The three equations for this problem are:
The total amount of flour used: 3.3kg = (225g/cake) * (number of chocolate cakes) + (320g/cake) * (number of fruit cakes) + (400g/cake) * (number of sponge cakes)The total amount of sugar used: 3.1kg = (300g/cake) * (number of chocolate cakes) + (250g/cake) * (number of fruit cakes) + (325g/cake) * (number of sponge cakes)The total revenue from sales: $114 = ($12/cake) * (number of chocolate cakes) + ($10/cake) * (number of fruit cakes) + ($8/cake) * (number of sponge cakes)Let's call the number of chocolate cakes x, the number of fruit cakes y, and the number of sponge cakes z
so the
first equation can be written as 3.31000 = (225x) + (320y) + (400z)second 3.11000 = (300x) + (250y) + (325z)and third one 114 = (12x) + (10y) + (8*z)let's use the third equation to get the value of x,y and z:
x = (114 - 10y - 8z) / 12y = (114 - 12x - 8z) / 10z = (114 - 12x - 10y) / 8If you get the values and substitute, then the answer would be:
4 chocolate cakes, 5 fruit cakes, 2 sponge cakes
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Suppoe that the tatitical power of a tudy deign i 80% to detect a treatment effect of 0. 5 tandard deviation, and that take-up of the program i 100%. Other thing equal, do we have more, le, or the ame amount of power to detect an effect ize of 0. 4 SD?
The correct option is option C which states that , less than 80% power to detect the standard deviation is 0.4.
We know that the power is less and the effect size is small therefore we can say that all other things given as equal, it's harder to detect than the larger effect. As a result power is reduced.
Statistical power is a measure of research efficiency that is estimated before the study begins . This is done so as to predict the likelihood of discovering an actual effect rather than receiving a false negative result or, in the worst case scenario, overestimating the effect by identifying noise in the data.
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A cleaning company charges a fixed amount for a house call and a second amount for each room it cleans the total cost to clean six rooms is $250 and the total cost to clean eight rooms is $320 how much would this company charge to clean two rooms
The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.
What is fixed amount?A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.
This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).
= ($250 - $320)/4
= $40
This will give you a price of for each additional room.
To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.
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please help: find m∠BCF
Step-by-step explanation:
so, clearly, the triangles BCF and DCF are congruent.
that makes the line CF a bisector of the kite figure.
and so, both angles are identical halves of the total angle at C.
therefore,
3x + 13 = 13x - 7
13 = 10x - 7
20 = 10x
x = 20/10 = 2
HELP
i been trying for a while and cant get it
The ordered pair for the function y = -(x/3) + 2 is (-3, 3), (0, 2), (3, 2) and (6, 0)
What is an equation?An equation is used to show the relationship between numbers and variables.
The standard form of a linear equation graph is:
y = mx + b
Where m is the slope of the line and b is the y intercept.
Given the function:
y = -(x/3) + 2
At x = -3:
y = -((-3)/3) + 2 = 3
At x = 0:
y = -(0/3) + 2 = 2
At x = 3:
y = -(3/3) + 2 = 1
At x = 6:
y = -(6/3) + 2 = 0
The value of y when x = -3 is 3
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√2x-1- x = 0
How do I solve this equation?
Answer:
x = 1
Step-by-step explanation:
Immediately, we will simplify like terms on the left side of the equation. This will give us:
[tex]\sqrt{2x-x-1}[/tex] = 0
Simplifying gives us:
[tex]\sqrt{x-1}[/tex] = 0
Now, an important thing to note, is that for the square root of a number to be 0, the number has to be 0. Therefore, x - 1 must equal 0. So, x = 1. Checking our work gives us:
[tex]\sqrt{2x - x - 1}[/tex] = 0
[tex]\\\sqrt{2 - 1 - 1}[/tex] = 0
[tex]\sqrt{0}[/tex] = 0
It all checks out.
