The Bakers make 85 glazed donuts.
To solve this problem, we need to determine how many glazed donuts and how many donut holes can be made from 80 pounds of dough. Then, we can compare the quantities of each to determine the difference.
First, we need to convert 80 pounds to ounces, since the amounts of dough for each type of donut are given in ounces. There are 16 ounces in a pound, so 80 pounds is equal to 80 x 16 = 1,280 ounces.
Next, we can set up two equations based on the amounts of dough needed for each type of donut:
Glazed donuts: 10 ounces of dough per donut
Donut holes: 2 ounces of dough per hole
Let's use "g" to represent the number of glazed donuts and "h" to represent the number of donut holes. We know that the total amount of dough used must be 1,280 ounces, so we can write:
10g + 2h = 1,280
We also know that the bakers divide the dough evenly between glazed donuts and donut holes, so the total number of donuts must be:
g + h = ?
We don't know the total number of donuts yet, but we do know that it must be an even number, since the dough is divided evenly between glazed donuts and donut holes.
To solve for g and h, we can use substitution or elimination. Let's use substitution. We can solve the first equation for one of the variables, such as h:
h = (1,280 - 10g) / 2
Then, we can substitute this expression for h in the second equation:
g + (1,280 - 10g) / 2 = ?
Simplifying this equation, we get:
g + 640 - 5g = ?
Combining like terms, we get:
5g + 640 = ?
Subtracting 640 from both sides, we get:
5g = -640
Dividing both sides by 5, we get:
g = -128
This doesn't make sense as a solution, since we can't have negative numbers of donuts. This means there must be an error in our calculations or assumptions.
Let's go back to the second equation:
g + h = ?
We know that the total number of donuts must be an even number, so we can write:g + h = 2n
where n is some positive integer. We can substitute this expression for g + h in the first equation:10g + 2h = 1,280
10g + 2(2n - g) = 1,280
Simplifying this equation, we get 14g - 4n = 1,28
Dividing both sides by 2, we get:7g - 2n = 640
Now we have two equations:7g - 2n = 640
g + h = 2n
We can use substitution or elimination to solve for g and h. Let's use elimination. We can multiply the first equation by 2 and add it to the second equation:14g - 4n = 1,280
2g + 2h = 4n
Multiplying the first equation by 2, we get:28g - 8n = 2,560
Adding this to the second equation, we get:30g = 2,560
Dividing both sides by 30, we get:g = 85.33
This means that the bakers make 85 glazed donuts. To find the number of donut holes, we can substitute this value
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You roll a 6-sided die.
What is P(odd or less than 2)?
Answer:
50%.
Step-by-step explanation:
If the die is perfectly balanced, the probability of rolling an odd number is 3 out of 6, or 50%.
The price of a home is $170,000. The bank requires a 15% down payment. The buyer is offered two mortgage options: 15-year fixed at 10% or 30-year fixed at 10%. Calculate the amount of interest paid for each option. How much does the buyer save in interest with the 15-year option? Use the following formula to determine the regular payment amount.
Answer:36000
Step-by-step explanation:
He saves 36000 dollars
5. Sketch rectangles with whole number dimension with perimeters that range from 12 to 16 units. a) For each perimeter, what are the dimensions of the rectangle that give the greatest area? b) For each perimeter, what are the dimensions of the rectangle that give the least area? 6. Draw a figure made from square tiles where adding an additional tile decreases the perimeter. 7. A student claims that perimeter is a 2-dimensional measure because one needs to know length and width (or base and height) in order to measure it. How would you respond to this student? 8. Compare a square, equilateral triangle, and circle that each have perimeter of 12 cm. Which has the greatest area? Which has the least area?
The solution to all parts are shown below.
a) For a rectangle with a perimeter of 12 units, the dimensions that give the greatest area are 3 units by 3 units.
For a perimeter of 13 units, the dimensions are 3 units by 3.5 units.
For a perimeter of 14 units, the dimensions are 3.5 units by 3.5 units.
For a perimeter of 15 units, the dimensions are 3.5 units by 4 units.
For a perimeter of 16 units, the dimensions are 4 units by 4 units.
b) For a rectangle with a perimeter of 12 units, the dimensions that give the least area are 1 unit by 5 units.
For a perimeter of 13 units, the dimensions are 1 unit by 6 units.
For a perimeter of 14 units, the dimensions are 2 units by 5 units.
For a perimeter of 15 units, the dimensions are 2 units by 6 units.
