I need help answering this

Answer:

Step-by-step explanation:

Let's call the present value of the loan P. The payments of $1,550 in 1 year and $2,400 in 4 years can be expressed as an ordinary annuity with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = $1,550 / 2 = $775 (semi-annual payment)

n = (4 x 2) + 2 = 10 (number of semi-annual periods)

r = 0.045 / 2 = 0.0225 (semi-annual interest rate)

So,

PV = $775 * (1 - (1 + 0.0225)^-10) / 0.0225 = $8,100.40

Thus, the present value of the loan is P = $8,100.40.

Next, we can calculate the present value of the payment of $1,050 in 24 months and the balance in 30 months.

The payment of $1,050 in 24 months can be expressed as a single amount due in 24 months. The present value of this payment can be calculated as:

PV = $1,050 / (1 + 0.0225)^(24/2) = $1,000.54

So, the balance of the loan after this payment would be P - $1,000.54 = $8,099.86.

The balance in 30 months can be expressed as an ordinary annuity due with semi-annual payments. We can calculate the present value of this annuity using the formula:

PV = A * (1 - (1 + r)^-n) / r

where

A = ($8,099.86) / 6 = $1,349.98 (semi-annual payment)

n = 6 (number of semi-annual periods)

r = 0.0225 (semi-annual interest rate)

So,

PV = $1,349.98 * (1 - (1 + 0.0225)^-6) / 0.0225 = $7,999.86

Therefore, the payment required in 30 months for the rescheduled option to settle the loan is $1,349.98 per semi-annual period.

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Answer:

The correct answer is c. 750

Step-by-step explanation:

if the shops makes 25 dozen in two days that makes it 300 cupcakes In two days because 1 dozen is 12 cupcakes, so you will see that they make 50 dozen in 4 days which is 600 then you know he/she is going to make half of the 25 dozen on the 5th day so you will take half of 300 which is 150 and add it all together, so will get 300+300+150= 750 as your answer.

The values of sec a - cosec a/sec a+cosec a is 4/25.

The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

In a right-angled triangle,

Here we have

tan A = 21/29

As we know Tan θ = Opposite side/Adjacent side  

=> Opposite side = 21

=> Adjacent side = 29

In a right-angle triangle,

=> Hypotenuse² = Opposite side² + Adjacent side²  

=> Hypotenuse² = 21² +29²    

=> Hypotenuse² = 441 + 841    

=> Hypotenuse² = (35.8)²  

Cos a = Adjacent side /Hyopenuse = 29/ 35.8

Sin a = Opposite side/Hypotenuse = 21/35.8

The given expression can be solved as follows

=> [tex]\frac{seca - coseca}{seca+coseca } = \frac{ \frac{1}{cos a}-\frac{1}{sina} }{\frac{1}{cos a }+\frac{1}{sin a} }[/tex]      

=> [tex]\frac{ \frac{sin a - cosa}{cos a sn a} }{\frac{sin a + cos a}{cos a sin a} }[/tex]  

=> [tex]\frac{sin a - cosa}{cos a+ sin a}[/tex]  

=> [tex]\frac{ \frac{21}{35.8} - \frac{29}{35.6} }{\frac{29}{35.8} + \frac{21}{35.8} }[/tex]  

=> [tex]\frac{21- 29}{29+21}[/tex]  

=>  [tex]\frac{8}{50}[/tex]  

=>  [tex]\frac{4}{25}[/tex]  

Therefore,

The values of sec a - cosec a/sec a+cosec a is 4/25.

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Answer:

6-oz bottle is a better deal

Step-by-step explanation:

To find which is a better value, find the unit rates for both types of bottles

The bottle with the lower unit rate is the better deal

6-ounce bottle costs $4.19
Unit rate = 4.19/6 oz = $0.70 per oz

14-ounce bottle costs $10.89
Unit rate = 10.89/14 = $0.78 per oz

Hence the 6-oz bottle is a better deal

Answer:x^3+x^2-8x-32

Step-by-step explanation:

Using a system of equations, the number of each type of coffee that Julia and her husband should buy is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations can also be described as simultaneous equations.