Hope this helped!
Radicals help please
√6/3 is the value after rationalization of √2/√3
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is √2/√3
Square root two divided by square root three.
We need to rationalize the denominator
To rationalize multiply numerator and denominator by √3
√2/√3×√3/√3
√2×3/3
√6/3
Hence, √6/3 is the value after rationalization of √2/√3
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If the sum of n term of an ap is sn = 3n^2+5n writ its common difference
In the given arithmetic progression Common difference is 14.
what is an arithmetic progression?An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).
Given, the n term of ap is Sₙ = 3n² + 5n
Where n is the number of terms
S₁ = 3* 1 + 5*1
S₁ = 8
S₂ = 3 * 4 + 5*2
S₂ = 22
common difference = 22-8
Common difference = 14
therefore, the Common difference in the given AP is 14.
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What is Y + 4 = 3x + (-5) as a y = mx + b equation??
Rebecca carries a balance on her credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is x and the APR is 24%. Rebecca is buying a friend an expensive gift that cost $1,400 that she plans to put on her credit card. this will be her only purchase this month, and she will be making this purchase on the last day of the month
Part A
If her Finance charge will be $51, write and solve an equation to determine her current balance on her credit card. Show work
Part B
How much in finance charges can she save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle? Explain how you determined your answer
Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The billing cycle for the month = 28 days
Current beginning balance = x
Annual percentage rate (APR) = 24%
Monthly percentage rate (MPR) = 2% (24% ÷ 12)
Purchase on the last day = $1,400
Total finance charge for the month = $51
Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)
Finance charge for the beginning balance = $50 ($51 - $1)
The current beginning balance, x = $2,500 ($50 ÷ 2%)
Equation for current beginning balance, x = 51 - 1 ÷ 0.02
Total finance charge for the last-day purchase = $28 ($1,400 x 2%)
Savings in finance charge by purchasing on the last day = $27 ($28 - $1)
Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.
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EX 2
QUAD ABCD is a rectangle with
diagonals that intersect at point P.
AC = 4x-13 and DP = x + 7. Find the
value of 'x'.
QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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Ben Nevis has a height of approximately 1300 metres above sea level.
Assuming that temperature decreases by 1°C for every 100 metres above
sea level, work out the temperature at the summit of Ben Nevis when the
sea level temperature is 5°C.
The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.
To work out the temperature at the summit of Ben Nevis, we can use the formula:
Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres
We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.
So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C
Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C
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What literary devices are used in The Importance of Being Earnest?
Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.
What is The Importance of Being Earnest?
Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.
It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.
The characters maintain false personae to avoid onerous social duties.
The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.
In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.
Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.
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Is (3,6) a solution to this system of equations?
y=2x+1
y=4x+6
Step-by-step explanation:
y = 2x + 1 -------- (I)
y = 4x + 6 --------(ii)
from eqn (I)
y = 2x + 1
sub y = 2x + 1 in eqn (ii)
2x + 1 = 4x + 6
2x - 4x = 6 - 1
-2x = 5
x = -5/2
sub x = -5/2 in eqn (I)
y = 2(-5/2) + 1
y = -5 + 1
y = -4
Therefore, (x, y) = (-5/2, -4)
Can someone please help me? :(
what number is in the same ratio to 64 as 5 is to 8
Answer: 102.4
Given ratio 5:8
Let's assume the answer to be x
5÷8 should be equal to 64÷x
∴ x= (64×8) ÷ 5
=102.4
The number that has the same ratio to 64 as 5:8 is gotten as; 40
How to Calculate Ratio?
We have the ratio 5:8.
