: It is because any number after decimal point contains zero at it's end then the number is considered as it is. For example here 0.800 so after decimal point is 8, and after 8 there are zero's. So numerically, it is 0.8 or 0.800 both are same . Hence it's fraction form would be 8/ 10.
Answer:
4/5
Step-by-step explanation:
0.800 = 800/1000 = 8/10 = 4/5
When a chartered accountant (CA) provided his services to Mr. Rao in filing his income
returns, his bill for services was ₹8260 inclusive of 18% GST. What is the original
amount of the bill? How much is the GST paid to the State Government by the CA
The original amount of the bill was $7000 and the GST paid to the State Government by the CA is $1260.
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 bill services including the GST = 8260
and, Rate of GST= 18%
So, let the original amount was x
x+ 18% of x= 8260
x + 0.18x = 8260
1.18x= 8260
x= $7000
and, the GST paid to Govt. = 8260 -7000 = $1260.
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Can anyone factor these equations?
7) The factors of the expression (x² + 17x + 60) is, (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is, (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is, 2 (x - 2) (x - 7)
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, We can factor as;
7) The factors of the expression (x² + 17x + 60) is,
⇒ x² + 17x + 60
By using quadratic formula as;
⇒ x = - 17 ± √(17² - 4×1×60 / 2
⇒ x = - 17 ± √289 - 240 / 2
⇒ x = - 17 ± √49 / 2
⇒ x = - 17 ± 7 / 2
⇒ x = - 17 + 7 / 2
⇒ x = - 10/2
⇒ x = - 5
And, x = - 17 - 7 / 2
⇒ x = - 24/2
⇒ x = - 12
Thus, The factors of the expression (x² + 17x + 60) is,
⇒ (x + 5) (x + 12)
8) The factors of the expression (x² - 6x - 27) is,
⇒ x² - 6x - 27
⇒ x² - 9x + 3x - 27
⇒ x (x - 9) + 3 (x - 9)
⇒ (x + 3) (x - 9)
Thus, The factors of the expression (x² - 6x - 27) is,
⇒ (x + 3) (x - 9)
9) The factors of the expression (2x² - 18x + 28) is,
⇒ 2x² - 18x + 28
⇒ 2 (x² - 9x + 14)
⇒ 2 (x² - 7x - 2x + 14)
⇒ 2 (x (x - 7) - 2 (x - 7))
⇒ 2 (x - 2) (x - 7)
Thus, The factors of the expression (2x² - 18x + 28) is,
⇒ 2 (x - 2) (x - 7)
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A home was bought 4 years ago. The purchase price was $92,000 and the buyer made a down payment of $11,000. The current loan balance is $79,000. The house was recently appraised for $116,000. What is the equity?
a)13,000
b)24,000
c)35,000
d)37,000
If the current loan balance is $79,000 and the house was recently appraised for $116,000, the equity in the house would be worth d) $37,000.
The home was bought at a price of $92,000 and a down payment of $11,000 was made. It is also given that the current loan balance is $79,000.
Also, the house was recently appraised for $116,000. We are asked to calculate the equity.
Now, equity is defined as the sum of money the owner of an item would receive if they sold it and all associated debts were settled is known as equity. For example, if one person owns a house which has a value of $100,000 and he has a mortgage of $40,000. Then, the equity in the home would be worth $60,000.
Here, in this question, the current debt is $79,000 and the current value of the house is $116,000.
So, the equity in the home would be:
Equity = 116,000 - 79000 = $37,000
Hence, the equity in the house would be worth $37,000.
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Work out the equation of the line shown below.
Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
An equation of the line shown above in slope-intercept form is y = x/8 + 5/2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y represents the data points.From the information provided in the graph above, we have the following data points on its line:
Points on the x-axis = (60, 140).Points on the y-axis = (10, 20).At data point (60, 10), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 10 = (20 - 10)/(140 - 60)(x - 60)
y - 10 = 1/8(x - 60)
y = x/8 - 7.5 + 10
y = x/8 + 5/2
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help me pleaseeee i need help
Answer:
see below
Step-by-step explanation:
z+66+z+69+43z=180
so 45z=180-66-69 = 45
so z=1
so angle U= 43 its opposite side length ST is the smallest
same logic for the other 2.
66+1=67
69+1=70
so ST<US <TU
Determine which of the following graphs represent the equation below. Also determine the y-intercept of the graph.
y = 5 (2 Superscript x Baseline)
a.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and approaches x = 1 in quadrant 1.
y-intercept = 1
c.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 2) and approaches x = 1 in quadrant 1.
y-intercept = 1
b.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 1) and (2, 4) in quadrant 1.
y-intercept = 2
d.
On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
Answer: The equation y = 5 * 2^x represents an exponential function where the base is 2 and the y-intercept is 5.
The graph that best fits this equation is:
d. On a coordinate plane, a curve approaches the x-axis in quadrant 2, and then increases through (0, 5) through quadrant 1.
y-intercept = 5
So, the correct answer is d.
Step-by-step explanation:
a function satisfies the differential equation (a) what are the constant solutions of this equation? separate your answers by commas.
The solutions are decreasing when y is in the set (1,3).
(A) Equilibrium solutions, also known as constant solutions, fulfill dy/dx=0.
