The correct option is c. $300,000. In 2007, the FDIC’s insurance limit was $100,000 per person per bank. Kit had three separate $50,000 CDs at Bank R, a $60,000 checking account and a $140,000 money market account at Bank S, and an $80,000 savings account at Bank T.
How much of Kit’s money was FDIC insured?The amount of Kit’s money that was FDIC insured was c. $300,000.In 2007, the Federal Deposit Insurance Corporation (FDIC) insured deposit accounts up to $100,000 per person per bank, or up to $250,000 for certain retirement accounts.
This means that if the bank fails, the FDIC will provide insurance coverage up to the specified amount for the deposits.Based on the details given in the question, we need to calculate the amount of Kit’s money that was FDIC insured.Kit has the following accounts:
Three $50,000 CDs at Bank R.$60,000 checking account and a $140,000 money market account at Bank S.$80,000 savings account at Bank T.
So, the total amount of money that Kit has is:$50,000 + $50,000 + $50,000 + $60,000 + $140,000 + $80,000 = $430,000Therefore, the total amount of Kit’s money that was FDIC insured is:$100,000 (maximum amount insured per person per bank) × 3 banks = $300,000.So, the correct option is c. $300,000.
For more such questions on FDIC’s insurance
https://brainly.com/question/28920538
#SPJ8
Answer:
The answer is B) 280,000
Step-by-step explanation:
Can somebody help me? A Committee is to consist of two members, if there are seven men and five women available to serve on the committee and you need to choose 1 man and 1 woman ,how many different committee's can be formed?
There are 35 different committees that can be formed, each consisting of one man and one woman.
To form the committee consisting of one man and one woman, we need to choose one man from the available seven men and one woman from the available five women.
Number of choices for selecting one man = 7
Number of choices for selecting one woman = 5
To find the total number of different committees that can be formed, we multiply these numbers together:
Total number of committees = 7 × 5
Total number of committees = 35
Therefore, there are 35 different committees that can be formed, each consisting of one man and one woman.
To learn more on Combinations click:
https://brainly.com/question/19692242
#SPJ1
The sum and product of two linear functions are shown. Which statements can be used to describe the original
functions f(x) and g(x)? Select two options.
The statement "When added, the sum of the y-intercepts must be 1" and "f(x) could have a rate of change equal to 1 and g(x) could have a rate of change of 2" can be used to describe the original functions f(x) and g(x).
What is a function?Within mathematical study, we encounter various types of relations between objects – but none quite so distinctive as a function. These relations are essentially collections or sets composed solely from ordered pairs – pairings containing precisely two distinct elements each.
The defining trait for functions lies in how they operate with regards to these paired elements: specifically that every element comprising the domain – representing all potential inputs – correspond with absolute exclusivity to just one solitary member within the codomain – signifying all possible outputs.
Learn about function here https://brainly.com/question/11624077
#SPJ1
HELP WITH GEOMETRY PLEASE!!! URGENT!!!
The variables for this problem are given as follows:
a = 16, [tex]b = 16\sqrt{2}[/tex] , c = 16, d = 16.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are obtained according to the rules presented as follows:
Sine of angle = opposite side/hypotenuse.Cosine of angle = adjacent side/hypotenuse.Tangent of angle = opposite side/adjacent side = sine/cosine.For side lengths a and c, we have a right triangle with angles of 45º, hence using the 45-45-90 Triangle Rule, with the hypotenuse of [tex]16\sqrt{2}[/tex], the lengths a and c are given as follows:
a = c = 16.
The length a is also the geometric mean of the lengths c and d, hence:
16² = 16d
d = 16.
Then the length b is obtained applying the Pythagorean Theorem as follows:
b² = 16² + 16²
[tex]b = \sqrt{2 \times 16^2}[/tex]
[tex]b = 16\sqrt{2}[/tex]
Learn more about trigonometric ratios at brainly.com/question/24349828
#SPJ1
Age of first heart attack - The horizontal axis is age. The vertical axis is frequency (number of people who had their first heart attack at that age). The population is people in the US who have had at least one heart attack. What is the shape of distribution:
A.skewed right
B. skewed left
C. uniform
D. symmetric
Answer the following questions.
