Answer:
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
Step-by-step explanation:
Let's assign variables to the masses involved to solve the problem systematically.
Let's say:
Mass of the trolley = T kg
Mass of the mangoes = M kg
Mass of the watermelons = W kg
According to the given information:
The total mass of the trolley and mangoes is 11 kg:
T + M = 11 -- Equation (1)
The mass of the watermelons is three times the mass of the mangoes:
W = 3M -- Equation (2)
Now, we can use these equations to find the values of T, M, and W.
From Equation (2), we can express M in terms of W:
M = W / 3
Substitute this value of M into Equation (1):
T + W / 3 = 11
Multiply through by 3 to eliminate the fraction:
3T + W = 33 -- Equation (3)
Now, we have a system of two equations (Equation 2 and Equation 3) with two unknowns (T and W). We can solve this system to find the values.
Since we don't have a specific value for any variable, we can express the solution in terms of the variables.
Therefore, the mass of the trolley (T) and the mass of the watermelons (W) cannot be determined uniquely based on the given information. We can only express their relationship using Equation (3): 3T + W = 33.
If 1, 2, and 4 are three of the digits of the four digit number n, and if n is divisible by 4, find the greatest possible value of n. (40pts) Explain how you know you have the largest possible number n. (60 pts)
Answer: n = 412
Step-by-step explanation:
If the last two digits of a number are divisible by 4, the whole number is divisible by 4 since any multiple of 100 is divisible by 4. The largest number that can be created is 421 since the largest number is in the hundreds place and then the second largest number is in the tens place, but 21 is not divisible by 4. The second largest number, 412, still has the greatest number as the hundreds place, but the tens place is now smaller. 12 is divisible by 4, so 412 is divisible by 4. We know that 412 is the largest possible number for n because there is only one larger number than 412, which is 421 and it is not divisible by 4.
Answer:
The largest possible n is 9412-----------------------------
Divisibility rule for 4:
If the last two digits of a number are divisible by 4, the number is divisible by 4We have 3 digits and the greatest number can be made by these digits is 421. But it has to be divisible by 4, hence we rearrange it to 412. Since 12 is divisible by 4, the number is divisible by 4.
Now, we choose 9 as the fourth digit. It will be a first digit from left and form the largest possible number n:
n = 94122. Write each of the following in algebraic notation:
: 2.1 Three times the difference between k and the square of p
The expression in algebraic notation is 3 * (k - p²)
Writing the expressions in algebraic notationFrom the question, we have the following parameters that can be used in our computation:
Three times the difference between k and the square of p
Three times means 3*
So, we have
3 * the difference between k and the square of p
the difference between k and the square of p means
k - p²
So, we have
3 * (k - p²)
So, we can conclude that
The expression"Three times the difference between k and the square of p" in algebraic notation is 3 * (k - p²)
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Milano Pizza is a small neighborhood pizzeria that has a small area for in-store dining as well as offering take-out and free home delivery services. The pizzeria’s owner has determined that the shop has two major cost drivers—the number of pizzas sold and the number of deliveries made.
The pizzeria’s cost formulas appear below:
Fixed Cost per Month Cost per Pizza Cost per Delivery
Pizza ingredients $ 4.30
Kitchen staff $ 6,330
Utilities $ 820 $ 0.40
Delivery person $ 3.20
Delivery vehicle $ 840 $ 1.30
Equipment depreciation $ 568
Rent $ 2,290
Miscellaneous $ 940 $ 0.20
In November, the pizzeria budgeted for 2,190 pizzas at an average selling price of $20 per pizza and for 190 deliveries.
Data concerning the pizzeria’s actual results in November were as follows:
Actual Results
Pizzas 2,290
Deliveries 170
Revenue $ 46,560
Pizza ingredients $ 10,990
Kitchen staff $ 6,270
Utilities $ 990
Delivery person $ 544
Delivery vehicle $ 1,028
Equipment depreciation $ 568
Rent $ 2,290
Miscellaneous $ 916
Required:
1. Complete the flexible budget performance report that shows both revenue and spending variances and activity variances for the pizzeria for November. (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values.)
