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?
when a decimal is written in word form,what indicates that the equivalent form is a mixed number and not a fraction
Final answer:
A decimal written in word form represents a mixed number if there's a whole number followed by 'and', then the fractional part, such as 'two and three tenths' for 2.3.
Explanation:
When a decimal is written in word form, the indication that the equivalent form is a mixed number rather than a fraction is the presence of a whole number followed by the word 'and', then the fractional part.
For example, 'two and three tenths' (2.3 in numeric form) is a mixed number, as it has a whole number 'two' and the fractional part 'three tenths'. In contrast, a number written solely as 'three tenths' would represent just a fraction (0.3 in numeric form).
Given that events a and b are independent and that p(a) = 0.8 and p(b|a) = 0.4, then p(a and
b.= 0.32.
a. True
b. False
What is the value of ▲ in the equation shown?
7 x 9 = (7 x 10) - (7 x ▲)
=_____
factor the expression 10x+40
Final answer:
To factor the expression 10x + 40, we can factor out the greatest common factor (GCF) of 10 from both terms, resulting in 10(x + 4).
Explanation:
To factor the expression 10x + 40, we can first find the common factor for both terms, which is 10. Factoring out 10, we get 10(x + 4). This expression represents the original 10x + 40. In simpler terms, we've taken out the common factor of 10 from both terms, leaving us with 10 multiplied by the quantity (x + 4). This factored form is useful for simplifying expressions or solving equations. Essentially, factoring helps us break down a more complex expression into simpler parts, making it easier to work with and understand in various mathematical contexts.
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
Dustin is 11 years younger than elias. In two years, Dustin will be half as old as elias. How old is Dustin
Final answer:
Dustin is currently 9 years old.
Explanation:
The question is asking us to solve for Dustin's current age given a relationship between his age and Elias's. To solve the problem, we need to set up an equation where Dustin's current age is represented by D and Elias's current age is represented by E.
We are told that Dustin is 11 years younger than Elias, which gives us the first equation:
E = D + 11
In two years, Dustin will be half as old as Elias. We can represent this future scenario with another equation:
D + 2 = (E + 2) / 2
To find Dustin's age, we will solve these two equations simultaneously. By substituting the expression for E from the first equation into the second equation, we get:
D + 2 = (D + 11 + 2) / 2
The equation simplifies to:
D + 2 = (D + 13) / 2
Now, we simplify and solve for D:
Multiply both sides of the equation by 2 to eliminate the fraction: 2(D + 2) = D + 13Distribute and simplify: 2D + 4 = D + 13Subtract D from both sides: D + 4 = 13Finally, subtract 4 from both sides to find D: D = 9Therefore, Dustin is currently 9 years old.
Ambrose has an indifference curve with equation x2= 20 − 4 x 1/21. when ambrose is consuming the bundle (4, 16), his marginal rate of substitution is 25/4.
An indifference curve is used in economics to show different combinations of goods that provide equal satisfaction to a consumer. Ambrose's indifference curve equation and marginal rate of substitution are given, representing his willingness to trade one good for another while holding utility constant.
Explanation:An indifference curve is a graphical representation used in economics to show the different combinations of two goods that provide equal satisfaction or utility to a consumer. In this case, Ambrose has an indifference curve with the equation x2 = 20 - 4x1/21. To find his marginal rate of substitution (MRS), we need to calculate the slope of the indifference curve at the point (4, 16). The MRS is given as 25/4, which means that Ambrose is willing to give up 25/4 units of x1 in exchange for 1 unit of x2, while keeping his utility constant.
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:
PLATO
10x-5y=25 solve for y
Create three different drawings showing a number of rectangles and circles in which the ratio of rectangles to circles is 3:1
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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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.
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.
Which of the following is a counterexample to "the sum of two numbers is always greater than either of the numbers"?
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.
There are 1,525 pages in a book. Julia and Kim round the number of pages to the nearest hundred. Julia says it is one thousand, five hundred. Kim says it is 15 hundreds. Who is correct? Explain your thinking.
Answer:
They are both correct.
Step-by-step explanation:
SInce they both are saying the same amount of pages just in different ways, Kim is saying a thousand plus five hundred, that is 1500, and Kim says 15 hundred, which is basically 1500, so they are both rounding up the number to the nearest cent correctly just are expressing the number in different ways.
Jogging is one of the few sports that has been consistently increasing over the past few years. the number of people jogging (in millions) from the years 2000 to 2009 is given by the equation y equals x plus 26y=x+26, where x is the number of years after 2000.
y=-4x-7 in standard form
will mark brainiest.
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.
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
Can you find the sum [5.5+ (-2.3)] + (-5.5+2.3) without performing any additions?
Taylor ran 2 1/4 miles and walked 2 4/5 miles. How far did she run and walk
The distributive property combines_____________and _____________ to make multiplying whole numbers simpler.
How many hours between 8:30 am to 5:30 pm
There are 9 hours between 8:30 am to 5:30 pm
How many hours between 8:30 am to 5:30 pmFrom the question, we have the following parameters that can be used in our computation:
Initial time = 8:30 am
Final time = 5:30 pm
using the above as a guide, we have the following:
Number of hours = Final time - Initial time
substitute the known values in the above equation, so, we have the following representation
Number of hours = 5:30 pm - 8:30 am
Evaluate
Number of hours = 9 hours
Hence, there are 9 hours between 8:30 am to 5:30 pm
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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.
If n = 6, then the value of n 2 is 12.
true or false
Simplify the following.
estimating products of fractions how do you figure 3/8 × 15
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).