Explanation:
Mr. Coffey bought a house for $195,000 with a 20% down payment.
A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.
He bought the bouse for $156,000.
5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.
He would pay $8,190 every 30 years. (if this was the interest rate.)
Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.
He would pay $2,047.50 every 30 years. (if this was the interest rate.)
There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years.
I don’t understand how to do this can’t oh help me please I’m so struggling
It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. The answer will be 4.4.
What is division mean?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
At a fundamental level, the process of counting how many times one number is included within another is referred to as the division of two natural numbers. This number of times need not be integer. For instance, if 20 apples are distributed equally among 4 persons, each person will get 5 apples.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
It is necessary to expand the natural numbers to rational numbers or real numbers in order for division to always result in one number rather than a quotient plus a remainder. In these expanded number systems, division operates in the opposite direction as multiplication, i.e., a = c / b implies that, if b is not zero, a b = c. This is a division by zero, which is not defined, if b = 0. In the case of the twenty-one apples, there would be no leftovers because each person would get five apples and a quarter of an apple.
Different algebraic structures, or ways of defining mathematical structure, use both modes of division. These are known as Euclidean domains and contain polynomial rings in one indeterminate space where a Euclidean division (with remainder) is defined (which define multiplication and addition over single-variabled formulas). Fields and division rings are those where a division (with a single result) by all nonzero elements is defined. The elements in a ring by which division is always feasible are known as the units; in the ring of integers, this would be 1 and 1. The quotient group is another way to apply division to algebraic structures; in this case, the outcome of "division" is a group rather than a number.
Just divide 3.96 by 0.9
[tex]\frac{3.96}{0.9}[/tex]= 4.4
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in thr figure,, PQ =PR, and PS & ST are medians. What QT and QR
QR = QS + SR
QS = y+1/2
QS= SR
SR= y+1/2
QR= y+1/2 +y+ 1/2 = 2y + 1
QT = TP
RP = 2 TP
RP = 10
10 = 2 TP
10/2= TP
5 = TP
TP= QT
QT= 5
Since y= 5
QR = 2y + 1 = 2 (5) + 1 = 10 + 1 = 11
Answers:
QT= 5
QR= 11
Find the number, if 0.7 of it is 42.
The number whose 0.7 is 42 is 5.715.
What do you mean by number?
In mathematics, a number serves as both a unit of measurement and a label. The first examples are the natural numbers 1, 2, 3, 4, and so forth. Language can express numbers by the use of number terms. Numerals are symbols that are used to symbolize specific numbers; for example, the number "5" can be symbolize as number five.
Let the required number be X
As given in the question 0.7 of X is 42,
We can write it as:
(0.7)X = 42
If a number make to change its side around the equal sign then if it is in divide on one side so it will become in multiplication on the other side.
So,
X = 4/0.7
X = 5.715 (approximately)
Therefore, The number whose 0.7 is 42 is 5.715
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The number of students in the tutoring center was recorded for 27 randomly selected times. The data is summarized in the frequency table below. What is the class width for this frequency distribution table
The class width for this frequency table is 5.
What is class width?The class width is described as the distance between the lower class of two consecutive classes.
How to calculate class width?One can calculate class width by finding the difference between the two consecutive lower classes.
In the figure above, the first two classes are described as
0-4
5-9
So, the lower classes of these intervals are 0,5
Thus the difference between them is 5
Therefore, the class width for this frequency distribution table is 5.
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M=W(1+rt) (solve the following formula for "t"
Given the following formula given in the exercise:
[tex]M=W\mleft(1+rt\mright)[/tex]You can solve for the variable "t" by following the steps shown below:
1. You must apply the Disrtributive proprerty on the right side of the equation:
[tex]\begin{gathered} M=(W)\mleft(1)+(W)(rt\mright) \\ M=W+Wrt \end{gathered}[/tex]2. Now you need to apply the Subtraction property of equality by subtracting "W" from both sides of the equation:
[tex]\begin{gathered} M-(W)=W+rtW-(W) \\ M-W=Wrt \end{gathered}[/tex]3. Finally, you can apply the Division property of equality by dividing both sides of the equation by "Wr":
[tex]\begin{gathered} \frac{M-W}{Wr}=\frac{Wrt}{Wr} \\ \\ t=\frac{M-W}{Wr} \end{gathered}[/tex]The answer is:
[tex]t=\frac{M-W}{Wr}[/tex][tex]a ^{2} - 3a + 2 = 0[/tex]put into standard form. identify a,b, and c
Answer:
a=1,b=-3,c=2
Explanation:
The standard form of a quadratic equation is given as:
[tex]ax^2+bx+c=0[/tex]Comparing with the equation:
[tex]a^2-3a+2=0[/tex]We observe that the equation is already in the standard form.