By completing the flexible budget performance report, Milano Pizza's owner can identify areas for improvement and make informed decisions to optimize the pizzeria's performance.
The flexible budget performance report for Milano Pizza for November will include revenue and spending variances, as well as activity variances. The two major cost drivers are the number of pizzas sold and the number of deliveries made.
1. Revenue variances: Calculate the difference between the actual revenue and the budgeted revenue for both in-store dining and delivery services. Label the variances as "F" for favorable (actual revenue higher than budgeted) or "U" for unfavorable (actual revenue lower than budgeted).
2. Spending variances: Analyze the costs related to pizza production and delivery person wages. Compare the actual costs to the budgeted costs, and label the variances as "F" for favorable (actual costs lower than budgeted) or "U" for unfavorable (actual costs higher than budgeted).
3. Activity variances: Assess the differences in the number of pizzas sold and deliveries made compared to the budgeted activity levels. Label these variances as "F" for favorable (higher activity than budgeted), "U" for unfavorable (lower activity than budgeted), or "None" for no effect (zero variance).
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50 Points! Multiple choice algebra question. Photo attached. State the number of real zeros for the function whose graph is shown. Thank you!
Answer:
D) 0------------------------
The graph has no intersection with the x-axis, therefore it has no zeros.
The matching choice is D.
100 Points! Algebra question. Solve the equation. Please show as much work as possible. Photo attached. Thank you!
mr evans deposited $1,200 in a new account at his bank.
the bank pays 8% interest compounded annually on his account.
mr evan makes no additional deposits or withdrawals.
how much interest will the account have earned at the end of 8 years?
ANSWER:
768
Step-by-step explanation:
He has 1,200. We need to find 8% of 1,200. 8%x1,200=96x8 years= 768
A rectangle topped by a triangle. The rectangle has length 5 centimeters and width 3 centimeters. The triangle has side lengths 5 centimeters, 3 centimeters, and 3 centimeters. What is the perimeter of the figure shown above? a. 17 cm c. 15 cm b. 21 cm d. 19 cm
The perimeter of the figure is 17cm. Option (a) is the correct answer.
The rectangle has a length of 5 centimeters and a width of 3 centimeters. So, the rectangle has two sides of length 5 cm and two sides of length 3 cm. Therefore, the total perimeter of the rectangle is:
The Triangle and the rectangle ae sharing a side of length 5 cm Therefore perimeter of the figure is sum of two other sides of triangle+ sum of three sides of rectangle
Perimeter of rectangle = 2(Length + Width) = 2(5 + 3) = 2(8) = 16 cm
The triangle has side lengths of 5 centimeters, 3 centimeters, and 3 centimeters. The sum of the lengths of the sides of the triangle is:
Perimeter of triangle = sum of two other sides = 3+3=6cm
To find the total perimeter of the figure, we add the perimeters of the rectangle and the triangle:
Total perimeter = The sum of two other sides of triangle sum of three sides of rectangle (3+5+3)
=3+3 +(3+5+3)
= 17cm
Therefore, Option (a) is the correct answer
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0.054 as a written word
What is the probability ethier event will occur?
From the given Venn diagram the value of P(A or B) is 0.
From the given Venn diagram, we have P(A)=14, P(B)=10 and (P and B)=24.
We know that, P(A or B)=P(A)+P(B)-P(A and B)
P(A or B)=14+10-24
P(A or B)=0
Therefore, from the given Venn diagram the value of P(A or B) is 0.
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Solve the system by the method of your choice.
X=10+6y
X-6y=5
The system of linear equations has no solution
What is system of linear equation?The system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
In this problem, we have two equations which are;
x = 10 + 6y ...eq(i)
x - 6y = 5 ...eq(ii)
From eq(i)
x = 10 + 6y;
We can substitute this into eq(ii)
10 + 6y - 6y = 5
10 +0 = 5
Since y is already canceled out, we don't have solution to this equations.