Now, we want to find the number that has the same ratio to 64 as 5:8. Thus, we will use proportion to get this;
x/64 = 5/8
Cross multiply to get;
x = 64 * 5/8
x = 40
T h e r e a r e 235 seven t h - g r a d e st u d e n t s g o i n g o n a fi e l d t r i p . T h e sc h o o l h a s 5 b u se s t o t a k e t h e st u d e n t s. E a c h b u s h a s 22 se a t s, a n d 2 st u d e n t s c a n si t i n e a c h se a t . B a se d o n t h i s i n f o r m a t i o n , h o w m a n y st u d e n t s w i l l n o t b e a b l e t o r i d e o n a b u s f o r t h e fi e l d t r i p ?
The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total number of students for the trip = 235 students
The number of buses = 5 buses
The number of students in a bus be = B
Now , each seat on the bus can occupy = 2 students
So , 22 seats can occupy = 22 x 2 students
22 seats in the bus can occupy = 44 students
So , the number of students in a bus B = 44 students
And , the total number of students in 5 buses = 5 x number of students in a bus B
Substituting the values in the equation , we get
The total number of students in 5 buses = 5 x 44
The total number of students in 5 buses = 220 students
So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses
Substituting the values in the equation , we get
The remaining number of students A = 235 - 220
The remaining number of students A = 15 students
Therefore , the value of A is 15 students
Hence , the number of students is 15 students
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The depth of water in a tank oscillates sinusoidally once every
8 hours. If the smallest depth is 6. 6 feet and the largest
depth is 9. 4 feet, find a possible formula for the depth in terms
of time t in hours. Assume that at t=0 the water level is at
the average of the depth and is rising.
.
The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.
Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D
where, A --> amplitude
B--> period in form of pi
C--> phase or horizontal shift
D --> vertical shift
We have, the depth of water in a tank oscillates sinusoidally.
The smallest depth of water in tank = 6.6 feet
The largest depth of water in tank = 9.4 feet
We have to determine the formula of depth of water in tank as a function of time in hours .
For sinusoidal function,
Amplitude , A = average depth
= ( largest depth + smallest depth)/2
= (6.6 + 9.4)/2
= 16.0/2 = 8
Now, The period of 8 hours so, B = 2π/8
=> B = 45° = π/4
Also, upward shift , D is 9.4 - 6.6 = 2.8
Horizontal shift, C = 0
So, required function is D = 2.8 + 8 sin(π t/4) .
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PLEASE HELP Water flowed out of a tank at a steady rate. A total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. Which expression determines the quantity of water leaving the tank per hour?
The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)
How to find which expression determines the quantity of water leaving the tank per hour?
Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.
If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:
rate = (18 1/2 gallons)/(4 1/4 hours)
rate = 4 6/17 gallons per hour
Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)
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please help: solve for x
Answer:
x=3
Step-by-step explanation:
Since the altitude of this triangle is at the midpoint of the base,
It is a isosceles triangle making MJ=MK
9x-18=3x
6x-18=0
6x=18
x=3
Solve the inequality 3 x+2 y≥−6 graphically.
Answer:
Step-by-step explanation:
Answer: y ≥ −3/2x − 3
Step-by-step explanation:
Graph the inequality by finding the boundary line, then shading the appropriate area.
Hope this helps!
What is the distance of 2/3 from the horizontal axis in Cartesian plane?
Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.
What is cartesian coordinate system?
The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.
In cartesian plane the reference axis are named as X - axis and Y -axis.
In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.
What is the distance of 2/3 from the horizontal axis in cartesian plane?The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.
hence, tan angle = 2/3
for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.
Finally, the distance of 2/3 from the horizontal axis is 2.
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a) Complete the prime factor trees for 24 and 40:
24
2
2
6
2
40
2
2
3
b) What is the Lowest Common Multiple of 24 and 40?
2
2
1
5
Submit Answer
Answer:
a)
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 120
Step-by-step explanation:
a)
24 40
/ \ / \
2 12 2 20
/ \ / \
2 6 2 10
/ \ / \
2 3 2 5
24 = 2³ × 3
40 = 2³ × 5
b)
LCM = 2³ × 3 × 5
LCM = 120
What is the interval of zero?
