Craig decides to purchase a property that has been valued at $475,000. He has $80,000 available as a deposit and will require a mortgage for the remaining amount. The bank offers him a 25 year mortgage at 2% interest. Calculate the total interest he will pay over the life of the loan, assuming he makes monthly payments. Give your answer in dollars to the nearest ten dollars. Do not include commas or the dollar sign in your answer.

THE REAL ANSWER IS $107, 270


First, we note that Craig requires a mortgage on $475,000−$80,000=$395,000. To calculate the monthly repayments we must apply the formula for P0 and solve for d, that is,
P0=d(1−(1+rk)−Nk)(rk).
We have P0=$395,000,r=0.02,k=12,N=25, so substituting in the numbers into the formula gives
$395,000=d(1−(1+0.0212)−25⋅12)(0.0212),
that is,
$395,000=235.9301d⟹d=$1,674.22.
Therefore the total interest payable is
I=$1,674.22×25×12−$395,000=$107,266
which is $107,270 to the nearest $1

Answer:

3(r + 5)(r - 5)

Step-by-step explanation:

Both 3 and 75 are divisible by 3, so we take out a 3.

3(r^2 - 25)

Next, we can factor r^2 - 25. It's a difference of squares.

3(r + 5)(r - 5)

Brainliest, please :)

The measure of the missing length from the given diagram is 25

According to the theorem, the altitude on the hypotenuse is equal to the geometric mean of line segments formed by altitude on the hypotenuse.

According to the given diagram, the expression below will be used to determine the value of x

x/60 = 60/144

Cross multiply yo have:

144x = 60 * 60

Simplify the result to have

144x = 3600

Divide both sides by 144

144x/144 = 3600/144
x = 3600/144

x = 25

Hence the measure of the missing length from the given diagram is 25

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Answer:

3 [tex]\frac{3}{4}[/tex] inches

Answer: I'm pretty sure it's 3 5/8, it's the S that's blocking the view but it gotta be 3 5/8.

Step-by-step explanation: PLS MAKE ME BRAINLIST

The period of this Ferris wheel can be calculated as 30 seconds. The amplitude is 25

a. We have 60 seconds in a minute

In a minute it makes 2 rotations. The period = 60 secs / 2 rotations

= 30 seconds

b. We have h = 25 - 25cos [tex]\frac{25}{30} t[/tex]

25 - 25cos[tex]\frac{25}{15} t[/tex]

We would have the table in the attachment

d. Amplitude

= max - min / 2

= 50 - 0 / 2

= 25

The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).

Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.

From the given information,

Let n=101 represents the size of the sample.

Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.

Let s= 3.2 represents the standard deviation of the sample.

Degrees of freedom:

df = n-1

df= 101-1

df= 100

The critical value of t at 0.2 level of significance with 100 degrees of freedom is,

[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]

The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:

[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]

Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).

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The true statements are:

B. N⊂R

C. S⊂N

D. ∅⊂N

F. {10.11.12,...}⊆S

Note that:

Following the points highlighted above, the true statements in the given options re:

B. N⊂R

C. S⊂N

D. ∅⊂N

F. {10.11.12,...}⊆S

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Answer:

The volume is

[tex]339.4 {yd}^{3} [/tex]

Step-by-step explanation:

The solution is in the image

Answer:

D

Step-by-step explanation:

It pass the vertical line test.

Hope this helps <3

As per the given graph, the graph fails the vertical line test. The correct option is B.

A graph is a visual representation of data that uses lines, bars, or other symbols to show how different values are related to each other.

Graphs are often used to display information in a way that is easy to understand and interpret.

The vertical line test is a way to determine whether a given graph represents a function.

According to this test, if any vertical line intersects the graph at more than one point, then the graph does not represent a function.

In the given graph, we can see that there are some vertical lines that intersect the graph at more than one point, such as the vertical line passing through x = 2.

Therefore, the graph does not pass the vertical line test and does not represent a function.

Thus, the correct answer is B.

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Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.

Antes de comenzar la resolución de este problema, asumimos que la base de calificación del curso de nivelación matemática es 100 y que la nota mínima para pasar es 70. Por otra parte, sabemos que la nota obtenida por Karina es divisible por 7 y que es el producto de aquel número primo y un polinomio formado por una relación de tres números primos, la cual es simplificada a continuación:

p (a, b, c) = a · (a + b - c) + b· (a + b - c) + c · (a + b - c)

p (a, b, c) = a² + a · b - a · c + a · b + b² - b · c + a · c - b · c - c²

p (a, b, c) = a² + 2 · a · b + b² - c²

p (a, b, c) = (a + b)² - c²

p (a, b, c) = (a + b + c) · (a + b - c)

Si asumimos que Karina obtuvo 84, entonces se tiene que 84 = 7 × 12 y 12 = 2 × 6. Tanto el dos como el seis son múltiplos de dos, entonces asumimos a = b = c y encontramos que:

n (2, 2, 2) = 7 · (2 + 2 + 2) · (2 + 2 - 2)

n (2, 2, 2) = 7 · 6 · 2

n (2, 2, 2) = 84

En síntesis, Karina obtuvo una nota final de 84 de 100 puntos en su curso de nivelación matemática.