Furthermore:
[tex]a=1,b=-3,c=2[/tex]In places where there are crickets, the outdoor temperature can be predicted by the rate at which crickets chirp. One equation that models the relationship between chirps and outdoor temperature is , where c is the number of chirps per minute and f is the temperature in degrees Fahrenheit.
Suppose 110 chirps are heard in a minute. If it is 75°F outside, about how many chirps can we expect to hear in one minute? Do not include units (chirps) in your answer. Round your answer to the nearest whole number.
Answer:
The crickets do not chirp at all below 40 degrees and at 75 degrees they chirp about 161 times per minute.
Can you help me answer part A and part B?
Now, Now,We are given the following vectors:
[tex]P\left(5,4\right),Q\left(7,3\right),R\left(8,6\right),S\left(4,1\right)[/tex]We are asked to determine the following vector:
[tex]PQ+3RS[/tex]First, we will determine the vector PQ and RS. To determine PQ we use the following:
[tex]PQ=Q-P[/tex]This means we need to subtract "P" from "Q". We do that by subtracting each component of the points, like this:
[tex]PQ=\left(7,3\right)-\lparen5,4)=\left(7-5,3-4\right)[/tex]Solving the operations:
[tex]PQ=\left(2,-1\right)[/tex]Now, we use a similar procedure to determine RS:
[tex]RS=S-R[/tex]Substituting we get:
[tex]RS=\left(4,1\right)-\left(8,6\right)=\left(4-8,1-6\right)[/tex]Solving the operations:
[tex]RS=\left(-4,-5\right)[/tex]Now, we substitute the values in the vector we are looking for:
[tex]PQ+3RS=\left(2,-1\right)+3\left(-4,-5\right)[/tex]Now, we solve the product by multiplying both components of RS:
[tex]PQ+3RS=(2,-1)+(-12,-15)[/tex]Now, we solve the addition by adding each corresponding component:
[tex]PQ+3RS=(2-12,-1-15)[/tex]Solving the operations:
[tex]PQ+3RS=(-10,-16)[/tex]And thus we have determined the components.
Part B. We area asked to determine the magnitude of the vector. To do that we will use the following:
Given a vector of the form:
[tex]X=\left(x,y\right)[/tex]Its magnitude is:
[tex]\lvert X\rvert=\sqrt{x^2+y^2}[/tex]This means that the magnitude is the square root of the sum of the square of the components. Applying the formula we get:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{\left(-10\right)^2+\left(-16\right)^2}[/tex]Now, we solve the squares:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{100+256}[/tex]Solving the addition:
[tex]\lvert\begin{equation*}PQ+3RS\end{equation*}\rvert=\sqrt{356}[/tex]Now, we factor the term inside the radical as follows:
[tex]\lvert PQ+3RS\rvert=\sqrt{4\left(89\right)}[/tex]Now, we distribute the radical:
[tex]\lvert PQ+3RS\rvert=\sqrt{4}\sqrt{89}[/tex]Taking the left square root:
[tex]\lvert PQ+3RS\rvert=2\sqrt{89}[/tex]And thus we have determined the magnitude.
In isosceles △ABC where AC≅BC, altitiude CD is drawn. If AC= 17 and AB= 30. Determine the altitiude of the triangle.
By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.
Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.
Based on this, you know that:
[tex]\begin{gathered} AD=BD=\frac{AB}{2} \\ \\ AC=BC \end{gathered}[/tex]Knowing that:
[tex]\begin{gathered} AB=30 \\ AC=17 \end{gathered}[/tex]You get that:
[tex]\begin{gathered} AD=BD=\frac{30}{2}=15 \\ \\ AC=BC=17 \end{gathered}[/tex]The Pythagorean Theorem states that:
[tex]a^2=b^2+c^2[/tex]Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
So you can identify that, for this case:
[tex]\begin{gathered} a=17 \\ b=15 \\ c=CD \end{gathered}[/tex]Where "CD" is the altitude of the triangle.
Therefore, substituting values and solving for "CD", you get this result:
[tex]\begin{gathered} 17^2=15^2+CD^2 \\ \sqrt[]{17^2-15^2}=CD \\ CD=8 \end{gathered}[/tex]The answer is: Option (1)
Rotate this hexagon 180º.