1.) Explain the significance of r<0 in an ordered pair (r, 0) in polar coordinates.
2.) Explain why a point in the plane can be represented by infinitely many ordered
pairs in polar coordinates.
3.) How is the component form of the vector related to the graph of the
vector in standard position?
4.)
A plane travels N30°W at 450 mph and encounters a wind blowing due west at 30 mph. (See Example 9)
a. Express the velocity of the plane Vp relative to the air in terms of I and J.
b. Express the velocity of the wind V in terms of i and j.
e. Express the true velocity of the plane vr in terms of i and j and find the true speed of the plane.
Answer:
1. An ordered pair in polar coordinates (r, θ) represents a point in the plane with a distance of r from the origin and an angle of θ with respect to the positive x-axis. When r < 0, this means that the point is located on the opposite side of the origin from the positive x-axis. In other words, the angle θ is shifted by 180 degrees.
2. In polar coordinates, a point can be represented by infinitely many ordered pairs because the distance r and the angle θ are not unique. For example, the point (1, π/4) and the point (1, 9π/4) both represent the same point in the plane.
3. The component form of a vector (a, b) represents the horizontal and vertical displacement of the vector from its initial point to its terminal point. The graph of a vector in standard position is a line segment from the origin to its terminal point. The horizontal and vertical components of the vector correspond to the x- and y-coordinates of the terminal point, respectively.
4a. The velocity of the plane Vp relative to the air can be expressed as Vp = (450 cos(60°), 450 sin(60°)) - (30, 0) = (225 - 30, 389.71) = (195, 389.71) mph.
4b. The velocity of the wind V can be expressed as V = (-30, 0) mph.
4e. The true velocity of the plane vr can be expressed as vr = Vp + V = (195 - 30, 389.71) = (165, 389.71) mph. The true speed of the plane is the magnitude of the true velocity, which is approximately 414.7 mph.
The average amount of money spent for lunch per person in the college cafeteria is $7.08 and the standard deviation is $2.29. Suppose that 45 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.
What is the distribution of
X? X~ N( , )
What is the distribution of
X? X ~ N( , )
For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between $6.9379 and $7.2186.
For the group of 45 patrons, find the probability that the average lunch cost is between $6.9379 and $7.2186.
For part d), is the assumption that the distribution is normal necessary? Yes or No
(a) The distribution of X ~ N(7.08, 2.29)
(b) The probability of a patron's lunch cost is 0.049
(b) The probability of a group patron's lunch cost is 0.049
(d) The assumption of normal distribution is not necessary
(a) What is the distribution of X?Given that
Mean = 7.08
Standard deviation = 2.29
The distribution of X is represented as
X ~ N(Mean , Standard deviation)
So, we have
X ~ N(7.08, 2.29)
(b) The probability that the lunch is between $6.9379 and $7.2186.The z-score is calculated as
z = (x - Mean)/Standard deviation
So, we have
z = (6.9379 - 7.08)/2.29 and z = (7.2186 - 7.08)/2.29
Evaluate
z = -0.062 and z = 0.061
So, we have
P = P(-0.062 < z < 0.061)
Evaluate
P = 0.049039
Approximate
P = 0.049
(c) The probability that the average lunch is between $6.9379 and $7.2186.This is same as part (b)
i.e. the probability that the average lunch is between $6.9379 and $7.2186 is 0.049
(d) Is the assumption necessaryNo, the assumption is not necessary
This is because
The distribution has a sample size less than 25 as required by the central limit theorem
Read more about normal distribution at
https://brainly.com/question/4079902
#SPJ1
AC is a straight line. Find the measure of
The measure of <BED = 135 degrees
How to determine the valueTo determine the value, we need to know the following;
Supplementary angles are defined as a pair of angles whose sum is 180 degrees.Angles on a straight line is the same measure as 180 degreesThe sum of the interior angles of a triangle is 180 degreesAngle at right angle is 90 degrees.From the information given, we have that;
Angle AED + Angle ACD are on a straight line
Now, susbtitute the values, we have that;
135 + ACD = 180
collect like terms
ACD = 180 - 135
subtract the values
ACD = 45
Then, we have that;
<BED = <ACD + <BEC
Substitute the values
<BED = 45 + 90
<BED = 135 degrees
Learn about angles at: https://brainly.com/question/25716982
#SPJ1
Shakira needs to rent a car for one day. She can get a Porsche from alpha car rental for $29.17 per day plus 57 cents per mile. She can get the same car from beta car rental for $50.23 per day plus 44 cents per mile. At what what number of miles are alpha and beta the same price?