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Answer:

y-intercept: (0,3)

Step-by-step explanation:

To find the y-intercept, we set x to equal 0, giving the equation:

-3(0)+2y = 6

0+2y = 6

y = 3

The temperature does not change after the percentage increase and decrease.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

Assume the initial temperature is 10.

Temperature after the 50% increase : (1 + 0.5) x 10 = 15

Temperature after the 33 1/3% decrease : (1 - 0.333) x 15 = 10.00

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Answer:

  True

Step-by-step explanation:

Lines in three dimensions can be one of ...

Lines are coplanar when a plane can be defined that includes the entirety of both of them. In the attached image, lines m₁ and n intersect and both lie in the gray plane. They are coplanar.

Lines m and m₁ are parallel, and both are contained in the turquoise plane. They are coplanar. A plane can always be drawn that will contain a pair of parallel lines. That is, any two parallel lines must be coplanar.

The lines m and n in the figure are skew, non-intersecting and non-parallel. They cannot be contained in a single plane.

__

Additional comment

Three or more parallel lines may not be coplanar. They will only definitely be coplanar when considered in pairs.

There are 180 numbers which are three-digit multiples of 5.

According to the statement

we have to find the three digit numbers which are multiples of 5.

we know that three digit numbers are start from 100 to 999 and in 1 line of counting means 100 to 110 there are 2 numbers are multiples of 5.

Here we use Multiplication method to find the number of digit which are a multiple of 5.

It means there are two numbers which are multiples of 5 in the one line of counting and there are 90 lines of  counting from 100 to 999.

So, it means the answer will become

2*90 = 180.

So, There are 180 numbers which are three-digit multiples of 5.

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Option b) is correct

In statistics, a histogram is a graphical representation of the distribution of data. A histogram is represented by a set of rectangles, adjacent to each other, where each column represents a certain type of data. Statistics is a stream of mathematics that is used in various fields. When figures are repeated in statistical data, this repetition is known as frequency and can be written in the form of a table, called a frequency distribution. Frequency distributions can be displayed graphically using different types of graphs and one of them is a histogram.

A histogram chart is used under certain conditions. They are:

Data should be numeric.

A histogram is used to check the shape of the data distribution.

It is used to check if the process changes from one period to another.

It is used to determine whether the output differs when it involves two or more processes.

It is used to analyze whether the given process meets the customer's requirements.

The data 1,2,12,14,15,16,18 is given

We need to find the histogram which best fits to the given data

Total number that falls between 0-9 is 2

Total Number that falls between 10-19 is 5

Total Number that falls between 20-29 is 1

Total Number that falls between 30-39 is 5

Total Number that falls between 40-49 is 3

Total Number that falls between 50-59 is 1

Hence the histogram is obtained

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Answer:

3:4    9:12

Step-by-step explanation:

Rewrite the ratios as fractions. 3:4 becomes 3/4, and 9:12 becomes 9/12, which simplifies to 3:4. Therefore A is a true proportion.

The expression matched with each scenario is;

Scenario 1: 0.82x

Scenario 2: 1.18x

Scenario 3: 7/10x

Scenario 4: 13/10x

The price of a game that’s been discounted

18% off its list price (x)

Total price = x

Discount = 18%x = 0.18x

New price = x - 0.18x

= 0.82x

The price of a toy that sells for 18% more

than the amount (x) needed to build the toy

Original price = x

Percentage increase = 18%x = 0.18x

New price = x + 0.18x

= 1.18x

The volume of water remaining in a tank after 3/10 of its original volume (x) is drained out

Original volume = x

Volume drained = 3/10x

New volume = x - 3/10x

= 7/10x

The total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)

Original stock = x

New stock = 3/10x

Total stock = x + 3/10x

= 13/10x

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Using the z-distribution, the observed test statistic is given as follows:

z = 3.69.

At the null hypothesis, it is tested if older students have the same mean as the general population, that is:

[tex]H_0: \mu = 115[/tex]

At the alternative hypothesis, it is tested if they have a greater mean, that is:

[tex]H_0: \mu > 115[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}[/tex]

z = 3.69.

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Answer:

Step-by-step explanation:

the legs

Step-by-step explanation:

T = 2×pi × sqrt(L/9.8)

now we know the time the swing should take for a complete back and forth cycle : 3 4 seconds.

the only unknown variable is now L (the length of the rope) :

3.4 = 2×pi × sqrt(L/9.8)

3.4/(2pi) = sqrt(L/9.8)

(3.4/(2pi))² = L/9.8

3.4²/(4pi²) = L/9.8

11.56/(4pi²) = L/9.8

2.89/pi² = L/9.8

9.8 × 2.89/pi² = L = 2.869618563... m ≈ 2.9 m

The value of  f –1(13) is 4

The table of values is given as:

x –4 0 2 5 9 13

f (x) –11 1 7 16 28 40

A linear function is represented as:

y = mx + b

Where b represents the y-intercept and m represents the slope

From the graph, when x = 0, y = 1.

