Using it's formula, it is found that the monthly payments for the loan of the apartment is of $7,260.50.
What is the monthly payment formula?It is given by:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
In which:
P is the initial amount.r is the interest rate.n is the number of payments.In this problem, the parameters are given as follows:
P = 500000, r = 0.123, n = 12 x 10 = 120.
Hence:
r/12 = 0.123/12 = 0.01025.
Then, the monthly payments will be of:
\(A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}\)
\(A = 500000\frac{0.01025(1+0.01025)^{120}}{(1+0.01025)^{120} - 1}\)
A = 7260.50.
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6x + y = 8
y= -6x + 8
Answer:
y = -6x + 8
Step-by-step explanation:
\begin{bmatrix}6x+y=8\\ y=-6x+8\end{bmatrix}
I don't know why it came out like this
Write this statement in your own words: ∃x ∈ ℕ, y ∈ ℤ|x² = y² Rewrite this using the appropriate mathematical notation: Even numbers are in the set of integers.
Answer:
See below.
Step-by-step explanation:
1)
So we have:
\(\exists x\in\mathbb{N},y\in\mathbb{Z}|x^2=y^2\)
This can be interpreted as:
"There exists a natural number x and an integer y such that x² is equal to y²."
2)
So we want even numbers are in the set of integers.
\(\{2n:n\in\mathbb{Z}\}\in\mathbb{Z}\)
This is interpreted as:
"The set of even numbers (2n such that n is an integer) is in the set of integers"
Use the values 2.120 kg and 2.12 kg. Write a comparison of the weights using < > or =.
"ω" Hurry please
Answer:
2.120 kg= 2.12 kg.
Step-by-step explanation:
As you can clearly tell, 2.120 is equal to 2.12, because the 0 to the right of all the numbers and the period doesn't add or substract anything from the number.
Therefore, 2.120 kg= 2.12 kg.
Find the midpoint of A and B where A has the coordinates (2,7) and B has coordinates (6,3)
Answer:
(4,5)
Step-by-step explanation:
Find the missing side or angle round to the nearest tenth b=15 a=30 c=29 A=[?]°
Answer: 79
Step-by-step explanation:
i just did it on acellus and its right
Five subtracted from a number equals 10. Find the number.
Answer:the number is 15
if i am correct give me brainliest
Step-by-step explanation:because 5-15=10 the number is 15
3.4( x + 7) - 2.1 = 35.5
Step-by-step explanation:
This is an equation, where we need to find the value of x.
To solve this equation, we can first use the distributive property to expand 3.4(x + 7) which gives 3.4x + 3.4 * 7 = 3.4x + 23.8
Now we have the equation:
3.4x + 23.8 - 2.1 = 35.5
Next, we can add 2.1 to both sides of the equation:
3.4x + 23.8 = 37.6
Then, we can subtract 23.8 from both sides of the equation:
3.4x = 13.8
Finally, we can divide both sides of the equation by 3.4 to find the value of x:
x = 4
Therefore, the value of x that solves the equation is 4.
in an epidemiological statistics study of the varicella vaccine, 338 children out of 450 received the vaccine and reported no incidence of varicella infection. use excel to find the proportion that separates the bottom 10% from the top 90% sample proportions in the sampling distribution of sample proportions of size 50. round your answer to three decimal places.
To find the proportion separating the bottom 10% from the top 90% in the sampling distribution of sample proportions, we will first calculate the population proportion and standard error, and then use Excel to find the corresponding z-score and proportion.
1. Calculate the population proportion (p): p = 338/450 = 0.7511
2. Calculate the standard error (SE): SE = sqrt[(p * (1-p)) / n] = sqrt[(0.7511 * (1-0.7511)) / 50] = 0.0654
3. Find the z-score corresponding to the bottom 10%: In Excel, use the formula =NORM.S.INV(0.10) which will give a z-score of -1.2816.
4. Calculate the sample proportion: Sample proportion = p + (z-score * SE) = 0.7511 + (-1.2816 * 0.0654) = 0.6685
Therefore, the proportion that separates the bottom 10% from the top 90% sample proportions in the sampling distribution of sample proportions of size 50 is approximately 0.668 (rounded to three decimal places).
