You have to bake a lot of brownies for your 6th-grade fundraiser! Although you have plenty of flour, cocoa, milk, and oil, you only have 8 1/2 sticks of butter. You need to know how many batches you can make, based upon your limited amount of butter. You can cook partial batches to use up every bit of butter and make the most brownies possible. Each batch needs 3/4 of a stick of butter. 4 How many batches of brownies can you bake? Justify your answer using equations, models, and/or words to explain your mathematical reasoning.
11 1/3 is the answer
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights. Use x
as the variable.
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
a. Write and solve an absolute value equation to find the minimum and maximum acceptable soccer ball weights. Use x
as the variable.
Answer:
The required absolute equation is: |x-430|=20
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Step-by-step explanation:
Consider the provided information.
The recommended weight of a soccer ball is 430 grams. The actual weight is allowed to vary by up to 20 grams.
Let x is the actual weight of the soccer ball.
The difference of actual weight and recommended weight can vary by 20 grams.
Thus, the required absolute equation is:
|x-430|=20
x-430=20 or x-430=-20
x=450 or x=410
The minimum and maximum acceptable soccer ball weights is 410 grams and 450 grams respectively.
Vertex A in quadrilateral ABCD lies at (-3, 2). If you rotate ABCD 180° clockwise about the origin, what will be the coordinates of A′ of the rotated quadrilateral A′B′C′D′?
Answer:
The coordinate of A' after rotated through 180° is (3,-2)
Step-by-step explanation:
Given vertex A in a quadrilateral ABCD lies at (-3,2). Now we have to rotate the quadrilateral ABCD 180° clockwise about the origin.
The point (x,y) is when rotated about the origin through 90° in clockwise direction then the new position will be (y,-x).
Now,the point A which is given is (-3,2)
First after rotation through 90° the new point will be (2-(-3)) = (2,3)
Again this point further rotated through 90° or we can say that rotation after 180° then the new point become A' = (3,-2).
Hence, The coordinate of A' after rotated through 180° is (3,-2)
the coordinates of A′ after a 180° clockwise rotation about the origin will be (3, -2).
To solve this problem, we need to apply a 180° clockwise rotation to the point (-3, 2). A 180° clockwise rotation about the origin will map any point (x, y) to the point (-x, -y).
The coordinates of the original point are:
A (-3, 2)
Apply the rotation rule, the new coordinates will be:
[tex](-(-3), -(2)) = (+3, -2)[/tex]
Therefore, the coordinates of A′ after a 180° clockwise rotation about the origin will be (3, -2).
An ice cream company made a profit of $24,000 in 2011. The same company had a loss of $11,000 in 2012. What is the difference between the company's financial results for 2011 and 2012
The required difference in the financial result is $13000.
given that,
An ice cream company made a profit of $24,000 in 2011. The same company had a loss of $11,000 in 2012. What is the difference between the company's financial results for 2011 and 2012 is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
In the year 2011, an ice cream company made a profit of $24,000
in the year 2012, the same company had a loss of $11,000.
Difference in the result = 24000 - 11000 = $13,000
Thus, the required difference in the financial result is $13000.
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(hard.) in a certain psychology experiment, each subject is presented with three ordinary playing cards, face down. the subject takes one of these cards. the subject also takes one card at random from a separate, full deck of playing cards. if the two cards are from the same suit, the subject wins a prize. what is the chance of winning
At age 45, an elephant grows teeth, each weighing 4 kg. About how many pounds do these teeth weigh? Use the conversion factor 1 kg = 2.2046 lbs. Round to the nearest tenth where necessary.
y = 5x – 1
–15x – 3y = 3
How many solutions does this linear system have?
one solution: (0, –1)
one solution: (1, 4)
no solution
infinite number of solutions
y = 5x - 1...so we sub 5x - 1 in for y in the other equation
-15x - 3y = 3
-15x - 3(5x - 1) = 3
-15x - 15x + 3 = 3
-30x = 3 - 3
-30x = 0
x = 0
y = 5x - 1
y = 5(0) - 1
y = -1
it has one solution (0,-1) <=
Trevor earns $7.80 an hour take home pay and works 20 hours each week. Trevor wants to buy a new laptop computer to take to college that costs $780. How many weeks will it take for Trevor to achieve his goal?
Answer: 5 weeks
Step-by-step explanation:
Evaluate. Write in simplest form.
6 - b for a = 10, b = –9
--------
3a
A.1/2
B.-/310
C.1/10
D. 2 HELP ME BROS
It is estimated that each guest at a party will eat
9/10 pounds of chocolates. How many guests can be served with 45 pounds of chocolate?
MODEL WITH MATHEMATICS
Write a problem about a real-world situation in which you would either write a percent as a decimal or write a decimal as a percent.
Solumedrol 1.5 mg/kg is ordered for a child weighing 50 lb. Solumedrol is available as 75 mg / 1 mL is available. How many mL must the nurse administer?
1meter =1x10^9 in sicentific notation
Write the following ratio using two other notations. 5/9 Use only the numbers above (not any others).
The ratio 5/9 can be expressed as a decimal (0.555) or as a percentage (55.6%).
Explanation:The given ratio is 5/9.
Decimal: A decimal is a way of expressing a number with a fractional part. It is based on powers of 10. For example, the decimal number 0.5556 means 5/10 + 5/100 + 5/1000 + 6/10,000.
Percentage: A percentage is a way to express a number as a fraction of 100. For example, the percentage 55.56% is equivalent to the fraction 55.56/100, which means 55.56 out of every 100.