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.
If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.
In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.
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Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. What will his monthly payments be? Round to the nearest cent.
If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.
What is monthly payment?Monthly payment can be defined as the amount a person received on a monthly basis.
Now let find the monthly payment
Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷ ( 1+ 0.0429/12)^12×10 -1
Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷ ( 1+ 0.003575)^120 -1
Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷ ( 1.003575)^120 -1
Monthly payment = $87.31
Therefore the monthly payment is $87.31.
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The complete question is:
Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?
What is the inverse of 7 5?
The multiplicative inverse of 7/5 is 5/7 using the formula of multiplicative inverse like (x)^-1 which equals to 1/x.
let's try to learn what is multiplicative inverse.
1/N or [tex]N^-1[/tex] is used to denote a number's multiplicative inverse, such as the number N. From the Latin word "reciprocus," it is also known as reciprocal. Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.
One is obtained when a number is multiplied by its own multiplicative inverse.
When a number is multiplied by its original number, the multiplicative inverse of that number, or x^-1, produces a value equal to 1. The multiplicative inverse of 2, for instance, is 2^-1 since it fulfils the formula: 2 x (2^-1) = 2 x (1/2) = 1.It is also known as a number's reciprocal.
Multiplicative inverse of 7/5 is (7/5)^-1 = 1/(7/5) = 5/7.
Given question is incomplete complete question here:
What is the multiplicative inverse of 7/5?
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Find $(-1)^{-10} (-1)^{-9} (-1)^{-8} \cdots (-1)^9 (-1)^{10}$. (The dots $\cdots$ mean that there are 21 numbers being added, one for each integer from $-10$ to 10.)
The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1
Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]
here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.
We need to find the sum.
We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1
We know that the formula of the sum of n-terms of a geometric sequence is:
[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]
For n = 21, r = -1 and a1 = 1
[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]
Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1
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PLEASE HELP!! And explain :) THANKS
Because two triangles are said to be congruent when all three of their corresponding sides and all three of their corresponding angles have the same measure, the right answer is SSS.
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found.
In the order below, beginning with triangles DAB and BCD, write the names of the vertices.
AB = CD
DA = BC
Since both triangles' BD sides are the same, BD = BD.
The SSS feature of a congruent triangle allows us to conclude that the triangles DAB and BCD are congruent since they share the same three sides.
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The diagram shows an isosceles triangle. All the measurements are in cm, work out the perimeter of the triangle.
Which tatement correctly compare the meaure of center of the data in the dot plot
A statement that correctly compares the measures of center in the two sets of data is: Both the mean and median are greater for Plot A than for Plot B.
The correct answer is an option (A)
Consider plot A.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 6, 6, 7, 7, 10
Using the formula of mean, the mean of Plot A would be:
mean = (3 + 4 + 4 + 5 + 5 + 6 + 6 + 7 + 7 + 10) / 10
mean = 57/10
mean = 5.7
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 6)/2
= 11/2
= 5.5
Consider plot B.
The data value represented on the dot plot:
3, 4, 4, 5, 5, 5, 6, 6, 6, 7
mean = (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 7)/10
mean = 51/10
mean = 5.1
The middle value of the data is: 5, 6
So, the median is:
Median = (5 + 5)/2
= 5
Hence, both the mean and median are greater for Plot A than for Plot B.
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The complete question is:
Which statement correctly compares the measures of center in the two sets of data? Both the mean and median are greater for Plot A than for Plot B. Both the mean and median are greater for Plot B than for Plot A. Plot A has a greater median than Plot B, but Plot B has a greater mean. Plot B has a greater median than Plot A, but Plot A has a greater mean.
What is the simplified value of the expression below?
1/3 divided by 2/3
0
1/3
1/2
1
Answer: 1/2
Step-by-step explanation:
( see image ) ( Keep Change Flip )