The cost per pound of City Roast Columbian coffee = $6.50

The cost per pound of French Roast Columbian coffee = $8.20

The total quantity of the blend = 34 pounds

The cost per pound of the blend = $6.90

The total cost of the 34 pounds = $234.60 ($6.90 x 34)

Let the number of pounds of City Roast coffee = x

Let the number of pounds of French Roast coffee = y

x + y = 34 ... Equation 1

6.5x + 8.2y = 234.6 ... Equation 2

Multiply Equation 1 by 6.5:

6.5x + 6.5y = 221 ... Equation 3

Subtraction Equation 3 from Equation 2:

6.5x + 8.2y = 234.6

-

6.5x + 6.5y = 221

1.7y = 13.6

y = 8

Substitute, y = 8 in Equation 1:

x + y = 34

x = 34 - 8

x = 26

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Answer: w=9cm l=21cm

Step-by-step explanation

l=3w-6

l+l+w+w=60

3w-6+3w-6+w+w=60

8w-12=60

8w=60+12=72

w=72/8

w=9

l=3w-6

l=27-6

l=21

No, the marked price of $73.25 is not correct.

To calculate the sale price, we start by multiplying the original price by the discount percentage:

$95.00 * 0.25 = $23.75

This means that the original price of $95.00 should be reduced by $23.75 to find the sale price:

$95.00 - $23.75 = $71.25

Since the marked price is $73.25, this means that the store made a mistake and overpriced the shoes by $2.00. The correct sale price should have been $71.25.

Answer:

Step-by-step explanation:

The satellites Sputnik, Yeltsin, and Plekov are in a great circle, which is a circular path on the surface of a sphere that passes through the center of the sphere. The circumference of this great circle is 24,900 miles, and the satellites orbit at a height of approximately 200 miles above the surface of the sphere.

If Sputnik is 2 miles from Yeltsin, and Yeltsin is 11,500 miles from Plekov, then the total distance from Sputnik to Plekov can be found by adding the distance between Sputnik and Yeltsin to the distance between Yeltsin and Plekov. So, the total distance is 2 miles + 11,500 miles = 11,502 miles.

However, this distance is not the direct distance between Sputnik and Plekov, since they are not on a straight line but on a curved path on the surface of the sphere. To find the actual distance between Sputnik and Plekov, we can use the formula for the great-circle distance between two points on a sphere, which is:

d = acos(sin(lat1) * sin(lat2) + cos(lat1) * cos(lat2) * cos(long2 - long1)) * R

where lat1 and lat2 are the latitudes of the two points, long2 - long1 is the difference in longitudes of the two points, R is the radius of the sphere, and acos is the inverse cosine function.

Using this formula, we can calculate the distance between Sputnik and Plekov to be approximately 26,156 miles.

Answer:

Below

Step-by-step explanation:

Put '9' where  'n' is and compute

(9)^2 + 6(9) ÷ 3 =

81  +    54 ÷3  =

81  + 18 =   99

Answer:

240 cm, 320 cm, 400 cm

Step-by-step explanation:

The drawing length multiplied by the scale factor gives the real length.

3 cm × 80 = 240 cm

4 cm × 80 = 320 cm

5 cm × 80 = 400 cm

Answer: 240 cm, 320 cm, 400 cm

Answer:

Answer is in the attached photo

Step-by-step explanation:

The solution is in the attached photo, do take note for this question, Sine rule can be used to find both x and y as well instead of Pythagoras' Theorem.

x=18, y=9√3

There is a theorem with 30 degrees 30 degrees 90 degrees triangles, it is that the side opposite of 30 degrees angle is a, the hypotenuse is 2a, and the other leg opposite the 60 degree angle is a√3

So, since a=9, x=2a=18 and y=a√3=9√3

The probability of it happening will be 0.0000628

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

The number of outcomes based on the information will be:

= 2(36)[52C2)

= 72 × 52! / 50!2!

= 1/95472

Number of favorable outcome is:

= 4!/2!2!