For a perimeter of 16 units, the dimensions are 2 units by 7 units.
6. One possible figure made from square tiles where adding an additional tile decreases the perimeter is a "U" shape.
If you arrange 9 square tiles in the shape of a "U", the perimeter is 12 units. If you add another tile to the middle of the "U", the perimeter will decrease to 10 units.
7. Perimeter is a 1-dimensional measure because it only involves adding up the lengths of the sides of a shape. The student's claim that perimeter is a 2-dimensional measure is incorrect.
8. For a square, equilateral triangle, and circle each with a perimeter of 12 cm, the circle has the greatest area and the equilateral triangle has the least area.
To see this, we can use the formulas for the perimeter and area of each shape:
A square with a perimeter of 12 cm has side length 3 cm.Its area is (3 cm)² = 9 cm².
An equilateral triangle with a perimeter of 12 cm has side length 4 cm.Its area can be calculated using the formula A = (√(3)/4) x s², where s is the side length of the triangle.
Thus, the area is (√(3)/4) x (4 cm)² = 4sqrt(3) cm², which is approximately 6.9 cm².
A circle with a perimeter of 12 cm has circumference 12 cm.Its radius can be calculated using the formula C = 2πr, where C is the circumference and r is the radius of the circle.
Thus, r = 6/(2π) cm, which is approximately 0.955 cm.
The area of the circle is πr², which is approximately 2.87 cm².
Therefore, the circle has the greatest area, followed by the square, and the equilateral triangle has the least area.
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A line has a slope of 7 and includes the points (-5,-5) and (-3,w). What is the value of w?
The value of w is 9.
We can use the slope formula to find the value of w.
The slope formula is:
m =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
where m is the slope of the line and [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex] are two points on the line.
We know that the slope of the line is 7, and the two points on the line are (-5, -5) and (-3, w). So we can plug in these values into the slope formula and solve for w:
7 = (w - (-5)) / (-3 - (-5))
Simplifying the right-hand side, we get:
7 = (w + 5) / 2
Multiplying both sides by 2, we get:
14 = w + 5
Subtracting 5 from both sides, we get:
w = 9
Therefore, the value of w is 9.
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Can you Please calculate this:
Answer:
14
Step-by-step explanation:
used a calculator to check the answer
Help pleaseee is just one problem
The matrices after the row operations are given as follows:
a) [tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
b) [tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
How to obtain the resultant matrices?The matrix in the context of this problem is defined as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\2&5&-6&-4\end{array}\right][/tex]
When we multiply a matrix row by a constant, each element of the row is multiplied by the constant.
Hence the resulting matrix after we multiply row 3 by 2 is given as follows:
[tex]\left[\begin{array}{cccc}-6&-5&-2&-3\\6&5&-1&-3\\4&10&-12&-8\end{array}\right][/tex]
We can also exchange rows of the matrix, hence the resulting matrix after rows 1 and 3 are exchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&5&-6&-4\\6&5&-1&-3\\-6&-5&-2&-3\end{array}\right][/tex]
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Which of the following algebraic steps will solve the equation 3x/4=7/3 what is the solution
The solution to the equation is x = 28/9
Given data ,
To solve the equation 3x/4 = 7/3, you can follow these algebraic steps:
Step 1 :
Multiply both sides of the equation by 4 to eliminate the fraction in the denominator of the left side:
(4) (3x/4) = (4) (7/3)
3x = (4/1) (7/3)
Step 2:
Simplify the right side of the equation:
3x = 28/3
Step 3 :
Divide both sides of the equation by 3 to isolate x:
(1/3) (3x) = (1/3)(28/3)
x = (28/3) / 3
Step 4 :
Simplify the right side of the equation:
x = 28/9
Hence , the solution to the equation 3x/4 = 7/3 is x = 28/9
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A school of 800 students has 60% girls.
Of them, 50% go to music classes. 10% of those music students are into volleyball. If the team is
32 Girls, how many are not into music?
Answer:
8
Step-by-step explanation:
I will just calculate the population of every detail for ease.
800 total students.
800 * 60% or 0.6 = 480
480 girls.
480 * 50% or 0.5 = 240
240 music class girls.
240 * 10% or 0.1 = 24
24 music class girls.
so 24 music class girls that are into volleyball and 32 team girls.
32-24 = 8
8 of the team girls are not into music.