(0, -8)
(3, -8)
(6,-5)
(6, 1)
(3, 2)
(0, 2)
After rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
Upon rotation of this hexagon by 180
The rule for a rotation by 180° about the origin is (x,y)→(−x,−y) .
After rotation, the co- ordinates change from
(0, -8) → (0, 8)
(3, -8) → (-3, 8)
(6,-5) → (-6, 5)
(6, 1) → (-6, -1)
(3, 2) → (-3, -2)
(0, 2) → (0, -2)
Therefore, after rotation the coordinates of the hexagon is (0, 8), (-3, 8), (-6, 5), (-6, -1), (-3, -2), (0, -2)
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Sun lei bought a computer for $1800. The total cost, including tax, came to $1890. What is the tax rate?
Given:
Cost of computer without tax $1800.
Total cost including tax is $1890
[tex]\text{Tax amount =1890-1800}[/tex][tex]\text{Tax amount = \$90}[/tex]Let the tax rate be x
[tex]90=1800\times\frac{x}{100}[/tex][tex]\frac{90}{18}=x[/tex][tex]x=5[/tex]Tax rate is 5%
write the ratio as a fraction in simplest form with whole numbers in the numerator and denominator 6.3 g to 3.6 g
the ratio 6.3 g to 3.6 g as a fraction is:
[tex]\frac{6.3}{3.6}=\frac{6.3}{3.6}\cdot\frac{10}{10}=\frac{63}{36}=\frac{7}{4}[/tex]A car travels 238 miles in 4 hours and 15 minutes. How many miles does it travel per
hour?
We can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
What are mathematical operations?An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value. The operation's arity is determined by the number of operands. The addition, subtraction, multiplication, division, exponentiation, and modulus operations are carried out by the arithmetic operators.So, the distance traveled in 1 hour:
Distance traveled in 4 hours and 15 minutes = 238 milesThen divide 238 by 4.15 as follows:
238 ÷ 4.1557.34Rounding off: 57 miles
Therefore, we can conclude that the distance traveled in 1 hour is 57 miles after doing some mathematical operations.
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three fourths of w + 5 is one half of w increased by 9
let's put the information given in a mathematical equation:
[tex]\frac{3}{4}w+5=\frac{1}{2}w+9[/tex]we pass all the terms thas has w in them to the left side and left the other terms in the right side:
[tex]undefined[/tex]Here is an ordered set of sample data.87 109 156 166 204210 279 416 500 534592 609 655 677 777837 873 998Identify the 5 number summary: (min, Q1, median, Q3, max).
Solution:
A boxplot is a standardized way of displaying the dataset based on a five-number summary: the minimum, the maximum, the median, the first quartile, and the third quartile.
The general representation for a box plot is given below;
Comparing this to the box plot given in the question, the following can be deduced;
[tex]\begin{gathered} \text{minimum, }\min =11 \\ lowerquartileQ_1=12 \\ \text{Median}=15 \\ \text{upper quartile, Q}_3=17 \\ \max imum,\text{ max=20} \end{gathered}[/tex]Therefore, the answer as arranged is;
[tex](11,12,15,17,20)[/tex]The interquartile range, IQR is given by;
[tex]\begin{gathered} Q_3-Q_1 \\ \text{where;} \\ Q_3=17 \\ Q_1=12 \\ \\ \text{IQR}=17-12 \\ \text{IQR}=5 \end{gathered}[/tex]Therefore, the interquartile range is 5.
Suppose Z follows the standard normal distribution. Calculate the following probability.
P(0.33 < Z < 1.50)
Answer:
ummm i don't know....
..,....
Residents in a city are charged for water usage every three months. The water bill is computed from a common fee, along with the amount of water the customers use. The last water bills for 40 neighborhood residents are displayed in the histogram below. A histogram titled Neighborhood Monthly water bill has monthly water bill (dollars) on the x-axis and frequency on the y-axis. 100 to 125, 1; 125 to 150, 2; 150 to 175, 5; 175 to 200, 10; 200 to 225, 13; 225 to 250, 8. Which interval shows the greatest change in water bills? $150–$175 $175–$200 $200–$225 $225–$250
$200-$225 interval shows the greatest change in water bills
What is Histogram?A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.
The interval which contains the median water bill is $200 - $225
The tabulated data is given in the attachment.
The median class = Cummulative frequency / 2
The median class = 40 / 2
The class interval which contains the 20th frequency.