We can express this ratio using two other notations:
As a decimal: 5/9 ≡ 0.555As a percentage: 5/9 ≡ 55.6%Learn more about Ratio here:https://brainly.com/question/32531170
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When two parallel lines are cut by a transversal, angles A and B are alternate interior angles that each measure 105°. What is the measure of each of the other alternate interior angles?
75°
90°
105°
180°
The measure of each of the other alternate interior angles is; 75°
How to find the Alternate Interior Angle?We know that according to Angle theorems, two adjacent alternate interior angles make up a straight line. Sum of angles on a straight line equals 180°.
Thus, if the measure of the other interior angle is x, then we have;
x + 105 = 180
x = 180 - 105
x = 75°
The measure of the other alternate angles is 75°.
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Factor the expression completely:
x³ - 3x² - 4x + 12
Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the distance in 1.5 h. Car B traveled 15 mph faster than Car A. How fast did Car B travel? (The formula R·T=D , where R is the rate of speed, T is the time, and D is the distance can be used.)
643=4×160+n in a related division form
The vertices of the feasible region represented by a system are (0, 100), (0, 80), (80, 60), (80, 0), and (120, 0). What are the minimum and maximum values of the objective function F = 8x + 5y?
The minimum and maximum values of the objective function f = 8x + 5y are 400 and 960
How to determine the minimum and the maximum values?The vertices of the feasible region are given as:
(0, 100), (0, 80), (80, 60), (80, 0), and (120, 0)
The objective function is given as:
z = 8x + 5y
Calculate the value of the objective function using the vertices
F = 8 * 0 + 5 * 100 = 500
F = 8 * 0 + 5 * 80 = 400
F = 8 * 80 + 5 * 60 = 940
F = 8 * 80 + 5 * 0 = 640
F = 8 * 120 + 5 * 0 = 960
The minimum value above is 400 and the maximum value is 960
Hence, the minimum and maximum values of the objective function F = 8x + 5y are 400 and 960
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What is 3/8 written as a decimal
2 times as much as 4 is
The answer is 8.
To solve the given mathematical question, we need to calculate twice as much as the number 4. The phrase 2 times as much as indicates multiplication by 2. Therefore, we multiply the number 4 by 2 to find the result.
Mathematically, this can be represented as:
[tex]\[ 2 \times 4 = 8 \][/tex]
So, 2 times as much as 4 is 8.
40 miles x 25 min.=?mph
A car drove 148 miles using 4 gallons of gasoline. How many gallons will it take to drive 9 1/4 miles?
How many ways are there to pick a starting five from a basketball team of twelve members
Answer:
95040
Step-by-step explanation:
Given : There are 12 members in basketball team.
To Find: How many ways are there to pick a starting five from a basketball team of twelve members
Solution:
Since we are asked to find no. of ways are there to pick a starting five from a basketball team of twelve members
So, we will use permutation over here.
Formula: [tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
n = 12
r = 5
Substitute the value sin the formula .
[tex]^{12}P_5=\frac{12!}{(12-5)!}[/tex]
[tex]^{12}P_5=\frac{12!}{(7)!}[/tex]
[tex]^{12}P_5=\frac{12 \times 11\times 10 \times 9\times 8 \times 7!}{7!}[/tex]
[tex]^{12}P_5=12 \times 11\times 10 \times 9\times 8[/tex]
[tex]^{12}P_5=95040[/tex]
Hence there are 95040 ways to pick a starting five from a basketball team of twelve members.
There are 95040 different ways to pick a starting five from a basketball team of twelve.
What are permutation and combination?A permutation is an arrangement of things where order matters, AB and BA are two different permutations.
The combination is a selection of things where order does not matter, AB and BA are the same combinations.
Given, The no. of ways to pick a starting five from a basketball team of twelve members.
As stated pick a starting five we'll use permutation.
∴ The no. of ways to pick a starting five from a basketball team of twelve members is [tex]^{12}P_5[/tex].
= 12!/(12 - 5)!.
= 12!/7!.
= 12×11×10×9×8.
= 95040 different ways.
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Which transformation would change the point (5,3) into (-5,3)?
Two bags had 100 kilograms of sugar each. After taking out 3 times as much sugar from bag one than bag two, bag one had half as much sugar left as bag two. How much sugar is left in each bag?
What two-dimensional cross-sections could we create by slicing the particular triangular prism
A man in a rowboat that is a = 2 miles from the nearest point A on a straight shoreline wishes to reach a house located at a point B that is b = 8 miles farther down the shoreline (see the figure). He plans to row to a point P that is between A and B and is x miles from the house, and then he will walk the remainder of the distance. Suppose he can row at a rate of 2 mi/hr and can walk at a rate of 4 mi/hr. If T is the total time required to reach the house, express T as a function of x.
The product of 5 and a number x is 14 . What is the value of x?
x=194
x=120
x=54
x=434
The relationship 1/sin(θ) is equivalent to which of the following trigonometric functions?
A. cot(θ)
B. csc(θ)
C. arcsin(θ)
D. sec(θ)
Answer:
Option B is the correct answer.
Step-by-step explanation:
We have the following trigonometric relations
[tex]cosec\theta =\frac{1}{sin\theta }\\\\sec\theta =\frac{1}{cos\theta }\\\\cot\theta =\frac{1}{tan\theta }\\\\cot\theta =\frac{cos\theta}{sin\theta }\\\\tan\theta =\frac{sin\theta}{cos\theta }[/tex]
Here cosec θ is the correct answer.
Option B is the correct answer.