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solve equation of
5/2x=25/4
Answer:
x = 5/2
Step-by-step explanation:
Solve for x:
(5 x)/2 = 25/4
Hint: | Multiply both sides by a constant to simplify the equation.
Multiply both sides of (5 x)/2 = 25/4 by 2/5:
(2×5 x)/(5×2) = 2/5×25/4
Hint: | Express 2/5×5/2 as a single fraction.
2/5×5/2 = (2×5)/(5×2):
(2×5)/(5×2) x = 2/5×25/4
Hint: | Express 2/5×25/4 as a single fraction.
2/5×25/4 = (2×25)/(5×4):
(2×5 x)/(5×2) = (2×25)/(5×4)
Hint: | Cancel common terms in the numerator and denominator of (2×5 x)/(5×2).
(2×5 x)/(5×2) = (5×2)/(5×2)×x = x:
x = (2×25)/(5×4)
Hint: | In (2×25)/(5×4), divide 25 in the numerator by 5 in the denominator.
25/5 = (5×5)/5 = 5:
x = (2×5)/4
Hint: | In (2×5)/4, divide 4 in the denominator by 2 in the numerator.
2/4 = 2/(2×2) = 1/2:
Answer: x = 5/2
a function is in the form g(x)= ax2 + d. if a is greater than 1 and d is positive, which could be the graph of g(x) ?
hello
to answer precisely, i have to see the graphs in the question but overall, the answer should look like something like the graph in the attached file
Need help
Pleaseeeee
Answer:
164 m^2
Step-by-step explanation:
You can think of the shaded area in different ways. One of the ways is the entire outer colored rectangle minus the area of the small white rectangle inside.
The large colored rectangle is 12 m by 15 m.
The inner rectangle is 8 m tall. The width is 12 m - 5 m - 5 m = 2 m
A = 12 m * 15 m - 2 m * 8 m
A = 180 m^2 - 16 m^2
A = 164 m^2
Please help me with this.
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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Zachary recorded the grade-level and instrument of everyone in the middle school
School of Rock below.
Seventh Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
7
14
15
9
Eighth Grade Students
Instrument # of Students
Guitar
Bass
Drums
Keyboard
2
15
2
11
Based on these results, express the probability that an eighth grader chosen at
random will play the drums as a percent to the nearest whole number.
Percent to the nearest whole number = 7%
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Probability = (Number of possible outcomes)/(Total number of outcomes)
Total number of outcomes = 2 + 15 + 2 + 11 = 30
Number of possible outcomes = 2
Probability = 2/30 = 1/15 = 0.0666
Percent to the nearest whole number = 0.0666 *100 = 7%
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Answer:7
Step-by-step explanation:
Solve the following inequality:
Answer:
\(r \geqslant - 16\)
Step-by-step explanation:
\( \frac{ - 10 + r}{2} \geqslant - 13\)
multiply both sides by 2:
\( - 10 + r \geqslant - 26\)
add 10 on both sides:
\(r \geqslant - 16\)
Answer:
\(r \ge -16\)
Step-by-step explanation:
To solve any equation/inequality:
1. get the variable to show up exactly once
2. isolate it
\(\frac{-10+r}{2} \ge -13\)
Multiply both sides by 2 and simplify (note that we're multiplying by a positive, not a negative, so the direction of the inequality stays the same, whereas multiplying or dividing by a negative would have changed the direction of the inequality)
\(\frac{-10+r}{2} *2 \ge -13 *2\)
\(-10+r \ge -26\)
Add 10 to both sides, and simplify
\((-10+r)+10 \ge (-26)+10\)
\(r \ge -16\)
Twelve cards are numbered from 1 to 12 and placed in a box. One card is selected at random and not replaced. Another is randomly selected. What is the probability of selecting two even numbers?
In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:
In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).
The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22
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Triangle ABC with vertices at A(4, 3), B(3, −2), C(−3, 1) is dilated using a scale factor of 1.5 to create triangle A′B′C′. Determine the vertex of point A′.
The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).