= 6

The probability will be;

= 6 / 95472

= 0.0000628

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The equation to represent the total cost, y, for x months is y = 12x + 30.

From the given table, we can observe that the total cost increases by $12 for each additional month of usage.

This means that the rate of change, or the slope of the equation, is $12 per month.

We can represent this relationship using the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope (rate of change) is $12, and the y-intercept can be determined by examining the table. When x = 0 months, the total cost is $30. Therefore, the y-intercept is $30.

Putting it all together, the equation to represent the total cost, y, for x months is:

y = 12x + 30

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Answer:

The correct answer is D. y = 3.35x + 73.96.

Step-by-step explanation:

D. y = 3.35x + 73.96

Answer:

Percentage of adults = 80%

Number of adults = 2000

Step-by-step explanation:

Percentage of men = 2/5 x 100 = 40%

Percentage of women = 2/5 x 100 = 40%

Percentage of adults = 40+ 40= 80%

If there are 2500 people, then number of adults
= 2500 x 80%

= 2500 x 80/100

= 2000 adults

The set builder notation is A = { 9x | x ∈ N } which is a set of all x’s containing multiples of 9

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set be represented as A

Now , the value of A is

A = { 9 , 18 , 27 , 36 , ... }

The set A contains all the positive multiples of 9

So , let x be the set of natural numbers and the value of A is

A =  { 9x | x ∈ N } , and

A = set of all x’s containing multiples of 9

Hence , the set builder notation is { 9x | x ∈ N }

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16 sample points (possible outcomes as to the classifications) exist.

What is the combination?

Combinations are ways to choose elements from a collection in mathematics where the order of the selection is irrelevant. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

Here, we have

Given: An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices.

There are 4 possible classifications for the president (freshman, sophomore, junior, senior) and 4 for the vice president.

A total of (4)(4) = 16 sample points.

Hence, 16 sample points (possible outcomes as to the classifications) exist.

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The sum of the first 8 terms is 13.5

From the question, we have the following parameters that can be used in our computation:

9, 3, 1, 1/3, ...

Using the above as a guide, we have the following:

First term, a = 9

Common ratio, r = 1/3

The sum of GP (of n terms) is calculated as

Sum = Sn = a(r^n - 1) / (r - 1)

substitute the known values in the above equation, so, we have the following representation

Sum = 9 * ((1/3)^8 - 1)/((1/3) - 1)

Evaluate

Sum = 13.5

Hence, the sum is 13.5

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Answer:

To find the coordinates of A′ and B′ after a dilation with a scale factor of 2 and with the center of dilation at the origin (0, 0), we need to apply the dilation formula:

(x', y') = (2 * (x - 0) + 0, 2 * (y - 0) + 0) = (2x, 2y)

For point A, the original coordinates are (-4, 1), so we substitute these values into the dilation formula:

(x', y') = (2 * (-4 - 0) + 0, 2 * (1 - 0) + 0) = (-8, 2)

So, after the dilation, the new coordinates of point A are (-8, 2).

For point B, the original coordinates are (-1, 3), so we substitute these values into the dilation formula:

(x', y') = (2 * (-1 - 0) + 0, 2 * (3 - 0) + 0) = (-2, 6)

So, after the dilation, the new coordinates of point B are (-2, 6).

Answer:

Step-by-step explanation:

Step 1: Understanding the Dilation

A dilation with a scale factor of 2 and a center of dilation at the origin is a transformation that enlarges or shrinks an object by a factor of 2, with the origin (0, 0) as the center of the dilation.

Step 2: Using the Formula

To find the coordinates of the dilated points, we use the formula:

(x', y') = (2 * x, 2 * y)

Where (x, y) are the original coordinates of the points, and (x', y') are the coordinates of the dilated points.

