Simplify the following.
Help me please Estimate 258+565
Can you find the sum [5.5+ (-2.3)] + (-5.5+2.3) without performing any additions?
To finance her community college education, Sarah takes out a loan for $3700. After a year Sarah decides to pay off the interest, which is 6% of $3700. How much will she pay?
Each small square on the grid is 1 cm².
Which estimate best describes the area of this figure?
15 cm²
20 cm²
25 cm²
35 cm²
Answer: The correct option is option third, i.e.,25 cm square.
Explanation:
From the given figure it is easily noticed that the shaded region contains two congruent parallelograms and 4 congruent triangles.
Area of a parallelogram is the product of base and height.
[tex]\text{Area of a parallelogram}=4\times 3=12[/tex]
The area of a parallelogram is 12 cm square.
Area of a triangle is half of the product of base and height.
[tex]\text{Area of a triangle}=\frac{1}{2}\times 2\times 0.25=0.25[/tex]
The area of a triangle is 0.25 cm square.
Since there are 2 parallelograms and 4 triangles in the figure, therefore the total area is,
[tex]A=2(12)+4(0.25)[/tex]
[tex]A=24+1=25[/tex]
Therefore, the area of figure is 25 cm square and the third option is correct.
Answer:
25 units²
Step-by-step explanation:
Count each whole box as one cm and count the ones that aren't whole as half a cm and you get 25 units²
Harriet counts 15 big boxes and 12 small boxes of notebooks. Each large box contains 189 notebooks, and each small box contains 79 notebooks. Estimate the total number of notebooks. Is your estimate an overestimate or an underestimate? Explain why it is better to have an overestimate than an underestimate.
185 in the ratio 2:3
Answer: 74:111
Step-by-step explanation: To find 185 in ratio 2:3:
First, add the ratios: 2 + 3 = 5
Second, each ratio will be put over the total: [tex]\frac{2}{5}[/tex] and [tex]\frac{3}{5}[/tex]
Third, multiply the number by the fraction of each proportion:
185 . [tex]\frac{2}{5}[/tex] = 74
185 . [tex]\frac{3}{5}[/tex] = 111
So, 185 in ration 2:3 gives ratio 74:111.
10x-5y=25 solve for y
Christopher made 3 1/4 dozen cupcakes. He added vanilla icing to 1/3 of the cupcakes and added chocolate icing to the rest. How many cupcakes, in dozens, have chocolate icing?
Taylor ran 2 1/4 miles and walked 2 4/5 miles. How far did she run and walk
Create three different drawings showing a number of rectangles and circles in which the ratio of rectangles to circles is 3:1
In a certain town, the wind speed, x, in km/h on a certain day is described by two statements: If 2 times the wind speed is increased by 2, the wind speed is still less than 46 km/h. Twice the wind speed minus 27 is greater than 11 km/h. Part A: Create a compound inequality to represent the wind speed range. (3 points) Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points) Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.
how many solutions are in 4x + 8 = 2x + 7 + 2x - 20
Can someone help me with these two questions?
what is 3/4 ÷ -2 3/4
If n = 6, then the value of n 2 is 12.
true or false
Lucy’s mom gave Lucy and her 3 friends an equal amount of juice from the 30 ounces she had left.
How much juice did each person receive?
Choose all answers that are correct.
Lucy and 3 friends = 4 people
30 ounces / 4 people = 7.5 ounces each
At sunrise, the temperature was –10.5°C. During the day, the temperature rose 5.2°C and then fell 3.6°C. What was the final temperature?
it started at -10.5 then rose 5.2
-10.5 +5.2 = -5.3
then fell 3.6
-5.3 - 3.6 = -8.9
so it was -8.9 degrees Celcius
As part of a school-wide fundraiser, the entire 8th grade class of a middle school is asked to split into groups. Each group must have the same number of boys and the same number of girls. If there are 126 boys and 135 girls in the 8th grade, what is the greatest number of groups they could form?
Answer:9 Groups
Step-by-step explanation:
Given
There are 126 boys and 135 girls
The greatest no of groups that could be form is determine by factorizing 126 and 135
[tex]126=2\times 7\times 9[/tex]
[tex]135=3\times 5\times 9[/tex]
both contains 9 as highest multiplying factor thus 9 groups can be formed.