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7. PART A:
Martin has 1/4 of a bag of chocolate chip cookies. The bag weighs 4 pounds. How
many pounds of cookies does he have?
Answer:
1 pound----------------------
Martin has 1/4 of a bag of chocolate chip cookies.
Since the bag weights 4 pounds, Martin has:
1/4 × 4 pounds = 1 pound of chocolate chip cookiesFactor out the greatest common factor. If the greatest common factor is 1, just retype the
polynomial.
9x³ - 6x²
0
Learn with an example
Submit
The greatest common factor is 3x² and GCF form of polynomial is
3x²(3x-2).
The given polynomial is
9x³ - 6x²
We can write it as;
3x²(3x-2)
We know that
The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor (HCF) is another name for it.
Therefore 3x² is its GCD.
Divide each term of polynomial 3c,
6c³ ÷ 3c = 2c² and -9c ÷ 3c = -3
Thus,
3x²(3x-2) is the factored version of the polynomial with the highest common factor.
Also if GCD is 1 then after dividing each term by 1 we get same result
thus the polynomial be 3x²(3x-2).
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Which of the following is the expression for 6 added to the sum of 9 and x
Answer:
15 + x is the expression for 6 added to sum of 9 and x
32493 correct to the nearest thousand
Answer: 32.493 maybe, dont quite understand the question
Step-by-step explanation:
It costs $16 dollars each day to run an ad in the newspaper. You advertise for 8 days. How much did you spend on advertising?
The LRAS Curve begins to slope
upward in the SECOND phase. What
does this mean?
A. Wages will decrease.
B. Wages will increase.
C. Wages will stay the same.
The correct answer is B. Wages will increase.
When the Long-Run Aggregate Supply (LRAS) curve begins to slope upward in the second phase, it indicates that as the economy moves towards full employment and productive capacity, wages will increase.
The upward slope of the LRAS curve suggests that as the economy expands and approaches its maximum potential output, the demand for labor increases, leading to higher wages.
This is because firms need to pay higher wages to attract and retain workers in a tightening labor market, where the supply of labor becomes relatively scarce compared to the demand.
The right answer is B. Wages will increase.
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What is the sum of 1-half and 0.75?
Answer:
1.25
Step-by-step explanation:
Convert 1-half to a decimal by dividing 1 by 2:
1 ÷ 2 = 0.5
Add the two decimals:
0.5 + 0.75 = 1.25
Therefore, the sum of 1-half and 0.75 is 1.25.
Help Quickly! What is 5x6 + (5x5-5) to the 2nd power
Answer: 2500
Step-by-step explanation: Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500
please help ASAPPPPPPPPPPP
Triangle A''B''C'' is given by the image presented at the end of the answer.
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x).The coordinates of triangle ABC are given as follows:
A(-5, 2), B(-3, 6), C(-1, 3).
Hence the coordinates after the rotation 90º clockwise are given as follows:
A'(2, 5), B'(6, 3), C'(3, 1).
y = 2 is an horizontal line, hence after the reflection, the x-coordinates remain constant, while the y-coordinates move in the opposite direction, hence:
A''(2, -1), B''(6,1), C''(3,3).
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For the given confidence level and values of x and n, find the following.
x=45, n=96, confidence level 95%
The confidence interval based on the given values (x = 45, n = 96, Confidence level = 95%.
The confidence level (95%), sample size (n = 96), and sample mean (x = 45), we can calculate the margin of error and the confidence interval. Here's how:
1. Margin of Error:
The margin of error represents the maximum expected difference between the true population parameter and the sample estimate. It depends on the confidence level and the standard deviation (which we don't have in this case).
Since the standard deviation is unknown, we can use the t-distribution to estimate it. With a sample size of n = 96, the degrees of freedom are (n - 1) = 95. Considering a 95% confidence level, the critical value for a two-tailed test is approximately 1.984 (referencing a t-distribution table or calculator).
The margin of error (E) can be calculated using the following formula:
E = critical value * (standard deviation / sqrt(n))
However, since we don't have the standard deviation, we can't compute the margin of error in this case.
