To determine which objects hold the same amount of liquid as a 96-fluid-ounce jug, we need to convert each of the given measurements to fluid ounces and then add them up. Here are the conversions:
Two 1-quart bottles = 64 fluid ounces (2 x 32)
Two 1-pint bottles = 32 fluid ounces (2 x 16)
One 1-quart bottle and eight 8-ounce fluid glasses = 96 fluid ounces (32 + 8 x 8)
So, the objects that hold the same amount of liquid as a 96-fluid-ounce jug are:
One 1-quart bottle and eight 8-ounce fluid glasses
Three 1-quart bottles
Therefore, the correct answer is:
one 1−quart bottle and eight 8−ounce fluid glasses
three 1−quart bottles
An appropriate tip for a waiter at a restaurant is at least 15%. For a tab of $20, how much money should be left, including tip?
An appropriate tip for a waiter at a restaurant is at least 15% of the total bill. For a tab of $20, the tip would be:
Tip amount = 15% of $20
Tip amount = 0.15 x $20
Tip amount = $3
Therefore, the total amount of money that should be left, including tip, is:
$20 (tab) + $3 (tip) = $23.
If the diameter of a circle is 8.4 in.. find the area and the circumference of the circle. Use 3.14 for pl. Round your answers to the nearest
hundredth.
Given that the diameter of a circle is 8.4 inches.
The radius (r) of the circle can be found by dividing the diameter by 2:
r = d/2 = 8.4/2 = 4.2 inches
The area (A) of a circle can be found using the formula:
A = πr^2
Substituting the value of r, we get:
A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches
The circumference (C) of a circle can be found using the formula:
C = 2πr
Substituting the value of r, we get:
C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches
Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.
We know that the area of a circle is given by the formula A = π×r²
Given the diameter of the circle = 8.4 in
Therefore radius of the circle = 8.4/2 = 4.2 in (diameter/2 = radius)
Now Area of the circle = π × 4.2²
= 3.14 × 17.64
= 55.3896
= 55.39 (round up to the nearest hundredth)
Circumference of the circle = 2 × π × r
= 2 × 3.14 × 4
= 26.376
= 26.38 (round up to the nearest hundredth)
Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.
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Marcus surveys the students in his school about their favorite lunch.
Lunch
Grilled Cheese
Roast Beef
Chili
Frequency
80
40
50
20
60
Use the data to describe the favorite lunch of students at Marcus's school. Round to the nearest percent and the nearest 10 students.
% of students surveyed preferred grilled cheese, so in a group of 3500 students, about
Chicken & Rice
Other
students will prefer grilled cheese.
32% of the students surveyed preferred grilled cheese, so in a group of 3500 students, about 1120 students will prefer grilled cheese.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of people surveyed is given as follows:
80 + 40 + 50 + 20 + 60 = 250.
80 students preferred grilled cheese sandwich, hence the percentage is obtained as follows:
p = 80/250 x 100%
p = 32%.
Hence the expected amount of 3500 students is given as follows:
0.32 x 3500 = 1120 students.
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Which pair of points are both located less than 3 units from the point (3,8) on a coordinate grid?
The required pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
Following the condition given in the question,
Assuming there are 3 points on the graph beside (3, 8) are (2, 7), (5, 5), and (6, 10)
The distance formula between two points is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
So, for each point, we can plug in the coordinates and simplify the following:
Point (2, 7):
d = √[(2 - 3)² + (7 - 8)²]
d = √[1² + 1²]
d = √2 (<3)
Points (6, 10):
d = √[(6 - 3)² + (10 - 8)²]
d = √[3² + 2²]
d = √13 (>3)
Point (5, 5):
d = √[(5 - 3)² + (5 - 8)²]
d = √[2² + 3²]
d = √13 (>3)
Point (1, 1):
d = √[(1 - 3)² + (1 - 8)²]
d = √[(-2)² + (-7)²]
d = √53 (>3)
Thus, the pair of points that are both located less than 3 units from points (3, 8) is (2, 7).
