The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:
n = 9604.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The margin of error is modeled as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We have no estimate of the proportion, hence it is used as follows:
[tex]\pi = 0.5[/tex]
The margin of error is of M = 0.01, hence the sample size is obtained as follows:
[tex]0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.96 \times 0.5[/tex]
[tex]\sqrt{n} = 98[/tex]
n = 98²
n = 9604.
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what is the ratio of 2:35
Answer:
2:35
Step-by-step explanation:
Use an appropriate infinite series method about x = 0 to find two solutions of the given differential equation. (Enter the first four nonzero terms for each linearly independent solution, if there are fewer than four nonzero terms then enter all terms. In each case, the first term has been provided for you. )
3xy" y+y=0
Y₁ = 1 -
12 = x2/3
The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
We can use the power series method to find the two solutions of the given differential equation:
Let y = ∑anxn be a power series solution. Then, we have:
y' = ∑nanxn-1
y'' = ∑nan(n-1)xn-2
Substituting these into the differential equation and equating coefficients of like powers of x, we get:
3x∑nan(n-1)xn-1 + ∑anxn = 0
Simplifying, we obtain:
∑[3nan(n-1) + an-1]xn = 0
Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:
an = -an-1/(3n(n-1)), n ≥ 1
Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:
y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...
To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:
y₂' = v'y₁ + vy₁'
y₂'' = v''y₁ + 2v'y₁' + vy₁''
Substituting these into the differential equation and simplifying, we get:
v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0
Since y₁(x) is a solution, we have:
y₁'' + (1/3x)y₁ = 0
Multiplying by y1 and integrating, we obtain:
(y₁')² + y₁²/3 = C
where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:
y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...
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the form Q+bar (D) where the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4)
In this expression, Q+bar (D) is a polynomial, and we are asked to compare the degree of R with that of the polynomial (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4).
The degree of a polynomial is determined by the highest power of the variable. The highest power of c in (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4) is 3, so this polynomial has a degree of 3.
To compare it to the degree of R, we need to know the highest power of R in our expression. If the degree of R is less than the degree of (c^(3)+2c^(2)-5c-2)/(c^(2)+c-4), then the expression Q+bar (D) will have a degree of 3.
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On a certain day, the temperature of the pool was 76°F at 10 A.M. and 91°F at 1 P.M. If the temperature rose at a constant rate from 10 A.M. to 1P.M. on that day, what was the temperature at 11 A.M.? a. 79°F d. 89°F b. 81°F e. 90°F c. 86°F
The correct answer is b. 81°F.
On a certain day, the temperature of the pool rose at a constant rate from 76°F at 10 A.M. to 91°F at 1 P.M. To find the temperature at 11 A.M., we need to find the rate of change in temperature and then use it to calculate the temperature at 11 A.M.
The rate of change in temperature can be found by dividing the difference in temperature by the difference in time:
Rate of change = (91°F - 76°F) / (1 P.M. - 10 A.M.) = 15°F / 3 hours = 5°F per hour
Now, we can use this rate of change to find the temperature at 11 A.M.:
Temperature at 11 A.M. = 76°F + (5°F per hour)(1 hour) = 81°F
Therefore, the correct answer is b. 81°F.
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Use the commutative or associative property to simplify the expression. (1)/(13)(13y)
The simplified expression of (1)/(13)(13y) is 169y.
To simplify the expression (1)/(13)(13y) using the commutative or associative property, we can rearrange the terms and group them together.
Using the commutative property, we can rearrange the terms so that the two 13's are next to each other:
(1)(13)(13y) = (13)(13y)(1)
Now, using the associative property, we can group the two 13's together and simplify:
(13)(13y)(1) = (13*13)(y)(1) = (169)(y)(1)
Finally, we can simplify further by multiplying the 169 and 1 together:
(169)(y)(1) = (169y)(1) = 169y
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True; by the Invertible Matrix Theorem if the equation Ax^(0) has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix.
The given statement, "by the Invertible Matrix Theorem if the equation [tex]Ax^{(0)}[/tex]has only the trivial solution, then the matrix is invertible. Thus, A must also be row equivalent to the identity matrix," is true (T).
This is because the theorem states that a square matrix is invertible if and only if it can be transformed into the identity matrix by a sequence of elementary row operations. And if the equation [tex]Ax^{(0)}[/tex] only has the trivial solution, then the matrix must be row equivalent to the identity matrix, implying that it is invertible.