Sample of 3 items is selected at random from a box containing 20 items of which 4 aredefective. find the expected number of defective items in the sample.
The clown Also bought 5 bags of heart shaped Balloons with 14 Balloons in each Bag
The clown bought a total of 70 heart-shaped balloons. This is found by multiplying the number of bags (5) by the number of balloons in each bag (14).
Explanation:
The question involves a basic multiplication operation in mathematics. The clown bought 5 bags of heart-shaped balloons and each bag contains 14 balloons. To find the total number of balloons, you multiply the number of bags (5) by the number of balloons in each bag (14). This is done as follows:
Identify the numbers in the question: 5 bags, 14 balloons in each. Perform the multiplication: 5 (bags) x 14 (balloons in each bag) = 70 balloons.So, the clown bought a total of 70 heart-shaped balloons.
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The mean, median, and mode are measures of _________.
The ___________ is based on the median.
The ___________ is based on the mean.
The ____________ is based on the mean
The mean, median, and mode are measures of central tendency. The median value is based on the median , while the arithmetic average is based on the mean. The most frequently occurring value in a data set is based on the mode .
The mean, median, and mode are measures of central tendency. These are statistical tools used to describe the center of a set of data.The median is based on the median. It is defined as the middle value in a data set when it is ordered from lowest to highest. If there is an even number of observations, the median is the average of the two middle numbers.The mean is based on the mean. The mean is the arithmetic average of a data set and is calculated by adding up all the individual values and then dividing by the number of values.The mode is also a measure of central tendency and is the value that appears most frequently in a data set.For example, if we have the following data set: {4, 18, 18, 19, 19, 19, 19, 19, 20, 20}, the mean is 17.5 (170/10), the median is 19, and the mode is 19.
Which set of line segments could create a right triangle? a 15, 30, 35 b 15, 36, 39 c 15, 20, 29 d 5, 15, 30
Final answer:
By applying the Pythagorean theorem, it's determined that the set of line segments that could create a right triangle is option b. (15, 36, 39), as it's the only set that satisfies the equation a² + b² = c².
Explanation:
The question asks which set of line segments could create a right triangle. To solve this, we apply the Pythagorean theorem, which states for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
For option a (15, 30, 35), applying the Pythagorean theorem: 15² + 30² = 225 + 900 = 1125, which is not equal to 35² (1225).For option b (15, 36, 39), we get: 15² + 36² = 225 + 1296 = 1521, and 39² = 1521, so this set satisfies the Pythagorean theorem.For option c (15, 20, 29), we have: 15² + 20² = 225 + 400 = 625, which is not equal to 29² (841).For option d (5, 15, 30), we get: 5² + 15² = 25 + 225 = 250, which is not equal to 30² (900).Therefore, the set of line segments that could create a right triangle is option b. (15, 36, 39).
Answer:
b. 15, 36, 39
Step-by-step explanation:
You want the set of line segments that could form a right triangle.
Pythagorean triplesA set of 3 integers is a Pythagorean triple if it satisfies the Pythagorean theorem:
a² +b² = c²
The most common primitive triples are {3, 4, 5}, {5, 12, 13}. If two of three numbers match these, but the third does not, a right triangle cannot be formed.
We note that {3, 4, 5} has the smallest first number of any Pythagorean triple, and it is the only triple that is an arithmetic sequence.
ChoicesWe can reduce the given numbers to their lowest form to see if we can determine whether any is a Pythagorean triple:
a. 15 : 30 : 35 = 3 : 6 : 7 . . . . . not a right triangle
b. 15 : 36 : 39 = 5 : 12 : 13 . . . . forms a right triangle
c. 15 : 20 : 29 = 3 : 4 : 5.8 . . . . . not a right triangle
d. 5 : 15 : 30 = 1 : 3 : 6 . . . . not a triangle
__
Additional comment
The attachment shows the values of a² +b² -c² for the different answer choices. That expression will evaluate to 0 if the numbers form a right triangle. If the sum is negative, any triangle formed would be obtuse. As we noted above, choice D values do not even form a triangle.
Other Pythagorean triples commonly seen in algebra problems are ...