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The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
The average rate of change for function f(x) = 1.85x² to the nearest tenth over the interval 10 ≤ x ≤ 20 is equal to 55.5 (Rounding to the nearest tenth).
Function models the cost of a square carpet
f(x) = 1.85x²
The average rate of change of a function f(x) over an interval [a, b] is,
Average rate of change = [f(b) - f(a)] / (b - a)
The average rate of change of f(x) over the interval 10 ≤ x ≤ 20.
Using the given function, we have,
f(10) = 1.85(10)²
= 185
f(20) = 1.85(20)²
= 740
Now calculate the average rate of change,
average rate of change
= [f(20) - f(10)] / (20 - 10)
= (740 - 185) / 10
= 55.5 (Rounding to the nearest tenth)
Therefore, the average rate of change of function f(x) over the interval 10 ≤ x ≤ 20 is approximately 55.5.
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Please find the surface area of this figure. Ps pls show your work on how you got your answer or explain.
Answer:
2(1/2)(11)(13) + 2(1/2)(10)(13.2) + 10(11)
= 143 + 132 + 110 = 385 square feet
B is the correct answer.
Triangle ABC shown below has m∠B=36∘, a=5, and c=13. Find the area of the triangle.
Answer: 19.1 is correct
Step-by-step explanation:
where a and c are the lengths of two sides of the triangle and C is the angle between them. To use this formula, we need to find side b and angle A.
We can use the Law of Cosines to find side b:
in a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win.
The calculated value of the probability of winning is 3.06501854e-7
Calculating the probability of winningFrom the question, we have the following parameters that can be used in our computation:
Select 6 numbers out of 39 to win
This means that when a number is selected, the number is returned and the total numbers reduces by 1
i.e. P(Current) = n/(39 - n)
Using the above as a guide, we have the following:
P(Win) = 6/39 * 5/38 * 4/37 * 3/36 * 2/35 * 1/34
Evaluate the product of tthe expressions
So, we have
P(Win) = 3.06501854e-7
Hence, the probability of winning is 3.06501854e-7
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Complete question
In a certain lottery, you must correctly select 6 numbers (in any order) out of 39 to win You purchase one lottery ticket What is the probability that you will win?
The probability of winning is
8[tex]\sqrt{x} -80[/tex]
Answer: [tex]8(\sqrt{x} -10)[/tex]
Step-by-step explanation:
[tex]8\sqrt{x} - 80[/tex]
[tex]8(\sqrt{x} -10)[/tex]
Determine if triangle PQR is similar to triangle LMK. If they are similar enter the scale factor from triangle LMK to triangle PQR.
Triangles PQR and LMK are not similar. Thus none.
What are similar triangles?Two or more triangles are said to be similar if on comparing their corresponding properties, some common relations holds. One important relation is the scale factor that relates one triangle with the other.
In the diagram given, we have;
scale factor = LK/ PR
= 18/ 10
scale factor = 1.8
But this scale factor can not be used to determine the side LM correctly.
That is,
LM ≠ 1.8*8
LM ≠ 14.4
since LM = 13
Therefore, it can be deduced that triangles PQR and LMK are not similar. Thus none.
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Use this table of values to draw the graph of y=2x+3 for values of x from -3 to 3
A graph of y = 2x + 3 for values of x from -3 to 3 is shown in the image attached below.
How to develop the table by using the linear function?Based on the information provided above, the required table can be constructed or developed as follows;
x y = 2x + 3 y___
-3 y = 2(-3) + 3 -3
-2 y = 2(-2) + 3 -1
-1 y = 2(-1) + 3 1
0 y = 2(0) + 3 3
1 y = 2(1) + 3 5
2 y = 2(2) + 3 7
3 y = 2(3) + 3 9
In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set in the table on a graph as shown in the image attached below.
In conclusion, we can reasonably infer and logically deduce that the domain of this linear function y = 2x + 3 is [-3, 3] and the range is [-3, 9].
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∠A and ∠B are vertical angles. If m ∠ A=(2x−2) ∘ and B=(3x−15) ∘ , then find the value of x
The value of x is 13°
What are Vertical Angles?When two lines intersect, four angles are formed. There are two pairs of nonadjacent angles. These pairs are called vertical angles.