Find the area of the regular polygon. Round your answer to the nearest hundredt
7
square units
Answer: A ≈ 127.31 units²
Step-by-step explanation:
We can use the given formula for the area of a regular hexagon, where a is equal to a given side (here, that is 7).
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]
We will substitute known values and solve by computing and simplifying.
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} a^2[/tex]
[tex]\displaystyle A=\frac{3\sqrt{3} }{2} (7)^2[/tex]
[tex]\displaystyle A=\frac{5.1961524}{2} 49[/tex]
[tex]\displaystyle A=(2.59807621)(49)[/tex]
[tex]\displaystyle A=127.3057[/tex]
[tex]\displaystyle A\approx 127.31[/tex]
Whats the probability either event will occur?
Answer: 0.68
Step-by-step explanation:
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 105 months, with a variance of 81 . If he is correct, what is the probability that the mean of a sample of 70 computers would differ from the population mean by less than 1.9 months? Round your answer to four decimal places.
The requried probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.
The mean of the sampling distribution of the sample means is:
u = 105
and the variance of the sampling distribution of the sample means is:
σ² = 81/70
We can standardize the distribution of the sample means by using the z-score formula:
z = (x - u) / (σ/ √(n))
where x is the sample mean, mu is the population mean, sigma is the population standard deviation, and n is the sample size.
We want to find the probability that the sample mean differs from the population mean by less than 1.9 months, or |x - u| < 1.9. This is equivalent to finding the probability that the standardized sample mean falls within the range:
-1.9 / (σ/ √(n)) < z < 1.9 / (σ/ √(n))
Substituting the values we have, we get:
-1.9 / (9 / √(70)) < z < 1.9 / (9 / √(70))
Simplifying, we get:
-1.1158 < z < 1.1158
Using a standard normal distribution table, we can find the probability that the z-score falls within this range:
P(-1.1158 < z < 1.1158) = 0.8671
Therefore, the probability that the mean of a sample of 70 computers would differ from the population means by less than 1.9 months is 0.8671, rounded to four decimal places.
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A, B & C form the vertices of a triangle.
∠
CAB = 90°,
∠
ABC = 58° and AB = 9.3.
Calculate the length of BC rounded to 3 SF.
Answer:
To calculate the length of BC in the triangle ABC, we can use the trigonometric functions sine and cosine.
Given that ∠CAB = 90° and ∠ABC = 58°, we can determine that ∠BCA = 180° - 90° - 58° = 32°.
Using the sine function, we can find the length of BC:
sin(∠BCA) = BC / AB
Rearranging the formula, we have:
BC = AB * sin(∠BCA)
Substituting the given values:
BC = 9.3 * sin(32°)
Using a calculator or trigonometric table, we find:
BC ≈ 9.3 * 0.529 = 4.917
Rounding to three significant figures (SF), the length of BC is approximately 4.92 units.
Step-by-step explanation:
Can someone help me pleaseeee
The solution to the system of equations, using the Gauss-Jordan method, is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]
How to solve the system of equations?The matrix representing the system of equations is given as follows:
[tex]\left[\begin{array}{cccc}-5&-3&-4&-12\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]
First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1/5, that is:
R1 -> -1/5R1
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]
First we want a value of 1 at line 2, column 2, hence we multiply the second line by -1/2, that is:
R2 -> -1/2R2
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&1&4&-22\end{array}\right][/tex]
We want an element of zero at line 3, column 2, hence:
R3 -> R3 - R2
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&2.5&-3\end{array}\right][/tex]
First we want a value of 1 at line 3, column 3, hence we multiply the third line by 2.5, that is:
R3 -> 1/2.5R3
Hence:
[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&1&1.2\end{array}\right][/tex]
Then the solution to the system of equations is given as follows:
z = 1.2.y = -19 - 1.5z = -21.4.x = 2.4 - 0.6y - 0.8z = 14.28.Hence the row-echelon form is given as follows:
[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]
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What is the mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs?
The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.
The mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population. This is due to the central limit theorem, which states that as the sample size increases, the distribution of sample means approaches a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, if we were to take all possible samples of size 81 from the population of GPAs and calculate the mean of each sample, the distribution of these means would be approximately normal with a mean equal to the population mean of GPAs. This means that if we take a large number of samples of size 81 and calculate the mean of each sample, the average of these means will be very close to the population mean of GPAs.
In conclusion, the mean of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population of GPAs is equal to the mean of the parent population of GPAs.
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A math quiz has 3 multiple choice questions and 2 true/false questions. Each multiple choice questions has 4 answer options: A, B, C, D.