The Invertible Matrix Theorem is a powerful result in linear algebra that allows us to determine whether a square matrix is invertible or not. It states that a square matrix is invertible if and only if its determinant is nonzero, which is equivalent to saying that the matrix can be transformed into the identity matrix by a sequence of elementary row operations.
If the matrix is not invertible, then its determinant is zero, and it is said to be singular. In this case, the equation [tex]Ax^{(0)}[/tex] will have infinitely many solutions or no solutions at all, depending on the specific values of the right-hand side vector.
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Find the minimum and maximum of P=4x+2y subject to 3x+5y>=20 3x+y<=16 -2x+y<=2 x>=0,y>=0
The minimum of P is 16 and the maximum of P is 24.
Calculating the value of P for these points, we get:
P(2,6) = 4*2 + 2*6 = 20
P(0,8) = 4*0 + 2*8 = 16
P(4,2) = 4*4 + 2*2 = 24
P(3,3) = 4*3 + 2*3 = 18
Therefore, the minimum of P is 16 and the maximum of P is 24.
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The surface area of a rectangular prism is 250 cm 2. If its height is 10 centimeters, and its width is 5 centimeters, what is its volume?
The volume of the rectangular prism whose surface area is 250 cm square is 250cubic centimeters.
The surface area of a rectanular prism is calculates by the formula
= 2( length*width + length*height + width*height ) square units
Let the length of the given prism be l centimeters.
Given, width is 5 centimeters and height is 10 centimeters of the rectangular prism.
The surface area of the rectangular prism is 250 cm square.
Thus by the above formula,
250 = 2 ( l*5 + l*10 +10*5)
⇒250 = 2 (15*l +50)
⇒ 250= 30*l + 100
⇒ 150 = 30*l
⇒l = 150/30 = 5 (centimeters)
Thus the volume of the given rectangular prism is calculated as
= ( length*width*height) cubic units
= (5*5*10) cubic centimeters
= 250 cubic centimeters
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Mrs.may mixed 4 gal of red paint with every 6 gal of blue paint in order to make purple paint. which ratio of gallons of red paint to gallons of blue pint will make the same shade of purple paint?
Answer: 20 gallons of red paint and 30 gallons blue paint
Step-by-step explanation:
How to express a two logarithm into a single logarithm
Answer:
There are different methods to express a two logarithm into a single logarithm, depending on the specific form of the logarithms involved. Here are some examples:
Logarithms with the same base:
If you have two logarithms with the same base, you can use the following logarithmic identity:
log_a(x) + log_a(y) = log_a(xy)
Using this identity, you can express a sum or difference of logarithms with the same base as a single logarithm:
Example 1: log_2(3) + log_2(5) = log_2(3*5) = log_2(15)
Example 2: log_5(7) - log_5(2) = log_5(7/2)
Logarithms with different bases:
If you have two logarithms with different bases, you can use the following change of base formula to express them with a common base:
log_a(x) = log_b(x) / log_b(a)
Using this formula, you can rewrite a logarithm with a base a as a logarithm with a base b:
Example 1: log_2(7) = log_10(7) / log_10(2)
Example 2: log_5(2) = log_2(2) / log_2(5)
Once you have expressed both logarithms with the same base, you can apply the logarithmic identity from method 1 to simplify them into a single logarithm.
Graph the inequality y+4<-2(x-4) on the set of axes below
Answer:
y < 2x + 4
Step-by-step explanation:
y+4<-2(x-4)
y + 4 < -2x +8
y < 2x + 4
Simplify the following expressicn using addition and subtraction. (x)/(3)+(2x)/(18)-(6x)/(3)
The answer is (-14x)/(9).
To simplify the given expression, we need to find a common denominator for all the fractions, which is 18. We can then multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions. Once we have the same denominator, we can combine the numerators using addition and subtraction. Finally, we can simplify the resulting fraction if possible.
The expression is: (x)/(3)+(2x)/(18)-(6x)/(3)
First, find a common denominator for all the fractions. The smallest common denominator is 18.
Next, multiply the numerators and denominators of each fraction by the same number to get the same denominator for all the fractions:
(x)/(3) * (6)/(6) = (6x)/(18)
(2x)/(18) * (1)/(1) = (2x)/(18)
(6x)/(3) * (6)/(6) = (36x)/(18)
Now, we can combine the numerators using addition and subtraction:
(6x)/(18) + (2x)/(18) - (36x)/(18) = (6x + 2x - 36x)/(18) = (-28x)/(18)
Finally, we can simplify the resulting fraction by dividing both the numerator and denominator by 2:
(-28x)/(18) = (-14x)/(9)
So the simplified expression is: (-14x)/(9)
Therefore, the answer is (-14x)/(9).