In a coordinate plane, a line parallel to the Y-axis is called Vertical Line. It is a straight line which goes from top to bottom and bottom to top. Any point in this line will have the same value for the x-coordinate.
We have:
The angles are:
m ∠ A=(2x−2) ∘ and ∠ B=(3x−15) ∘
We have to find the value of x
Now, We know that :
m ∠A = m ∠B (Def. of Vertical Angles)
(2x−2) = (3x−15)
Combine the like terms:
2x - 3x = -15 + 2
-x = -13
x = 13
The value of x is 13°
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The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $5500 to rent trucks plus an additional
fee of $200.25 for each ton of sugar.
The second company charges $4995 to rent trucks plus an additional fee of $225.50 for each ton of sugar.
For what amount of sugar do the two companies charge
the same?
What is the cost when the two companies charge the
same?
$
Let’s solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons.
The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x.
Setting these two expressions equal to each other, we get:
5500 + 200.25x = 4995 + 225.50x
Solving for x, we get:
25.25x = 505
x = 20
So, the two companies charge the same when the amount of sugar is 20 tons.
The cost when the two companies charge the same is:
5500 + 200.25 * 20 = $9505
So, when the two companies charge the same, the cost is $9505.
Received message. Let's solve this problem by setting the cost of the two companies equal to each other and solving for the amount of sugar. Let x be the amount of sugar in tons. The cost for the first company is 5500 + 200.25x and the cost for the second company is 4995 + 225.50x. Setting these two expressions equal to each other, we get: 5500 + 200.25x = 4995 + 225.50x Solving for x, we get: 25.25x = 505 x = 20 So, the two companies charge the same when the amount of sugar is **20 tons**. The cost when the two companies charge the same is: 5500 + 200.25 * 20 = $9505 So, when the two companies charge the same, the cost is **$9505**.
MARK ME BRAINLEISTAn experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
The probability representing the no heads in the outcome of flipping a coin 200 times is given by 25%.
Total number of times coin flipped = 200
Number of times we get,
Heads, Heads = 40
Heads, Tails = 75
Tails, Tails = 50
Tails, Heads = 35
The probability of getting no heads that is two tails in a coin toss. Probability is frequency of the outcome 'Tails, Tails' divided by the total number of trials.
⇒P(No Heads) = Frequency of 'Tails, Tails' / Total number of trials
From the table, the frequency of 'Tails, Tails' is 50,
And the total number of trials is 200.
This implies,
P(No Heads)
= 50 / 200
= 0.25
= 25%
Therefore, the probability of the no heads is equal to 25%.
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At Dela's Deli, Dela fills containers with homemade vinaigrette salad dressing. The table shows the amount of vinegar and olive oil used for the dressing.
Number of containers Vinegar (tsp) Olive Oil (tsp)
1 4 12.5
6
At this rate, how much vinegar and olive oil will be used to make 6 containers of salad dressing?
Dela will use 10 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 10 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 18.5 teaspoons of olive oil to make 6 containers of salad dressing.
Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
We have,
Dela uses a ratio of 4 teaspoons of vinegar to 12.5 teaspoons of olive oil.
So, for 6 containers
= 4 x 6
= 24 teaspoons of vinegar
and, = 12.5 x 6
= 75 teaspoons of olive oil
Thus, Dela will use 24 teaspoons of vinegar and 75 teaspoons of olive oil to make 6 containers of salad dressing.
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The histogram displays the ages of 50 randomly selected users of an online music service. Based on the data, if the service has 25,000 users, how many of them are 30 and older?
The number of users that are 30 and older is 10,500.
We have,
From the histogram,
The number of users that are 30 and older.
= 7 + 9 + 3 + 2
= 21
Now,
The percentage of 30 and older users.
= 21/50 x 100
= 21 x 2
= 42%
Now,
Total users = 25,000
So,
The percentage of 30 and older users.
= 42% of 25,000
= 42/100 x 25,000
= 42 x 250
= 10500
Thus,
The number of users that are 30 and older is 10,500.