2. Confidence Interval:
The confidence interval represents a range of values within which the true population parameter is likely to fall.
The confidence interval can be calculated using the formula:
CI = x ± (critical value * standard deviation / sqrt(n))
The confidence interval based on the given values (x = 45, n = 96, confidence level = 95%.
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Helpppppp pleaseeeeeee
The reduced row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]
How to obtain the reduced row echelon form?The reduced row echelon form of a matrix is matrix in which the matrix except the last column has the format of an identity matrix, that is, a matrix in which the principal diagonal elements are of 1 and the rest of the elements are of 0.
Hence we can use a mix of row operations, along with the solution of a system of equations, to obtain the reduced row echelon form of a matrix.
The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-1&5&-3&6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]
First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1, that is:
R1 -> -R1.
Hence:
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&3&6&-42\\0&-6&-1&18\end{array}\right][/tex]
Then we want a value of 1 at line 2 column 2, thus:
R2 -> R2/3.
Hence:
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&-6&-1&18\end{array}\right][/tex]
Then we want a value of 0 at line 3, column 2, hence:
L3 -> L3 + 6L2
[tex]\left[\begin{array}{cccc}1&-5&3&-6\\0&1&2&-14\\0&0&11&-66\end{array}\right][/tex]
Then the solution to the system of equations is given as follows:
11z = -66 -> z = -6.y + 2z = -14 -> y - 12 = -14 -> y = -2.x - 5y + 4z = -6 -> x + 10 - 24 = -6 -> x = 8.Hence the row echelon form of the matrix is given as follows:
[tex]\left[\begin{array}{cccc}-1&0&0&8\\0&1&0&-2\\0&0&1&-6\end{array}\right][/tex]
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REMEMBER
5 Compare the fractions by using >> or < Explain your thinking by using
10
नज
How to compare fractions is explained in the solution below.
One way to compare fractions is to convert them into their decimal form and decide which is the smaller of the two.
Example: 7/10 and 3/5 become 0.7 and 0.6.
Hence 3/5 is smaller than 7/10.
The other way is to convert them into fractions with identical denominator.
For that multiply the denominator of one fraction with the numerator and denominator of the other.
Do the same with the other denominator and the other fraction. Then decide which fraction is the smaller of the two.
Example: 7/8 and 13/15 become (7*15)/(8*15) = 105/120 and
(13*8)/(15*8) = 104/120.
Hence 13/15 is smaller than 7/8.
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Select the correct answer. What is 12% of 50? A. 6 B. 7 C. 10 D. 12
Answer:
A. 6
Step-by-step explanation:
We know that 12% can be written in fraction form as [tex]\frac{12}{100}[/tex]. So, 12% of 100 is [tex]100\cdot\frac{12}{100} = 12[/tex].
We also know that 50 is half of 100. Therefore, 12% of 50 is exactly half of 12% of 100:
[tex]12\% \cdot 50[/tex]
[tex]= \frac{1}{2}(12\% \cdot 100)[/tex]
[tex]= \frac{1}{2}(12)[/tex]
[tex]\boxed{=6}[/tex]
AABC has vertices A(-2, 2), B(2, 0), and C(1,-2). For the similarity transformation, find the image of vertex C.
D₂° Ry-axts
Input answer as (x, y)
The image of vertex C under the given similarity transformation is (4, 2).
To apply the given similarity transformation, we need to perform two transformations: a rotation of 90 degrees counterclockwise about the origin (denoted by R) and a dilation by a factor of 2 (denoted by D2). We perform the transformations in order: first the rotation, then the dilation.
The image of a point (x, y) after a rotation of 90 degrees counterclockwise about the origin is (-y, x).
Thus, the image of C after the rotation is:
C' = (-(-2), 1) = (2, 1)
To find the image of C' after the dilation by a factor of 2, we multiply each coordinate by 2:
C" = (22, 21) = (4, 2)
Therefore, the image of vertex C under the given similarity transformation is (4, 2).