This is the 200 - 225 class
The interval which contains the median water bill is $200 - $225
Hence $200-$225 interval shows the greatest change in water bills
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Answer:
C)$200–$225
Step-by-step explanation:
edge 2023
Use the equation below and the indicated value to find an ordered pair that is a solution.
y=2x-1 Let x = 4.
The ordered pair is 4.
The ordered pair is 4 is 7.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
Given that,
The equation is
y = 2x-1
Substitute the value of x =4
y = 2x-1
y = 2×4-1
y = 7
The value of y at x = 4 is 7.
Hence, the ordered pair of 4 is 7.
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The water company has a different monthly pricing plan for residential customers than for business customers. For each pricing plan, cost (in dollars) depends on water used (in hundreds of cubic feet, HCF), as shown below.
(a) For an HCF of 22, the residential plan costs $44 and the business plan costs $36.
So, the business plan costs $8 less.(b) $14, business plan.
The plans cost the same when the graphs intersect.After $14, the business plan graph is lower than the residential plan graph, meaning the business plan will cost less.Which fraction is equal to 0/03 ?
A. 3/100
B. 1/33
C. 1/11
D.1/3
Answer:
It depends on what the question is.
Step-by-step explanation:
Your question is unclear.
If the question is the fraction 0/03, then that equals 0, but that is not a choice.
If the question is 0.03, then the answer is 3/100.
If the question is 0.03030303... (repeating 03, then the answer is worked out below.
Let x = 0.030303...
100x = 3.0303030...
- x = 0.0303030...
---------------------------------
99x = 3
x = 3/99
x = 1/33
Sam bought 9 tickets all in the same row to a KC Royals game for himself and his
friends next week. His friends are Eric, Sarah, Renee, David, Julie, Derek, Kelsey and
Kyle.
(a) How many different ways can the friends be seated in the row?
(b) Sam has a crush on Sarah, so he wants to make sure his seat is next to hers. How
many ways are there to assign the seats now?
(c) How many ways are there to assign the seats if Sam wants to ensure that they
are all seated boy-girl-boy-girl?
Using the arrangements formula, the number of ways that they can be seated for each case is given as follows:
a) No restrictions: 362,880.
b) Sam next to Sarah: 80,640.
c) Boy-girl-boy-girl: 2,880.
What is the arrangements formula?The number of possible arrangements of a set containing n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
For item a, we consider that 9 people will be seated with no restrictions, hence the number of ways is given as follows:
9! = 362,880
For item b, there is the restriction that Sam has to be seated next to Sarah, hence:
There are 8 pairs of seats in which they can be seat, each in 2 ways(Sam-Sarah or Sarah-Sam).The other 7 people can be seated in 7! ways, as there are no restrictions for them.Hence the number of ways is:
2 x 8 x 7! = 80,640.
For item c, we can treat the boys and the girls places as independent, hence:
There are 5! ways for the boys to sit, as there are five boys in the group.There are 4! ways for the girls to sit, as there are four girls in the group.Hence the number of ways is:
5! x 4! = 2,880.
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Determine the open intervals on which the function is increasing, decreasing, or constant.(Enter your answers using interval notation. If an answer does not exist, enter DNE.)
Given:
[tex]f(x)=\sqrt{x^2-4}[/tex]To find:
The interval at which the function is increasing, decreasing and constant.
Explanation:
We know that,
For a function, y = F(x), if the value of y is increasing on increasing the value of x, then the function is known as an increasing function.
For a function, y = F(x), if the value of y is decreasing on increasing the value of x, then the function is known as a decreasing function.
According to the graph,
The function is increasing in the interval,
[tex][2,\infty)[/tex]Because, if x increases from 2, the value of y increases.
The function is decreasing in the interval,
[tex](-\infty,-2][/tex]Because, if x increases from negative infinity, the value of y decreases.
As we know, a constant function is a function whose output value is the same for every input value.
Here, the function is not constant at any of the intervals.
Final answer:
Increasing:
[tex][2,\infty)[/tex]Decreasing:
[tex](-\infty,-2][/tex]Constant: DNE.
Find the critical value (tα/2) for a 99% confidence interval if the sample size is 15. Round your answer to three decimal places.
tα/2 =
The critical value (tα/2) for a 99% confidence interval for the sample size 15 is 2.977 .
We have to find the critical value tα/2 for 99% confidence interval, we are given the sample size.
First we will find the alpha value to get the critical value.