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when flying on an air plane the weight limit for carry on luggage is 30 pounds there are approximately 453.6 grams in 1 pound which measurement is closet to the weight of the checked luggage in grams
Answer:
Step-by-step explanation:
30x453.6=13608 grams
Question 3 of 12 , Step 1 of 1 Find three consecutive integers whose sum is 360.
The three consecutive integers whose sum is 360 are 119, 120, and 121.
To find three consecutive integers whose sum is 360, we can use algebra to set up an equation and solve for the first integer. Let x be the first integer, then the next two consecutive integers will be x+1 and x+2. The sum of these three integers is 360, so we can write the equation:
x + (x+1) + (x+2) = 360
Simplifying the equation gives us:
3x + 3 = 360
Subtracting 3 from both sides gives us:
3x = 357
Dividing both sides by 3 gives us:
x = 119
So the first integer is 119. The next two consecutive integers are 120 and 121. Therefore, the three consecutive integers whose sum is 360 are 119, 120, and 121.
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NEED HELP DUE FRIDAY!!!!!!!!!!!
Find cos(A), sin(A), and tan(A) for triangle ABC.
Answer:
It’s a right triangle
Step-by-step explanation:
15 squared plus 8 squared equals 17 squared which 289=289
Find the measure of pkt
Answer:
32°
Step-by-step explanation:
You want the measure of the smaller angle of the linear pair marked (3g+23) and (7g+127).
Linear pairThe angles of a linear pair total 180°, so we have ...
(3g +23) +(7g +127) = 180
10g = 30 . . . . . . . . . subtract 150
g = 3 . . . . . . . . . divide by 10
The smaller angle is ...
∠PKT = (3·3 +23)°
∠PKT = 32°
Designing an Addition A 40-ft-wide house has a roof with a
6-12 pitch (the roof rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will have a 3-12 pitch to its roof. Find the lengths of AB and BC in the accompanying figure.
We can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
What is sine formula in trigonometry?Sine formula is used to calculate the sine angle of a right-angled triangle which is the ratio of the opposite side and the hypotenuse.
Given is that a 40-ft-wide house has a roof with a 6-12 pitch (the roof
rises 6 ft for a run of 12 ft). The owner plans a 14-ft-wide addition that will
have a 3-12 pitch to its roof.
We can write the measure of length AB as -
AB = 6 + √(9 + 296)
AB = 6 + 17.46
AB = 23.46 ft
We can write the measure of length BC as -
BC = 6 + 1/4 x 12
BC = 6 + 3
BC = 9 ft
Therefore, we can conclude that the measure of length AB is 23.46 ft and the measure of length BC is 9 ft.
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Use a calculator to find the trigonometric value to 4 decimal places. sin 14° = __________
The trigonometric value of sin 14° to 4 decimal places is sin 14° = 0.241.
Step 1: Enter the value of 14 into the calculatorStep 2: Press the sin button on the calculatorStep 3: The calculator will display the value of sin 14°Step 4: Round the value to 4 decimal places
The value of sin 14° to 4 decimal places is 0.2419.
An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.
The unit of measurement associated with angles is degrees.
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The selling price of each cup of lemon juice is 3/2 times as much as the selling price of a cup of apple juice. For every 2 cups of lemon juice sold, Mr Tan sells 5 cups of apple juice. He earns $12 more from apple juice than from lemon juice. How much does Mr Tan earn altogether?
He makes $8/49 for every 7 cups of juice, so his overall profits will be some multiple of $8/49.
what is unitary method ?Finding the worth of one unit of a quantity, then using this value to determine the value of a specified number of units of the quantity, is known as the unitary technique. When solving issues involving rates, ratios, and proportions, this approach is helpful. The fundamental tenet of the unitary technique is that we can use the value of one unit of a quantity to determine the value of any number of additional units of the same quantity.
given
Let's symbolise the cost of a cup of apple juice by the variable x.
So, a cup of lemon juice is sold for 3/2 times x, or (3/2)x.
Mr. Tan offers 5 cups of apple juice for every 2 cups of lemon juice. This indicates that there are 2.5 sales of lemon juice for every 1 sales of apple juice.
Assume Mr. Tan sells 5y cups of apple juice and 2y cups of lemon juice.