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A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A (8,8), B(5, 3), and C(11,3)
. One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
Find the exact length of each side.
AB =
BC =
AC =
We can actually see here that the triangle ABC is an isosceles triangle. This is because two sides of the triangle are equal.
What is an isosceles triangle?An isosceles triangle is actually a geometric shape having three sides, two of which are equal in length. Consequently, two of the angles that are across from those sides are also equal.
In order to prove that the triangle is an isosceles triangle, we will find the following:
Distance between vertices A and B:
AB = √((8-5)² + (8-3)²) = √(3² + 5²) = √34 = 5.83mm
Then, we also find the distance between vertices B and C:
BC = √((11-5)² + (3-3)²) = 6mm
Finally, we find the distance between vertices A and C:
AC = √((11-8)² + (3-8)²) = √(3² + 5²) = √34 = 5.83mm
Thus, we see here that AB and AC are actually equal which makes the triangle an isosceles.
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Please help its due soon
The ratio of sec θ is determined as 5/3.
option A.
What is the ratio of secθ?The ratio is sec θ is calculated by applying the following method;
sec θ = 1/cosθ
Given that tanθ = -4/3 = oppo/adjacent
The hypotenuse side is calculated by applying Pythagoras theorem as shown below;
h = √ 4² + 3²
h = 5
The ratio of sec θ is calculated as follows;
sec θ = 1/cosθ
1/cosθ = 1/(3/5)
1/cosθ = 5/3
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Abdoulaye is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of 1 inch = 5 miles. City X and City Y are 11/2 between
City X ---------- 11/2 ------------- City Y
What is the actual distance between the two cities?
The actual distance between the two cities is [tex]7\frac{1}{2}[/tex] miles .
What is the actual distance?A scale drawing is the reduced version of a larger image. The scale drawing is reduced at a constant proportion to the original image using a scale. An example of a scale drawing is a map of the city.
Actual distance between the cities can be determined by multiplying the distance in the scale drawing by the scale.
Actual distance = 1[tex]\frac{1}{2}[/tex] x 5
= [tex]\frac{3}{2}[/tex] x 5 = [tex]\frac{15}{2}[/tex] = [tex]7\frac{1}{2}[/tex] miles
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Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run?
A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by.
Select all that apply.
You know the difference in the distances the boys ran, so this is a subtraction problem.
You are finding the total distance the boys ran, so this is an addition problem.
Dean ran part of the distance Sam ran, so this is a multiplication problem.
The correct equation is s + 2.3 = 6.8.
The correct equation is s – 2.3 = 6.8.
The correct equation is 2.3s = 6.8.
Answer:
A,E
Step-by-step explanation:
Operation: Minus
To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.
6.8 km - 2.3 km = 4.5 km
Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.
Answer:
a and e
Step-by-step explanation:
got it right on homework
Round to the nearest tenth, then find the difference. 13.56 − 10.02 = ___ pleas help in test and am about to leave soon.
The difference between 13.56 and 10.02 is 3.54.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
The difference between 13.56 and 10.02 can be calculated by doing the subtraction. As,
(13 + 0.56) - (10 + 0.02)
= (13 - 10) + (0.56 - 0.02)
= 3 + 0.54
= 3.54
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30 POINTS ANSWER FOR BRAINLIST
Solve m^2 − 6m = 3. Use the Quadratic Formula. Leave your answers as simplified radicals.
Answer:
To solve m^2 - 6m = 3 using the quadratic formula, we first need to put the equation in standard form, which is ax^2 + bx + c = 0.
m^2 - 6m - 3 = 0
Now we can identify a, b, and c:
a = 1, b = -6, c = -3
Next, we can plug these values into the quadratic formula:
m = (-b ± sqrt(b^2 - 4ac)) / 2a
m = (-(-6) ± sqrt((-6)^2 - 4(1)(-3))) / 2(1)
m = (6 ± sqrt(48)) / 2
Simplifying the square root of 48, we get:
m = (6 ± 4sqrt(3)) / 2
Now we can simplify by factoring out a 2 from the numerator:
m = 3 ± 2sqrt(3)
So the solutions to the equation are:
m = 3 + 2sqrt(3) or m = 3 - 2sqrt(3)
Step-by-step explanation:
Answer: 3±2√3
Step-by-step explanation:
see image for explanation
Let me know if you more explanation with simplifying the root. That is a whole lesson in itself.