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12. What is the cosine of angle B
The value of the cosine of angle B is,
⇒ cos B = 5 √89 / 89
We have to given that;
A triangle is shown in image.
Now, By trigonometry formula we get;
⇒ cos B = Base / Hypotenuse
Here, We can find the c as;
c² = 8² + 5²
c² = 64 + 25
c² = 89
c = √89
Hence, The value of the cosine of angle B is,
⇒ cos B = Base / Hypotenuse
⇒ cos B = 5 / √89
⇒ cos B = 5 √89 / 89
Thus, Option B; cos B = 5 √89 / 89 is correct.
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f(x)=x^3+5x+k and x+2 is a factor of f(x), then what is the value of k?
The value of k is 18.
If x + 2 is a factor of f(x) = x^3 + 5x + k, it means that when x = -2, the expression f(x) becomes zero.
Substituting x = -2 into f(x), we have:
f(-2) = (-2)³ + 5(-2) + k
= -8 - 10 + k
= -18 + k
Since f(-2) should equal zero, we have:
-18 + k = 0
k = 18
Therefore, the value of k is 18.
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HELP PLEASE Which of the following properties completes the proof?
Given: x – 6 = 4. Prove: x = 10
A) Subtraction Property of Equality
B) Reflexive Property of Equality
C) Transitive Property of Equality
D) Addition Property of Equality
Answer:
D
Step-by-step explanation:
A plastic pipe 8 cm long has an
outside radius of 6 cm and an
inside radius of 5 cm. If the density
of the plastic is 0.92 g/cm³, what is
the mass of the pipe? Use 3.14 for
π, and round your answer to the
nearest gram.
The mass of the pipe is 254 grams.
First, The volume of the outer cylinder (V1) can be calculated using the formula for the volume of a cylinder:
V1 = π (radius_outer)² x height
V1 = 3.14 (6)² (8)
and, the volume of inner cylinder
V2 = π(inner radius)² height
V2= 3.14 (5)² (8)
Now, let's calculate the volume of the plastic pipe:
Volume = V1 - V2
= 3.14 (6)² (8) - 3.14 (5)² (8)
= 3.14 x 8 (36- 25)
= 276.32 cm³
Now, Mass = Volume x density
Mass = 276.32 x 0.92
Mass = 254.19 grams
Thus, the mass of the pipe is 254 grams.
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Kristin and deshawn are selling flower bulbs for a school fundraiser customers can buy bags of windflower bulbs and packages of crocus bulbs Kristen sold 4 bags of windflower bulbs and 9 packages of crocus for a total of 200 deshawn sold 2 bags of windflower bulbs and 6 packages of crocus bulbs for a total of 124 find the cost each of one of the bag of windflower bulbs and one package of crocus bulbs ?
The cost each of one of the bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.
What is the cost of each of bag of windflower bulbs and a package of crocus bulbs?Let
cost each of one of the bag of windflower bulbs = x
Cost of each one package of crocus bulbs = y
4x + 9y = 200
2x + 6y = 124
Multiply (2) by 2
4x + 12y = 148
So,
4x + 9y = 200
4x + 12y = 248
Subtract to eliminate x
12y - 9y = 248 - 200
3y = 48
divide both sides by 3
y = 48/3
y = 16
Substitute y = 16 into (1)
4x + 9y = 200
4x + 9(16) = 200
4x + 144 = 200
4x = 200 - 144
4x = 56
x = 56/4
x = 14
Therefore, each one bag of windflower bulbs and one package of crocus bulbs is $14 and $16 respectively.
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Answer:
Explanation:
Answer:
Median → 13Step-by-step explanation:
To find the median we first need to arrange the data points from smallest to largest:-
[tex]\sf 12, 13, 16, 5, 8, 18, 14, 19, 2[/tex]
Arranged:- 2, 5, 8, 12, 13, 14, 16, 18, 19.
Now, if the number of data points is even, the median is the average of the two middle data points in the list. Since the numbers are odd, the median is the middle data point. which, in this case, it's 13.
2, 5, 8, 12, 13, 14, 16, 18, 19
______________________
Hope this helps!