When the right-hand side of the equation is taken into account, we have
dy/dx equals y2(y-1) (y-3). We get the constant solutions y=0, y=1, and y=3 by setting the right side to zero.
(b) Solutions rise when dy/dx exceeds 0. For the set of y values (-,0) (0,1) (3,) see that dy/dx > 0. Therefore, when y in is the set (-,0) (0,1) (3,), solutions are growing.
(c) When dy/dx 0, solutions are decreasing, and dy/dx 0 when 1 y 3. That is, while y is in the set, solutions are decreasing (1,3).
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The table below shows how far a person driving in their car was able to go over different intervals of time. Perform a regression to model the data, using the form y = kx + h. What is your value for k? (Round your answer to the nearest tenth.)
Answer:
kxh is the answer to this question
five whole positive numbers add up to 47 one of the numbers is a multiple of nine the other four numbers are equal
The positive whole numbers are 27 and 5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the 5 positive whole numbers be a, b, c, d and e.
One of the numbers is a multiple of nine the other four numbers are equal.
Now, 9a+b+b+b+b=47
9a+4b=47
If b=1
9a=43
Here, we don't get whole number.
If b=2
9a=39
Here, we don't get whole number.
If b=3
9a=35
Here, we don't get whole number.
If b=4
9a=31
Here, we don't get whole number.
If b=5
9a=27
a=3
Substitute a=3 in equation 9a+4b=47
b=5
Therefore, the positive whole numbers are 27 and 5.
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. Taylor can cut a standard size lawn in 3 hours. Jamie can do the same job in 2 hours.
If Taylor works twice as many hours as Jamie and they complete 4 lawns, how many hours
does Taylor work?
Let's call the number of hours Jamie works "J" and the number of hours Taylor works "T".
We know from the problem that T = 2 * J, because Taylor works twice as many hours as Jamie.
We also know that J + T = 4 * (3 + 2), because they are working together to complete 4 lawns and it takes 3 hours for Taylor and 2 hours for Jamie to complete one lawn.
So we can substitute the first equation into the second equation:
2J + J = 4 * (3 + 2)
3J = 4 * 5
J = 4
So Jamie works 4 hours and Taylor works 2 * 4 = 8 hours.
Twenty students in Class A and 20 students in Class B were asked how many hours they took to prepare for an exam. The data sets represent their answers. Class A: {2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5} Class B: {3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6} Which statement is true for the data sets? Group of answer choices The mean study time of students in Class A is less than students in Class B. The range of study time of students in Class A is less than students in Class B. The mean and median study time of students in Class A and Class B is equal. The median study time of students in Class B is greater than students in Class A. The mean study time of students in Class B is less than students in Class A.
The mean study time of students in Class B is less than students in
Class A.
Option E is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
Class A:
{2, 5, 7, 6, 4, 3, 8, 7, 4, 5, 7, 6, 3, 5, 4, 2, 4, 6, 3, 5}
Mean:
(2 + 5 + 7 + 6 + 4 + 3 + 8 + 7 + 4 + 5 + 7 + 6 + 3 + 5 + 4 + 2 + 4 + 6 + 3 + 5) / 20
= 96/20
= 4.8
Arrange the numbers in order.
= 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8
Median = 5
Range = Highest - Lowest = 8 - 2 = 6
Class B:
{3, 7, 6, 4, 3, 2, 4, 5, 6, 7, 2, 2, 2, 3, 4, 5, 2, 2, 5, 6}
Mean:
= (2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7 + 7 = 84/20
= 4.2
Arrange the numbers in order.
= 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7
Median = 4
Range = Highest - Lowest = 7 - 2 = 5
Thus,
Mean of class A > Mean of class B
Median of class A > Median of class B
Range of class A > Range of class B
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Use the points (-3, 5) and (8, -17) to write an equation in standard form (show all work)
Answer:
2x+y=-1
Step-by-step explanation:
I can't really explain,But the equation is AX+BY=C
which expressions are equivalent to 5(x+7)+7(x+5)
Equivalent to 5(x+7)+7(x+5) is expression 12x + 70 .
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression
5(x+7)+7(x+5)
Using distributive property
= 5x + 35 + 7x + 35
Adding like terms
= 12x + 70
Hence, expression 12x + 70 is equivalent to 5(x+7)+7(x+5).
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Increase R245 in the ratio 5:6.
Answer:
To increase R245 in the ratio 5:6, you can add an amount proportional to the ratio 5:6 to R245.
Let's say you want to increase R245 by x.
The new value for 5 parts will be 5x + 245, and the new value for 6 parts will be 6x + 245.
So, the new ratio would be (5x + 245) : (6x + 245), which is still 5:6.
Therefore, to increase R245 in the ratio 5:6, you would add x to R245.
The table shows the parts of powder and water used to make gelatin.
Boxes of Gelatin Powder (oz) Water (cups)
3 9 6
8
At this rate, how much powder and water will Jeff use to make 8 boxes of gelatin?
To make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
From the given table, we have
Boxes Gelatin Powder (oz) Water (cups)
3 9 6
Here,
Gelatin Powder = 3 × Boxes
Water = 2 × Boxes
The equations for 8 boxes is
Gelatin Powder = 3 × 8
= 24 oz
Water = 2 × 8
= 16 cups
Hence, to make 8 boxes of gelatin Jeff used 24 oz of gelatin powder and 16 cups of water.
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