Based on the information provided, we can conclude that apple juice generates $12 more revenue than lemon juice.
in order to create an equation:
5yx = 2(3/2)x + 12
Simplifying:
5yx = 3x + 12
adding two to both sides:
10yx = 6x + 24
x(10y - 3) = 12
x = 12 / (10y - 3) (10y - 3)
We can now re-use this number of x to represent the revenue from apple juice in the equation:
5yx = 3x + 12
5y(12 / (10y - 3)) = 3(12 / (10y - 3)) + 12
Therefore, Mr. Tan charges $1/7 for each cup of apple juice and (3/2)($1/7) Equals $3/14 for each cup of lemon juice.
He charges (5/7)($1/7) = $5/49 for 5y = 5(1/7) = 5/7 glasses of apple juice.
For a sum of (2/7)($3/14) = $3/49, he sells 2y = 2(1/7) = 2/7 cups of lemon juice.
For each 7 cups of juice sold, Mr. Tan makes a sum of $5/49 + $3/49 = $8/49.
Consider that he offers 2n cups of lemon juice and 5n glasses of apple juice. (2n)($3/14) + (5n)($1/7) = $6n/49 + $5n/49 = $11n/49
He makes $8/49 for every 7 cups of juice sold, so his overall profits will be some multiple of $8/49.
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Please note that for 1 pound of bananas the cost is
$0.63/lb
(according to the US Bureau of Labor Statistics.) In 1939 , the cost of bananas was
14%
lower. Pam buys 5 pounds of bananas for children at the camp she works for. What would these bananas have cost in 1939?
The cost of 5 pounds of bananas in 1939 would have been $2.709.
According to the US Bureau of Labor Statistics, the cost of 1 pound of bananas is $0.63/lb. In 1939, the cost of bananas was 14% lower. Therefore, to find the cost of bananas in 1939, we need to calculate 14% of $0.63/lb and then subtract it from $0.63/lb.
Calculate 14% of $0.63/lb
0.14 * $0.63/lb = $0.0882/lb
Subtract $0.0882/lb from $0.63/lb to get the cost of bananas in 1939
$0.63/lb - $0.0882/lb = $0.5418/lb
Multiply the cost of bananas in 1939 by the number of pounds Pam buys
$0.5418/lb * 5 lb = $2.709
Therefore, the cost of 5 pounds of bananas in 1939 would have been $2.709.
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e) Solve: f(x) = g(x) for x = [-240°; 240°]
Answer:
218.88
Step-by-step explanation:
point (s) possible Find the LCD (least common denominator ) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)
The answer are LCD (least common denominator) of the set of fractions (7)/(20) and (9)/(40) is 40.
Here is a step-by-step explanation on how to find the LCD:
1. Find the multiples of each denominator.
- Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200...
- Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400...
2. Compare the multiples of each denominator and find the smallest number that appears in both lists.
- The smallest number that appears in both lists is 40.
3. The smallest number that appears in both lists is the LCD.
- Therefore, the LCD of the set of fractions (7)/(20) and (9)/(40) is 40.
So the answer to the question "Find the LCD (least common denominator) of the set of fractions. Do not combine the fractions; only find the LCD. (7)/(20) and (9)/(40)" is 40.
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The perimeter of a rectangular field is 294 m. If the length of the field is 96 m, what is its width?
The width of the rectangular field is 51 m. To find the width of the rectangular field, we can use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given:
P = 294 m
L = 96 m
Substituting the given values into the formula, we get:
294 = 2(96) + 2W
Simplifying the equation, we get:
294 = 192 + 2W
Subtracting 192 from both sides of the equation, we get:
102 = 2W
Dividing both sides of the equation by 2, we get:
W = 51
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PLEASE? ILL GIVE BRAINLIEST AND PUT THE MOST AMOUNT OF POINTS
The value οf x is 1000 kg/m³ and the cοrrespοnding value οf y in lb/ft³ is 62.0 lb/ft³. The value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.
What is Quantities and measurements?Quantities and measurements are essential cοmpοnents οf the study οf mathematics and the physical sciences. A quantity is any prοperty οr characteristic that can be measured οr expressed in numerical terms, such as length, mass, time, temperature, and vοlume.
Frοm the prοject research part 2: Densities in lb/ft3 (pοunds per cubic fοοt). Cοnvert the densities as belοw,
Cοnvert kilοgrams per cubic meter tο the pοunds per cubic fοοt by multiplying by 0.062:
(x kg/m³) (0.062) = y lb/ft³
If we have a value οf x, we can multiply it by 0.062 tο get the cοrrespοnding value οf y in lb/ft³.