{7, 24, 25}, {8, 15, 17}, {9, 40, 41}, {20, 21, 29}
You may also notice that when the two largest numbers differ by 1, the smallest is the root of their sum: 3 = √(4+5), 5 = √(12+13), 7 = √(24+25), and so on. This is another way we can tell {3, 6, 7} is not a Pythagorean triple: 3 ≠ √(6+7).
Which of the following is a counterexample to "the sum of two numbers is always greater than either of the numbers"?
A tank and a pail contain a total of 5136 milliliter of water. Jacob pours 314 milliliters of water from the pail into tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?
To find the initial amount of water in the pail, set up a system of equations based on the total volume and the information provided after transferring some water. Solve the equations to obtain the initial quantity of 957 milliliters in the pail.
Explanation:A student posed a problem: A tank and a pail contain a total of 5136 milliliters of water. Jacob pours 314 milliliters of water from the pail into the tank. The amount of water in the tank is now 7 times what is left in the pail. How much water was in the pail at first?
Let's denote the initial amount of water in the tank as T milliliters and in the pail as P milliliters. According to the given information, the combined quantity of water in both is 5136 milliliters:
T + P = 5136After transferring 314 milliliters from the pail to the tank, the tank now has T + 314 milliliters, and the pail has P - 314 milliliters. It is also given that the water in the tank is now 7 times the water left in the pail:
(T + 314) = 7*(P - 314)Now, we have a system of two equations:
By solving these equations, we can find the initial amount of water in the pail, P. First, modify the second equation to isolate T:
T = 7P - 2206 - 314T = 7P - 2520Next, substitute the expression for T from the second equation into the first equation and solve for P:
7P - 2520 + P = 51368P = 5136 + 25208P = 7656P = 7656 / 8P = 957 millilitersInitially, there were 957 milliliters of water in the pail.
Use distributive property and partial products to find 7 x 12
To calculate 7 x 12 using distributive property and partial products, decompose 12 into 10 and 2, then multiply 7 by each part and add the results. The sum of 70 and 14 gives you 84, which is the product of 7 and 12.
To find the product of 7 x 12 using the distributive property and partial products, we first break down the number 12 into 10 + 2. Then we use the distributive property to multiply 7 by each of these parts separately:
7 x 10 = 707 x 2 = 14Now, we add these partial products together to find the total:
70 + 14 = 84
Therefore, 7 x 12 equals 84 when we use distributive property and partial products.
Given: mTRV = 60° mTRS = (4x)° Prove: x = 30 What is the missing reason in step 3? substitution property of equality angle addition postulate subtraction property of equality addition property of equality
Answer: Angle addition postulate.
Explanation: If [tex]\angle TRV= 60^{\circ}[/tex] and [tex]\angle TRS=4x^{\circ}[/tex]
here, if we have to prove x=30
If there is a condition that TR is a line which meets with the line segment VS at point R then by the Angle addition postulate, we can say that [tex]\angle TRV+\angle TRS=180^{\circ}[/tex]⇒[tex]x=30^{\circ}[/tex]
But,
In option (1) substitution property of equality
If there is condition that [tex]\angle TRV=\angle TRS[/tex]
then we can use substitution property of equality,
And, in this case [tex]4x^{\circ}=60^{\circ}[/tex]⇒[tex]x=15^{\circ}[/tex]
which is wrong. So, we can not use this property here.
In option (3) subtraction property of equality
There is no use of this property to find the value x.
In option (4) addition property of equality
There is no use of this property to find the value x.
The omitted reason in step 3 should be the angle addition postulate.
According to the angle addition postulate , the value or measurement of an angle is the sum of all the angles which makes up that segment.From the diagram attached ;
mTRV = 60 ; ∠TRS = 4x
According to the addition postulate :
mTRV + ∠TRS = 180° (sum of linear pair of angles).
Though obtaining the value of the missing angle required substituting 30 for the value of x. However, it is because of the addition postulate which gives the sum of a linear pair of angles that we were able to establish that mTRV + ∠TRS = 180°.Hence, the missing reason for the third step is the angle addition postulate.
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30,6 in the sequence above each term after the 1st term is 1/5 of the term preceding it what is the 5th term of this sequence
estimating products of fractions how do you figure 3/8 × 15
Using the sum or difference formulas,how do we find the exact value of sin (285°)?
Answer:
[tex]\frac{-\sqrt{2}-\sqrt{6}}{4}[/tex]
Step-by-step explanation:
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