Find the number of possible outcomes.
Answer:
The total number of possible outcomes for the math quiz is 16
Step-by-step explanation:
3.the diameter of a drum is 150 cm. What is the area of the space where the drum stands
4.Rachel is making a circular table cloth with a radius of 48 dm. How much area of the wall did it occupy?
5.A circular clock with a circumference of 75 cm is attached on a wall. How much area of the wall did it occupy?
Please answer it and do not please joke around
Answer:
All you have to do is to find the area of a circle to know the area it will contain.
Step-by-step explanation:
3. d=150cm= 150/100m=1.5m
r= 1.5/2= 0.75m
since a drum is circular under it will take a circular area
Area of a circle=πr^2
=π×(0.75)^2
=0.5625π = 1.77m^2
4. r=48dm=48/10=4.8m
since the clock is circular it will contact a circular area
Area of a circle= πr^2
=π(4.8)^2
=23.04π= 72.38m^2
5. since it's circular
C=75cm=75/100m=0.75m
Circumference of a circle=2πr
0.75=2πr
r=0.75/2π
r=0.119m
Area of a circle= πr^2
=π×(0.119)^2
=0.045m^2
I hope it helps.
The triangular prism below has a height of 13.4 units3 and a volume of 536 units
Find the area of one of its bases.
Answer: 40
Step-by-step explanation:
PLEASE SEE IMAGE TO SOLVE PROBLEM
Answer:
r(x) = x(x - 7)
Step-by-step explanation:
given the roots of a parabola x = a , x = b , then
the corresponding factors are (x - a) and (x - b)
from the graph the roots are where the graph crosses the x- axis
the graph crosses the x- axis at x = 0 and x = 7 , then
the corresponding factors are (x - 0) and (x - 7) , that is x and (x - 7)
the equation is then the product of the factors , that is
r(x) = x(x - 7)
what the answer for this?
Nam asked his mother's permission to go buy toys to give to Tuan's friend on the occasion of his birthday. Men buy two toys with list prices of VND 45,000 and VND 25,000 respectively and receive a 10% discount. how much does the male have to pay to buy those two toys?
Answer:
The total cost of the two toys before the discount is VND 45,000 + VND 25,000 = VND 70,000.
Step-by-step explanation:
The discount is 10% of the total cost, which is 0.1 x VND 70,000 = VND 7,000.
Therefore, the final cost after the discount is VND 70,000 - VND 7,000 = VND 63,000.
Nam will have to pay VND 63,000 to buy the two toys after the discount.
Please help me with these questions
The value of each angle 6x + 7 and 4x + 3 will be 55° and 35°, respectively.
Given that:
Angles, ∠1 = 6x + 7 and ∠2 = 4x + 3
Two angles are said to be complementary angles if their sum is 90 degrees.
The equation is given as,
∠1 + ∠2 = 90°
6x + 7 + 4x + 3 = 90°
10x + 10 = 90°
10x = 80°
x = 8
The value of each angle is calculated as,
∠1 = 6 * 8 + 7
∠1 = 55°
∠2 = 4 * 8 + 3
∠2 = 35°
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A truck driver travels 400 miles on day one and 215 miles on day two. The driver spent a total of 10 hours and 12 minutes driving on the two days. What was the truck driver's average speed in miles per hour (mph)? (Round to the nearest tenth.)
Answer:37.5 average
Step-by-step explanation:I think
determine unkown side length in a right triangle. round to nearest tenth.
side 1= 9
side 2= 3
Step-by-step explanation:
If side 1 and side 2 are LEGS of the triangle, then hypotenuse is found by
hyp^2 = 9^2 + 3^2 using pythagorean theorem
hyp^2 = 90
hyp = sqrt 90 = 3 sqt 10 =9.5 units
If hyp is 9 and 3 is one leg:
9^2 = 3^2 + L^2
L = 6 sqrt 2 =8.5 units
The surface area of a cylinder is 2,285.92 square inches. What is the height?
The height of the cylinder is determined as 36.2 inches.
What is the height of the cylinder?The height of the cylinder is calculated by applying the formula for surface area of a cylinder as shown below;
S.A = 2πr(r + h)
where;
r is the radius of the cylinder h is the height of the cylinderThe height of the cylinder is calculated as follows;
2,285.92 = 2π x 8.2 (8.2 + h)
2,285.92 = 51.52(8.2 + h)
8.2 + h = 2,285.92/51.52
8.2 + h = 44.37
h = 36.2 inches
Thus, the height of the cylinder for the given radius and surface area is determined by using the equation for surface area of a cylinder.