Shakira needs to rent a car for one day and she is trying to decide which car rental company to use. Alpha Car Rental offers a Porsche for $29.17 per day, plus 57 cents per mile. Beta Car Rental also offers the same car for $50.23 per day, plus 44 cents per mile.
To determine which car rental is a better deal, Shakira needs to calculate at what number of miles the prices for both Alpha and Beta Car Rental are the same. To do this, she can use the following equation:
50.23 - 29.17 = x (44 - 57)The variable of x is the number of miles. This equation simplifies to x = 21.06 miles. Therefore, at 21.06 miles, Alpha and Beta Car Rental will be the same price.
Hope this helps! Have a nice day. :)Dawson Toys, Limited, produces a toy called the Maze. The company has recently created a standard cost system to help control costs and has established the following standards for the Maze toy:
Direct materials: 7 microns per toy at $0.33 per micron
Direct labor: 1.2 hours per toy at $7.10 per hour
During July, the company produced 4,700 Maze toys. The toy's production data for the month are as follows:
Direct materials: 77,000 microns were purchased at a cost of $0.30 per micron. 35,875 of these microns were still in inventory at the end of the month.
Direct labor: 6,040 direct labor-hours were worked at a cost of $45,904.
Required:
1. Compute the following variances for July: (Indicate the effect of each variance by selecting "F" for favorable, "U" for unfavorable, and "None" for no effect (i.e., zero variance). Input all amounts as positive values. Do not round intermediate calculations. Round final answer to the nearest whole dollar amount.)
a. The materials price and quantity variances.
b. The labor rate and efficiency variances.
a. Materials price variance: U$990 and Materials quantity variance: F$198
b. Labor rate variance: F$248
Labor efficiency variance: U$752
a. Materials price and quantity variances:
Materials price variance:
The materials price variance measures the difference between the actual cost of materials purchased and the standard cost of materials.
Actual quantity purchased = 77,000 microns
Actual cost per micron = $0.30 per micron
Standard quantity allowed for production = (7 microns per toy) x (4,700 toys) = 32,900 microns
Standard cost per micron = $0.33 per micron
Materials price variance = (Actual quantity purchased x Actual cost per micron) - (Standard quantity allowed x Standard cost per micron)
Materials price variance = (77,000 x $0.30) - (32,900 x $0.33)
Materials quantity variance:
The materials quantity variance measures the difference between the actual quantity of materials used and the standard quantity allowed for production.
Actual quantity used = (77,000 microns purchased) - (35,875 microns in ending inventory)
Standard quantity allowed = (7 microns per toy) x (4,700 toys)
Materials quantity variance = (Actual quantity used - Standard quantity allowed) x Standard cost per micron
Materials quantity variance = ((77,000 - 35,875) - (7 x 4,700)) x $0.33
b. Labor rate and efficiency variances:
Labor rate variance:
The labor rate variance measures the difference between the actual labor rate paid and the standard labor rate.
Actual labor hours worked = 6,040 hours
Actual labor cost per hour = $45,904 / 6,040 hours
Standard labor hours allowed for production = (1.2 hours per toy) x (4,700 toys)
Standard labor cost per hour = $7.10 per hour
Labor rate variance = (Actual labor hours worked x Actual labor cost per hour) - (Standard labor hours allowed * Standard labor cost per hour)
Labor rate variance = (6,040 x Actual labor cost per hour) - (5,640 x $7.10)
Labor efficiency variance:
The labor efficiency variance measures the difference between the actual labor hours used and the standard labor hours allowed for production.
Labor efficiency variance = (Actual labor hours worked - Standard labor hours allowed) x Standard labor cost per hour
Labor efficiency variance = (6,040 - (1.2 x 4,700)) x $7.10
Please note that the actual labor cost per hour and the actual labor cost per micron need to be calculated before computing the variances.