Step 3: Finding the Coordinates of A′

We are given that the original coordinates of point A are (-4, 1), so we substitute these values into the formula:

A′ = (2 * -4, 2 * 1) = (-8, 2)

Step 4: Finding the Coordinates of B′

We are given that the original coordinates of point B are (-1, 3), so we substitute these values into the formula:

B′ = (2 * -1, 2 * 3) = (-2, 6)

Step 5: Conclusion

So, after a dilation with a scale factor of 2 and a center of dilation at the origin, the new coordinates of A′ and B′ are (-8, 2) and (-2, 6) respectively.

Answer:

The answer is thirty (30)

The perimeter of the triangle is equal to 28.7 using the trigonometric ratio

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths. The basic trigonometric ratios includes;

sine, cosine and tangent.

tan60 = q/4 {opposite/adjacent}

q = 4 × tan60 {cross multiplication}

q = 6.9282

sin60 = q/r {opposite/hypotenuse}

sin60 = 6.9282/r

r = 6.9282/sin60 {cross multiplication}

r = 8

sin45 = q/s {opposite/hypotenuse}

sin45 = 6.9282/s

s = 6.9282/sin45 {cross multiplication}

s = 9.8

cos45 = p/s {adjacent/hypotenuse}

cos45 = p/9.8

p = 6.9282 {cross multiplication}

perimeter of the triangle = 4 + p + s + r

perimeter of the triangle = 4 + 6.9282 + 9.8 + 8

perimeter of the triangle = 28.7282

Therefore, the perimeter of the triangle is equal to 28.7 using the trigonometric ratio.

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The location of Kris' signature on the $601.73 check Elmo wrote to Kris and which Kris deposited into her checking account is on the back of the check. The correct option is option C.

C. Only on the back of the check

A checking account is an account opened at a financial institution into which deposits and withdrawals can be made by a customer. A checking account can also be referred to as a transaction account, a credit unions share draft account, demand deposit account or current account.

The amount of check Elmo wrote Kris = $601.73

The amount Kris deposited into her checking account = The check Elmo issued to her

The location to sign before depositing a check into a checking account is at the back of the check, including informing the cashier that the specified  check is to be deposited into the checking account.

The correct option is therefore option C.

C. Only on the back of the check

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[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]

Distance of the house from the base of the cliff is 282.27 m.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

From the figure attached,

AB = Height of the cliff = 60 m

Let the distance between the base of the cliff and the house 'C' = x m

If the angle of depression = 12°

Then angle of elevation of the top of the cliff from the house = 12°

Now from right triangle ABC,

tan12=60/x

x=60/tan 12

x=60/0.21256

x = 282.27 m

Therefore, distance of the house from the base of the cliff is 282.27 m.

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Using the a pair of adjacent angles, we will see that:

Z° = 137°

When we have an intersection between two lines, we know that any pair of adjacent angles (they share a side) are congruent angles, thus, their measures add up to 180°.

Then here we can write a linear equation for z.

z + 43 = 180

Solving that for z, we will get:

z = 180 - 43

z = 137

That is the measure of the angle.

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The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.

The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.

To find the probability of choosing a girl who prefers blue, we need to use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.

The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.

Putting these values in the formula, we get:

Probability = 15/50 = 0.3

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Complete Question;

70 preschoolers were asked whether they preferred blue or pink.

35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.

Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.

Answer:

0.0075

Step-by-step explanation:

The y-coordinate of point P is 16/3, which rounded to two decimal places is approximately 5.33.

First, we need to find the coordinates of point P. Since point P partitions the directed segment AB in the part-to-part ratio of 2:4, we can use the following formula to find its coordinates:

P = (4A + 2B) / 6

Substituting the coordinates of A and B, we get:

P = (4(5,7) + 2(1,-6)) / 6

P = (20,28) + (2,-12) / 6

P = (22,16) / 6

P = (11/3, 16/3)

y-value = 5.33

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The perimeter of the parallelogram is; 184

In geometry, the perimeter of a shape is defined as the total length of its boundary.

Now, from the given image, we don't know the vertical sides XW and YZ and we can find it from Pythagoras theorem;

XW = √(68² - 60²)

XW = 32

Thus, the perimeter of the parallelogram is;

Perimeter = 2(32 + 60)

= 2 * 92

= 184

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