This means that b = 1

So, we have

y = mx + 1

Also from the graph, when x = 2, y = 7.

So, we have:

7 = 2m + 1

Subtract 1 from both sides

7 - 1 = 2m + 1 - 1

Evaluate the difference

6 = 2m

Rewrite the above equation as:

2m = 6

Divide both sides of the equation by 2

m = 3

Substitute m = 3 in y = mx + 1

y = 3x + 1

The notation  f –1(13) implies that y = 13

So, we have

13 = 3x + 1

Subtract by 1

3x = 12

Divide by 3

x = 4

Hence, the value of  f –1(13) is 4

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When the number of hours decreases, the number of miles increases.

Average speed is the total distance travelled per time.

Average speed = total distance / total time

There is an inverse relationship between the distance travelled and the time travelled. If time increases, the distance travelled decreases.

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Answer:

48 Square feet

Step-by-step explanation:

A=((a+b)/2)*h,

((6.3+9.7)/2)*6=48ft^2

Using the normal distribution, we have that:

a) The probability of a student scoring less than 19 is 0.2709 = 27.09%.

b) The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.

c) The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.

d) The correct option is: B. The event in part (c) is unusual because its probability is less than 0.05.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 22.4, \sigma = 5.1[/tex]

Item a:

The probability is the p-value of Z when X = 19, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{19 - 22.4}{5.1}[/tex]

Z = -0.67.

Z = -0.67 has a p-value of 0.2709.

The probability of a student scoring less than 19 is 0.2709 = 27.09%.

Item b:

The probability is the p-value of Z when X = 27.1 subtracted by the p-value of Z when X = 17.7, hence:

X = 27.1:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{27.1 - 22.4}{5.1}[/tex]

Z = 0.92.

Z = 0.92 has a p-value of 0.8212.

X = 17.7:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{17.7 - 22.4}{5.1}[/tex]

Z = -0.92.

Z = -0.92 has a p-value of 0.1788.

0.8212 - 0.1788 = 0.6424.

The probability of a student scoring between 17.7 and 27.1 is 0.6424 = 64.24%.

Item c:

The probability is one subtracted by the p-value of Z when X = 33.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{33.1 - 22.4}{5.1}[/tex]

Z = 2.1.

Z = 2.1 has a p-value of 0.9821.

1 - 0.9821 = 0.0179.

The probability of a student scoring more than 33.1 is 0.0179 = 1.79%.

Item d:

Probabilities less than 0.05 are unusual, hence the correct option is:

B. The event in part (c) is unusual because its probability is less than 0.05.

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Answer:

3.42

Step-by-step explanation:

The career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.

Data analysis skills are known as technical skills used by a data analyst to  report insights and analyze data.

Some data analysis skills include;

A career that requires data analysis skills is a data scientists

A data scientist is one that computes and analyzes large amounts of data from different sources and makes useful interpretations from it.

The skills such career needs include statistics, calculus, probability, programming, excel, visualization, database management, and machine earning.

There is also need for a high level of accuracy when solving problems.

Thus, the career that requires data analysis skills is a data scientist because the skills helps in computing and analyzing large amounts of data from several sources.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What does \boxed{median} mean in math?}}[/tex]

[tex]\boxed{\text{Median}}\rightarrow\textsf{ is the number in the middle.}[/tex]

[tex]\huge\textbf{How do you find the \boxed{median}?}[/tex]

[tex]\text{You can found it by putting the numbers from \bf least to greatest.}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\text{Find the median for the scores 91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95,}\\\text{72, 75}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\text{91, 69, 71, 82, 71, 95, 87, 74, 71, 89, 89, 95, 72, 75}[/tex]

[tex]\huge\textbf{Rearrange the problems to:}[/tex]

[tex]\text{69,71,71,71,72,74,75,82,87, 89,89,91,95,95}[/tex]

[tex]\huge\textbf{The expression:}[/tex]

[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{\dfrac{75 + 82}{2} = median}[/tex]

[tex]\mathsf{\dfrac{157}{2} = median}[/tex]

[tex]\mathsf{257\div2 = median}[/tex]

[tex]\mathsf{78.5 = median}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{78.5}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Th measure of arc AB will be 60 degrees

The figure shown shows a circle with lines AC and BD intersecting the circle at the point E

From the figure given the measure of the arc AB is congruent to the arc CD.Given that the measure of arc CD is 60 degrees, hence the measure of arc AB will also be 60 degrees

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Answer:

A

Step-by-step explanation:

Substitute a + 2 for x:

f(a + 2) = 3 [ (a + 2) + 5 ]  + 4 / (a + 2)

            = 3 [ a + 7 ] + 4 / (a + 2)

Answer:

A.

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

solution

Here

P=8a=8·7=56

Answer:

56 units

Step-by-step explanation:

the perimeter of a rectangular octagon  with sides of length a

is equal to:  8 × a

Then

the perimeter of a regular octagon with a side length of 7 units

is equal to:  8 × 7 = 56 units