For similar questions on rate variance
https://brainly.com/question/17167100
#SPJ11
♥
Translations
Essential Question: What are the properties of a translation?
Do Now :
What is a reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1)
and its image D'(1, 6), E (8, -3), F'(-2, 1)?
The reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).
A translation is a type of transformation that moves all the points of a figure the same distance and in the same direction.
The shape and size of the figure do not change, only its position in the plane.
(3, 6)--->(1,6)
3-x=1
x=-2
(x-2, y)
To find the reflection rule that maps the triangle D(3, 6), E(-4,-3), F(6, 1) onto its image D'(1, 6), E(8, -3), F'(-2, 1), we need to determine the line of reflection.
In triangle the point where the perpendicular bisectors intersect will be the center of the reflection.
We find that the midpoint of DE is (−0.5,1.5), the midpoint of DF is (4.5,3.5), and the midpoint of EF is (1,−1).
The perpendicular bisectors of DE and DF intersect at (2,2), and the perpendicular bisectors of DE and EF intersect at (−1.25,2.75).
Therefore, the reflection rule that maps triangle DEF onto triangle D'E'F' is a reflection across the line that passes through (2,2) and (−1.25,2.75).
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ1
PLS HELP ASAP I WILL GIVE BRAINLIEST GEOMETRY
Answer: A. 32
Step-by-step explanation:
Rule: That if an angle is created on the end of circle The arc that it creates is 2 times the angle.
arc AX = 2 (<B)
arc AX = 2(56)
arc AX = 112
Rule: The angle of 2 secants = 1/2 (outer arc - inner arc)
<C = 1/2 (arc AB - arc AX)
<C = 1/2 ( 176 - 112)
<C = 1/2 (64)
<C = 32 >A
If the diameter of a circle is 22 in what is its area
Answer:If the Diameter of a circle is 22 inches, the area will be 380.13in².
Step-by-step explanation:
These are the formulas you use:
Area=pi*Radius^2 or A=pi*Radius*Radius
Diameter=2*Radius
A=1
4*pi*Diameter*2=1 2
4*pi*222=380.13271in
380.13271in is approximately 380.13in².
−9, −4, 1, 6, .. aremetric or geometric
.will give brainless
Step-by-step explanation:
OK, 'Brainless'.... the triangle side length rule states that any two sides of a triangle must sum to greater than the remaining side length...
42 + 20 > x then 12 , 20, 22, 32, 42, 50 will work here
42+x > 20 all of the possibles work here
20 + x > 42 32, 42, 50, 62 and 70 work here
so 32 and 42 are in all of the lists ....that is your answer
Alice is cutting pieces of cloth to sew into a quilt. She cut one piece of cloth into a parallelogram with a base of 7 inches and a height of 4 inches. What is the area of this piece of cloth?
Answer:
28 in²
Step-by-step explanation:
Area of parallelogram = base X vertical height
= 7 X 4
= 28 in²
1s Jeremy drew Figure 1 and Louisa drew Figure 2.
Part A
Figure 1
Figure 2
Jeremy says both figures are rectangles. Do you agree with Jeremy?
Support your answer.
Jeremy is wrong as I explained below.
As we know,
A rectangle is a quadrilateral with four right angles (90-degree angles). It is a type of parallelogram where opposite sides are equal in length. In a rectangle, the opposite sides are parallel and all angles are right angles. A square is a specific type of rectangle where all sides are equal in length. It is a regular quadrilateral with all angles equal to 90 degrees. In a square, all four sides are equal and all angles are right angles.Thus, as we can see from the figure figure 1 is a rectangle and Figure 2 is a square so,
I do not agree with Jeremy.
Read more on regular polygon here:
brainly.com/question/20911145
#SPJ1
Complete question:
summary of this shape help u will get 100 points I need it cry cyr ycr
The line of symmetry for the above figure is attached accordingly.
What is a line of symmetry?In mathematics, symmetry with regard to a reflection is known as reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry.
That is, a figure with reflectional symmetry does not alter when it is reflected. A line/axis of symmetry exists in 2D, while a plane of symmetry exists in 3D.
After inserting the symmetry lines, the above resulted in a kite.