1. Start by calculating the distance between the vertices of the original triangle ABC:
- Distance between A(4, 3) and B(3, -2):
Δx = 3 - 4 = -1
Δy = -2 - 3 = -5
Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26
- Distance between B(3, -2) and C(-3, 1):
Δx = -3 - 3 = -6
Δy = 1 - (-2) = 3
Distance = √((-6)² + 3²) = √45 = 3√5
- Distance between C(-3, 1) and A(4, 3):
Δx = 4 - (-3) = 7
Δy = 3 - 1 = 2
Distance = √(7² + 2²) = √53
2. Apply the scale factor of 1.5 to the distances calculated above:
- Distance between A' and B' = 1.5 * √26
- Distance between B' and C' = 1.5 * 3√5
- Distance between C' and A' = 1.5 * √53
3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):
- A' is located Δx units horizontally and Δy units vertically from A.
- Δx = 1.5 * (-1) = -1.5
- Δy = 1.5 * (-5) = -7.5
- Coordinates of A':
x-coordinate: 4 + (-1.5) = 2.5
y-coordinate: 3 + (-7.5) = -4.5
4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).
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whats is the only solution of 2x2+8x2-16?
Answer:
4
Step-by-step explanation:
please help. I don’t get this one
Answer:
I guess it's (-3,-2)?(-3,a)
1. f(x) = 3x – 2; f(4)??
Answer:
the answer is 5
Step-by-step explanation:
f(4) = 3(4) -2
7 - 2 = 5
Mano you new wom a) Divide 70,756 by 19. b) Subtract 940 from your answer to part a).
The solution of the expression is,
a) 3,724
b) 2,784
We have to given that,
a) Divide 70,756 by 19.
b) Subtract 940 from your answer to part a).
Now, We can simplify as,
a) Divide 70,756 by 19.
⇒ 70,756 ÷ 19
⇒ 3,724
And, Subtract 940 from your answer to part a). that is, 3724
⇒ 3724 - 940
⇒ 2,784
Therefore, The solution of the expression is,
a) 3,724
b) 2,784
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one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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Solve the quadratic equation x2 + 2x – 20 = 0 by completing the square.
Answer:
x^2 + 2x - 20 = 0
x^2 + 2x - 20 + 20 = 0 + 20 ( add 20 to both sides)
x^2 + 2x = 20
x^2 + 2x + 1^2 = 20 + 1^2 ( add 1^2 to both sides)
( x + 1 )^2 = 21
x = \(\sqrt{21}-1\)
x = \(-\sqrt{21}-1\)
Answer:
A) x = –1 ± square root 21
is the answer:)
PLEASE HELP SIMPLIFY 4(m + ( -2) + 15
Answer:
\( \sf \large \: 4m+52\)
Step-by-step explanation:
4(m−2+15)
=(4)(m+−2+15)
=(4)(m)+(4)(−2)+(4)(15)
=4m−8+60
=4m+52
Answer:
4m+52
Step-by-step explanation:
3
Multiple Choice Find the measure of 21.
A 40°
40°
B 70°
C 80°
D 140°
E Cannot be determined
A is the correct answer
O B is the correct answer
O C is the correct answer
O Dis the correct answer
E is the correct answer
Answer:
Dont understands the lay out of this question.
Step-by-step explanation:
Please Explain in details.
Q7 PLEASE HELP ME !!!!!!!!!!!!!!!!!!!
The outcomes that are contained in the events are
X = 3 and 10 ⇒ P(X) = 1/5Not X =1, 2, 4, 5, 6, 7, 8 ⇒ P(Not X) = 4/51 - P(X) = 4/5 and 1 - P(X) is the same as P(Not X)
The outcomes contained in the eventsFrom the question, we have the following parameters that can be used in our computation:
X = gray colours
Given that
gray colours = 3 and 10
We have
X = 3 and 10
Not X =1, 2, 4, 5, 6, 7, 8
The probability is then calculated as
P(X) = 2/10 = 1/5
For P(Not X), we have
P(Not X) = 1 - 1/5 = 4/5
The equation of P(Not X)In (a), we have
P(Not X) = 1 - 1/5 = 4/5
This means that
P(Not X) = 1 - P(X)
So, the solution is
1 - P(X) = 4/5
The equivalent expressionUsing the above (a) and (b) as a guide, we have the following:
1 - P(X) is the same as P(Not X)
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A man buys 12 shirts at $24.69 each. There is a 6% sales tax. Find his bill.