=100%-99%
=1-0.99
=0.01
α=0.01
α/2=0.01/2
α/2=0.005
degrees of freedom(df)= n-1=15-1=14
We will use degrees of freedom and α/2 values to find the critical value that is tα/2.
By using the t table we get the critical value of tα/2=2.977.
Therefore, the critical value for 99% confidence interval with sample size 15 is 2.977.
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The hypotenuse of right triangle XYZ is 28 and m
Solution
For this case we can do the following:
m < X = 60
One angle in a right triangle needs to be 90º
So then we can find the measure of the other angle like this.
180 -90-60 = 30º
We can find the following identity:
[tex]\sin 60=\frac{y}{28}[/tex]And solving for thw leg opposite we got:
[tex]y=28\cdot\sin 60=24.25[/tex]
I can’t figure this out I need help. I’ve been stuck on it for about an hour and a half.
SOLUTION
From the question, we are told to distribute the multiplication across in
[tex](4v^4-6z^5).4z^4[/tex]This means we should expand.
This becomes
Shelley works in a dental office as an administrative assistant and uses a desktop computer for scheduling appointments. What type of keyboard is she MOST likely to use?
Mechanical keyboard
Virtual Keyboard
Tablet keyboard
laptop keyboard
Answer:
Mechanical Keyboard
The type of keyboard that Shelley is most likely to use is a mechanical keyboard. The correct option is a.
What is a mechanical keyboard?Mechanical keyboards offer a considerably more comfortable typing experience, as well as a plethora of customization options in terms of style and feel, and they're also more durable and easier to repair.
Mechanical keyboards often require only a half-press of a key to transmit a signal to your computer, allowing for faster and easier typing.
Here a mechanical keyboard will be used because she is an assistant and uses a desktop computer for scheduling appointments. She would not use tablets and laptops or virtual keyboards.
Therefore, the correct option is a. Mechanical keyboard.
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Converting Mixed to Improper
Write the mixed number as an
improper fraction. 8 2/9
8[tex]\frac{2}{9}[/tex] as improper fraction is [tex]\frac{74}{9}[/tex]
Define improper fraction.A fraction that has the numerator higher than or equal to the denominator is said to be improper. A mixed fraction is one that has both a correct fraction and a whole number portion, and whose value is consistently greater than 1. When the numerator is always higher than or equal to the denominator, the fraction is said to be inappropriate. 4/3, 7/3, 11/5, and other incorrect fractions are a few instances. In fact, using improper fractions in mathematics is simpler than using mixed fractions. However, mixed numbers are easier for individuals to understand in daily life. It is crucial that you understand how to change from one form to another.
Given,
Mixed Fraction
8[tex]\frac{2}{9}[/tex]
Improper fraction:
[tex]\frac{8(9) +2}{9}[/tex]
[tex]\frac{72 +2}{9}[/tex]
[tex]\frac{74}{9}[/tex]
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Safety standards require a pool to add 333 chlorine tablets to every 2,0002,0002, comma, 000 liters of water. Today, the lifeguards at Park Pool added 888 chlorine tablets to their pool's10,00010,00010, comma, 000 liters of water.How does Park Pool's chlorine compare to the safety standards?
SOLUTION
The standard quantity of water is 2000 liters
The quantity of water in the pool is 10,000
Since 3 chlorine is added to every 2000 liters of water then the number of chlorine added to 10000 liters of water is:
[tex]\begin{gathered} \frac{10000}{2000}\times3 \\ =5\times3 \\ =15 \end{gathered}[/tex]Since 8 tablets is added instead of 15 then:
The park pool has less chlorine than the safety standards require
Place a on the number line to illustrate that a+b=0
To make a+b= 0
Since b is positive ( to the right of zero), a must be positive and must be have the same distance from 0.
So:
CD is the mid segment of trapezoid WXYZ.-What is the value of X?-What is XY?-What is WZ?
The midsegment theorem states that the length of the midsegment is equal to half the length of the base. From the information given,
midsegment = CD = 22
base = XY = 4x + 1
By applying the midsegment theorem, we have
CD = 1/2XY
22 = 1/2(4x + 1)
By crossmultiplying, we have
22 * 2 = 4x + 1
44 = 4x + 1
4x = 44 - 1
4x = 43
x = 43/4
x = 10.75
Thus,
Substituting x = 10.75 into XY = 4x + 1, it becomes
XY = 4(10.75) + 1
XY = 43 + 1
XY = 44
Substituting x = 10.75 into WZ = x + 3, it becomes
WZ = 10.75 + 3
WZ = 13.75