Let's say we have x = 1000 kg/m³. We can find y in lb/ft³ as fοllοws:
y lb/ft3 = (1000 kg/m3) (0.062) = 62.0 lb/ft3
Therefοre, the value οf x is 1000 kg/m3 and the cοrrespοnding value οf y in lb/ft3 is 62.0 lb/ft³.
Anοther questiοn is, Cοnvert pοunds per cubic yard tο pοunds per cubic fοοt by multiplying by 0.037:
(x lbs/yard³) (0.037) = y lb/ft³
Let's say we have x = 2000 lbs/yard³. We can find y in lb/ft³ as fοllοws:
y lb/ft³ = (2000 lbs/yard³) (0.037) = 74 lb/ft³
Therefοre, the value οf x is 2000 lbs/yard³ and the cοrrespοnding value οf y in lb/ft³ is 74 lb/ft³.
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In Exercises 11-14|, use a matrix equation to solve the system of linear equations. \( 11\left\{\begin{array}{r}x+2 y=3 \\ 2 x+6 y=5\end{array}\right. \)
x = 4/3 and y = 2/3
To solve this system of linear equations using a matrix equation, we first need to construct a matrix by writing the coefficients of the variables and the constants from the equation in a rectangular array.
The matrix for the given equations will be:
Now, we can solve the system by multiplying the inverse of the matrix of coefficients with the matrix of constants. To find the inverse of the matrix, we can use the following equation:
where |A| is the determinant of the matrix, and adj(A) is the adjoint of the matrix.
We can use this equation to find the inverse of the matrix, which is:
We can then multiply this inverse by the matrix of constants to get the solution for the system:
Therefore, the solution for the system is x = 4/3 and y = 2/3.
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23
b. Complete the double number line diagram that represents the situation.
Photos
0
0
Minutes!
:: 1
7
2
4
:: 4
:: 6
1
#15
21
8
3
28
:: 9
80
#20
# 10
35
12
:: 14
PLEASE HELP I NEEEDA LIKE FINISH IT RN HELP
Answer:
10mins for 35 photos
Step-by-step explanation:
If it takes 8mins to produce 28photos, that is ratio 1:3.5
For 7 photos, divide by 3.5, that is 2mins
For 4mins, multiply by 3.5, that will be 14photos
For 21 photos, divide by 3.5, that will be 6 mins
extra points for help (dont guess please)
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
What exactly are exponential functions?
Exponential functions are functions that involve a variable exponent. They are of the form f(x) = aˣ, where "a" is a positive constant base and "x" is the variable exponent.
Exponential functions exhibit rapid growth or decay, depending on the value of "a" and the sign of "x". For example, if "a" is greater than 1, the function grows rapidly as "x" increases, while if "a" is between 0 and 1, the function decays rapidly as "x" increases.
Now,
As stated above that for exponential function y=aˣ
when a>1 it shows exponential growth
and when a<1 it shows decay.
hence,
The exponential functions y=1.2ˣ shows exponential growth and y=0.71ˣ shows exponential decay.
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cindy bought 7/8 yard of ribbon jacob bought 4/5 more than cindy how much did he buy
In linear equation, 7/10 did he buy .
What in mathematics is a linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
multiply the fractions by each other.
7/8*4/5
7*4=28
8*5=40
28/40
"B" would be the correct answer but, it the fraction should be reduced to 7/10.
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For each relationship described, type an equation using the variables y and z to create an identity. a. addition and subtraction: b. multiplication and division: (when y 0 or when z = 0)
Step-by-step explanation:
addition and subtraction:
y + z - z = y
b. multiplication and division:
When y ≠ 0:
yz / y = z
When z ≠ 0:
y / z * z = y
Ina makes cakes in a pan shaped like a rectangular prism. The base of the pan is an 8-inch by 12-inch rectangle, and the volume of the pan is 288 cubic inches. Find the surface area of a cheesecake baked in this pan
Answer:
312 square inches
Step-by-step explanation:
To find the surface area of a cake baked in a rectangular pan with an 8-inch by 12-inch base and a volume of 288 cubic inches, we need to find the dimensions of the pan. We can do this by dividing the volume by the area of the base, which gives us the height of the pan. Once we know the height, we can use the dimensions of the base and the height to find the surface area of the cake.