Answer:
$26.48
Step-by-step explanation:
First you find out what 6 percent OF 24.99 dollars is,
OF stands for multiplication
so multiply 6 percent of 24.99
= 0.06 x 24.99
= $1.4994 (That's a point not a comma, so it's around 1 dollar)
Then once you have found the sales tax which we found up there, you add it to the total cost of the shirts. (If it was a discount you would subtract it because it's a discounted price which means it's less - just another tip :) )
Anyway so you add it to the price,
24.99 + 1.49
= $26.48
Hope this helps! :)
Model the data in the table with a linear equation
in slope-intercept form. Then tell what the slope and y-intercept
represent.
Write the linear equation in slope-intercept form.
y =
(Use integers or decimals for any numbers in the expression.)
Time Worked, Wages Earned
x (h)
1
3
6
9
y (S)
8.00
24.00
48.00
72.00
The data in the table can be modeled by this linear equation in slope-intercept form: y = 8x - 5.
The slope is 8, which means the wages earned increases at rate of 8 dollars per hour as the time increases.
The y-intercept is -5 and it represent the initial wages earned.
How to determine an equation of this line?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (24.00 - 8.00)/(3 - 1)
Slope (m) = 16.00/2
Slope (m) = 8
At data point (1, 3), a linear equation in slope-intercept form for this line can be calculated as follows:
y - y₁ = m(x - x₁)
y - 3 = 8(x - 1)
y = 8x - 8 + 3
y = 8x - 5
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If 15% of the customers total is $98,880, then the sum total equals what
The sum total by the given data is equals to $658,880.
We are given that;
Percent=15%
Amount= $98,880
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
To divide by a percentage, we can convert it to a decimal by moving the decimal point two places to the left. This gives us:
15% = 0.15
To divide by 0.15, we can multiply by its reciprocal, which is 1/0.15. This gives us:
$98,880 / 0.15 = $98,880 x 1/0.15
To multiply by 100, we can move the decimal point two places to the right. This gives us:
$98,880 x 1/0.15 x 100 = $658,880
Therefore, by the percentage the answer will be $658,880.
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Help please!
S = 180m
How many strides would a runner take during a 1-hour run (60 min)
The number of strides the runner will make during 1 hour run will be =
10,800.
How to calculate the total number of strides made by the runner in a hour?To calculate the distance or number of strides made by the runner in an
hour, the graph given above is considered as follows;
The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.
From the graph
20 minutes= 3600 strides
60 minutes = X strides
make X the subject of formula;
x= 3600×60/20
= 216000/20
= 10,800
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HELPPPPPPPPPPPPPP 100 POINTS IF YOU ANSWER ALL CORRECT
Answer:
\(\left[\begin{array}{ccc}y=x&y=\frac{2}{3}x&y=\frac{2}{3}x +1 \\-6&-4&-3\\-3&-2&-1\\0&0&1\\3&2&3\\6&4&5\end{array}\right]\)
Step-by-step explanation:
-6: y = -6
y = \(\frac{2}{3}\) (-6)
y = -4
y = \(\frac{2}{3}\) (-6) + 1
y = -4 + 1
y = -3
-3: y = -3
y = \(\frac{2}{3}\) (-3)
y = -2
y = \(\frac{2}{3}\) (-3) + 1
y = -2 + 1
y = -1
0: y = 0
y = \(\frac{2}{3}\) (0)
y = 0
y = \(\frac{2}{3}\) (0) + 1
y = 1
3: y = 3
y = \(\frac{2}{3}\) (3)
y = 2
y = \(\frac{2}{3}\) (3) + 1
y = 2 + 1
y = 3
6: y = 6
y = \(\frac{2}{3}\) (6)
y = 4
y = \(\frac{2}{3}\) (6) + 1
y = 4 + 1
y = 5