Rachel works at a lemonade stand at the park on Monday she used 1 2/5 bags of lemons on Tuesday she use 1 1/4 times as many lemons as on Monday how many bags of lemons does Rachel have use on Tuesday
Answer:
1.75 Bags of Lemons
Step-by-step explanation:
1 2/5 = 1.4
1 1/4 = 1.25
1.4 * 1.25 = 1.75 Bags of Lemons
Selective serotonin reuptake inhibitors (SSRIs) are drugs that
Oprevent unused neurotransmitters from being transported back to the neuron.
increase reuptake of unused serotonin
Ostrengthen the effect of a neurotransmitters by mimicking it at the receptor site.
block effects of neurotransmitters by binding to receptors without activating them.
Selective serotonin reuptake inhibitors (SSRIs) are drugs that A. prevent unused neurotransmitters from being transported back to the neuron.
What are Selective serotonin reuptake inhibitors ?By inhibiting the serotonin transporter, SSRIs prevent the reuptake of serotonin into neurons after synapse release, thereby increasing available serotonin in the brain. Such changes help to alleviate symptoms associated with anxiety, depression and other mood disorders.
Overall, a rise in serotonin activity is significant in transforming an individual's mood pattern. When more serotonin remains within synapses, it binds with and activates its receptors, leading to increased levels of hormonal activity proven to be effective in treating various mood imbalances in patients.
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I REALLY NEED THIS IMMEDIATELY PLEASE HELP !
(Use The Image)
Patrica is building a garden in her backyard that is shaped like a triangle. She has already built two sides of the garden and they have lengths of 6 feet and 7 feet.
Answer:
Step-by-step explanation:
The third side of Patricia's garden should be approximately 10.64 feet long.
To determine the length of the third side of Patricia's garden, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles. In this case, we have two known side lengths (6 feet and 7 feet) and the angle between them (110 degrees).
The Law of Cosines states that for a triangle with side lengths a, b, and c, and angle C opposite side c:
c² = a² + b² - 2ab*cos(C)
We want to find the length of the third side, so let's call it c. Plugging in the known values:
c² = 6² + 7 - 267*cos(110°)
Simplifying the equation:
c² = 36 + 49 - 84*cos(110°)
Now, we can calculate the value of cos(110°) using a calculator or trigonometric tables. Once we have that value, we can substitute it back into the equation to find c². Taking the square root of c² will give us the length of the third side.
Note: The value of cos(110°) is approximately -0.342.
c² = 36 + 49 - 84*(-0.342)
c² ≈ 36 + 49 + 28.248
c^2 ≈ 113.248
Taking the square root:
c ≈ √113.248
c ≈ 10.64
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How many 1/4 cups of water fit inside of a 2 1/2 cup water bottle?
Answer:
There are 10 1/4 cups of water that fit inside a 2 1/2 cup water bottle.
To see why, note that 2 1/2 cups is equivalent to 10 quarter cups (2 x 4 = 8 and 8 + 2 = 10). Therefore, you can fill the water bottle with 10 1/4 cups of water.
A 138 foot antenna is on top of the top of a tall building. From a point on the ground, the angle of elevation to the top of the antenna is 30.5ﾟ while the angle of elevation to the bottom of of the antenna from the same point is 23.5ﾟHow tall is the building
Answer:
289
Step-by-step explanation:
Let's call the height of the building "h" and the distance from the point on the ground to the base of the building "d".
From the point on the ground, the distance to the top of the antenna is d + 138, and the distance to the bottom of the antenna is d.