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The complete question is below:
The surface area of a cylinder is 2,285.92 square inches. What is the height? if the radius of the cylinder is 8.2 inches.
Find the derivative of f(x) = cot-1(2x + 1).
The first derivative of the inverse trigonometric function is equal to f'(x) = - 2 / [1 + (2 · x + 1)².
How to get the first derivative of an inverse trigonometric function
Herein we find the definition of an inverse trigonometric function, whose first derivative must be found by using derivative rules and especially derivative formulas for inverse trigonometric functions and chain rule. First, write the original function:
f(x) = cot⁻¹ (2 · x + 1)
Second, use derivative rules to determine the derivative:
f'(x) = [- 1 / [1 + (2 · x + 1)²]] · 2
f'(x) = - 2 / [1 + (2 · x + 1)²
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Can someone please help me with this? I’ll give brainlist!!
Answer:
12) x = 6. 13) not tangent
Step-by-step explanation:
12) x² - 5 = 31 (since they are both tangents)
x² = 31 + 5 = 36
x = ±6
x = +6 (has to be positive since it's a length).
13) if it was tangent, angle BAC would be 90°.
that would also mean AB² = BC² - AC²
= 15² - 5²
= 225 - 25
= 200
AB = √200 ≠ 14.
Since the values are different, AB is not a tangent to the circle
Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
The remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] is
[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
To find the remainder when dividing
[tex](10m^8 + 4m^6 + 10m^5) by (2m^2 + 5m^6 + 4m^4 + 10m^3),[/tex] we can use polynomial long division.
The dividend is[tex](10m^8 + 4m^6 + 10m^5)[/tex] and the divisor is [tex](2m^2 + 5m^6 + 4m^4 + 10m^3).[/tex]
Starting with the highest degree term, we divide ([tex]10m^8[/tex]) by ([tex]2m^2[/tex]) which gives us [tex]5m^6[/tex].
Next, we multiply the entire divisor [tex](2m^2 + 5m^6 + 4m^4 + 10m^3)[/tex] by [tex]5m^6[/tex], which gives us ([tex]10m^8 + 25m^{12} + 20m^{10} + 50m^9[/tex]).
We then subtract this product from the original dividend:
[tex](10m^8 + 4m^6 + 10m^5) - (10m^8 + 25m^{12} + 20m^{10} + 50m^9)[/tex] =[tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
We repeat the process with the new dividend ([tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex]) and the divisor ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]).
Continuing the long division process, we eventually find the remainder to be: [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5.[/tex]
Therefore, the remainder when dividing ([tex]10m^8 + 4m^6 + 10m^5[/tex]) by ([tex]2m^2 + 5m^6 + 4m^4 + 10m^3[/tex]) is [tex]-25m^{12} - 20m^{10} - 50m^9 + 4m^6 + 10m^5[/tex].
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Note the full question is:
Divide. (10m8 + 4m6 + 10m5) ÷ 2m2 5m6 + 4m4 + 10m3 5m6 + 2m4 + 10m5 5m6 + 2m4 + 5m3 5m8 + 2m6 + 5m5
What is the reminder
Tick the box to show where the hyphen is needed in the sentence below.
Answer:
I’m sorry but I don’t see any sentence below. Could you please provide me with the sentence?
A company is making concrete blocks. The blocks are in the form of right trapezoidal prisms and have the dimensions shown. What is the volume of one block? Show your work
Please help I give 40 brainly
Answer:
9180 (cm³)
Step-by-step explanation:
area of cross-section (trapezium) = 0.5 X (12 + 22) X 9
= 0.5 X 34 X 9 = 153 cm²
then multiply that by the length (60)
153 X 60 = 9180 (cm³)
Annabel's water bottle holds 6 cups of water. How many fluid
ounces does it hold?
The amount of fluid ounces of water the water bottle can hold is 48 fluid ounces.
How to find the volume of water in fluid ounces?Annabel's water bottle holds 6 cups of water. Therefore, the amount in fluid ounces the bottle water can hold can be calculated as follows:
Therefore,
1 cup = 8 fluid ounces
6 cups = ?
cross multiply
Hence,
number of fluid ounces of water the water bottle can hold = 8 × 6
number of fluid ounces of water the water bottle can hold = 48 fluid ounces.
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