Using trigonometry, we can set up two equations:
tan(30.5°) = (d + 138) / h (1)
tan(23.5°) = d / h (2)
We can solve equation (2) for d:
d = h tan(23.5°)
Substituting this into equation (1), we get:
tan(30.5°) = (h tan(23.5°) + 138) / h
Simplifying:
tan(30.5°) = tan(23.5°) + 138/h
tan(30.5°) - tan(23.5°) = 138/h
h = 138 / (tan(30.5°) - tan(23.5°)) ≈ 289.12 feet
Therefore, the height of the building is approximately 289.12 feet.
Each week, Nursen saves $5 and shares $3.75. She also spends $4.95 on bus fare to get home from music lessons. This week she earned $24 babysitting. How much money does Nursen have left that she can spend?
Answer: In one week, Nursen saves $5 and shares $3.75, so she has $5 + $3.75 = $8.75 per week.
She spends $4.95 on bus fare, so she has $8.75 - $4.95 = $3.80 per week to spend.
This week, Nursen earned $24 babysitting, so she has an additional $24 to spend.
Therefore, Nursen has $3.80 + $24 = $27.80 to spend.
Step-by-step explanation:
help please
(instructions: chose from the word bank below to describe the type of multiplication being used. you may use an answer more than once.)
[ identity commutative associative inverse distributive]
1. 14 x 6 = 6 x 14 ________
2. 4(5 + 7) = (4 x 5) + (4 x 7) ________
3. 8 x 1 = 8 ________
4. 7 x (6 x 2) = (7 x 6) x 2 ________
5. 12 x 3 = 3 x 12 ________
6. 1/8 x 8/1 = 1 ________
7. 1 x 9 = 9 ________
8. 3 x (7 x 2) = (3 x 7) x 2 ________
9. 2(8 + 5) = (2 x 8 ) + (2 x 5) ________
(page 2)
(instructions: choose the correct multiplication property for the problems below)
10. which property is demonstrated below?
12 x 1 = 12
A. identity
B. commutative
C. associative
D. inverse
E. distributive
11. which property is demonstrated below?
2/5 x 5/2 = 1
A. identity
B. commutative
C. associative
D. inverse
E. distributive
12. which property is demonstrated below
5 x 8 = 8 x 5
A. identity
B. commutative
C. associative
D. inverse
E. distributive
13. which property is demonstrated below?
8 x (7 x 9) = (8 x 7) x 9
A. identity
B. commutative
C. associative
D. inverse
E. distributive
14.which property is demonstrated below?
4(6 + 3) = (4 x 6) + (4 x 3)
A. identity
B. commutative
C. associative
D. inverse
E. distributive
The blanks are filled as follows
1. Commutative
2. Distributive
3. Identity
4. Associative
5. Commutative
6. Inverse
7. Identity
8. Associative
9. Distributive
10. A. Identity
11. A. Identity
12. B. Commutative
13. C. Associative
14. E. Distributive
What is distributive law of multiplication?The distributive law of multiplication is a distinct attribute in mathematics that distinguishes how multiplication interacts with the operations of addition or subtraction.
It is exemplified in the problem as
2(8 + 5) = (2 x 8 ) + (2 x 5Learn more about distributive property at
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Write in terms of x and y only.
Result:
sin(tan⁻¹(x) - tan⁻¹(y)) in terms of x and y only = (x - y) / (1 + xy).
How do we express the equation in term of x and y?For us to write the expression, we shall use this formular formula:
tan(a - b) = (tan(a) - tan(b)) / (1 + tan(a)tan(b))
where:
a = tan⁻¹(x)
b = tan⁻¹(y)
Next, we have:
tan(tan⁻¹(x) - tan⁻¹(y)) = (tan(tan⁻¹(x)) - tan(tan⁻¹(y))) / (1 + tan(tan⁻¹(x))tan(tan⁻¹(y)))
= (x - y) / (1 + xy)
From both sides, we have sine:
sin(tan⁻¹(x) - tan⁻¹(y)) = sin(tan(x - y / 1 + xy))
So, sin(tan⁻¹(x) - tan⁻¹(y))
= sin(tan⁻¹(x) - tan⁻¹(y))
= (x - y) / (1 + xy) in terms of x and y.
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