Learn more about lines of symmetry:
https://brainly.com/question/28709515
#SPJ1
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.6 ppm and standard deviation 1.3 ppm. 15 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.a-What is the distribution of X? X ~ N(........,.......) b-What is the distribution of X bar? X bar ~ N(......,.....) c-What is the probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants?
d-For the 15 cities, find the probability that the average amount of pollutants is less than 9.3 ppm.
e)For part d), is the assumption that the distribution is normal necessary? yes or no f. Find the IQR for the average of 15 cities.
Q1 = ............ ounces
Q3 = ............ ounces
IQR: ............ ounces
The interquartile range for the average of 15 cities is 1.8.
a) X ~ N(9.6, 1.3)
b) X bar ~ N(9.6, 0.13)
c) The probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants can be calculated using the z-score formula: P(X < 9.3) = P(Z < (9.3 - 9.6) / 1.3) = 0.338.
d) The probability that the average amount of pollutants is less than 9.3 can be calculated using the z-score formula: P(Xbar < 9.3) = P(Z < (9.3 - 9.6) / 0.13) = 0.819.
e) The assumption that the distribution is normal is indeed necessary for part d.
f) The IQR for the average of 15 cities can be calculated as follows: Q1 = 8.7 and Q3 = 10.5. IQR = 10.5 - 8.7 = 1.8.
Therefore, the interquartile range for the average of 15 cities is 1.8.
Learn more about the interquartile range here:
https://brainly.com/question/4135956.
#SPJ1
can someone please help me out?
The radius of the circle is [tex]\sqrt{59[/tex] and the coordinates are (6,8).
The given equation of the circle is:
[tex]x^2+Y^2-12x-16y+51=0[/tex]
To find the center and radius of the given circle, we need to rewrite the equation in the standard form [tex](x-a)^2 + (y-b)^2 = r^2[/tex],
where (a,b) is the center of the circle and r is the radius.
We can start by completing the square for the x and y terms. For the x terms, we add and subtract (12/2)² = 36 to get:
[tex]x^2 - 12x + 36 + y^2 - 16y = -51 + 36 + 0[/tex]
Similarly, for the y terms, we add and subtract (16/2)² = 64 to get:
[tex]x^2 - 12x + 36 + y^2 - 16y + 64 = -51 + 36 + 64[/tex]
Simplifying:
[tex](x - 6)^2 + (y - 8)^2 = 59[/tex]
Now we can see that the center of the circle is at (6, 8), and the radius is [tex]\sqrt{59[/tex].
Learn more about Circle here:
https://brainly.com/question/23026602
#SPJ1
The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest. if the account balance is $15,160 after 12 years, what is the value of the principal?
The value of the principal is $10,000.
The equation A = P(1 + 0.043t) represents the amount of money earned on a savings account with 4.3% annual simple interest A is the account balance after t years P is the principal amount, and 0.043 is the interest rate per year.
The account balance is $15,160 after 12 years.
Substituting these values into the equation, we get:
15,160 = P(1 + 0.043(12))
Simplifying the right-hand side, we get:
15,160 = P(1 + 0.516)
15,160 = P(1.516)
Dividing both sides by 1.516, we get:
P = 10,000
This means that the account was initially opened with a principal of $10,000 and it earned simple interest of 4.3% per year for 12 years resulting in an account balance of $15,160.
The principal and it does not take into account the interest that is earned on the interest itself.
In contrast compound interest takes into account the interest that is earned on both the principal and the previously earned interest.
The account in question had been earning compound interest instead of simple interest the final account balance after 12 years would have been higher than $15,160.
For similar questions on principal
https://brainly.com/question/25720319
#SPJ11
End Behavior
Describe the end behavior of the following functions using limit notation, please.
1. f(x) = (2x² + 4x + 4) / x³ = 0; as lim x→∞, and lim x→-∞
2. g(x) = (2x² + 4x + 4)/x² = ∞; as lim x→∞, and lim x→-∞]
3. h(x) = (2x² + 4x + 4)/x = ∞ as lim x→∞, and -∞ as lim x→-∞.
What is the behavior of the functions?To find the end behavior of each of the functions, we can take the limit as x approaches infinity and negative infinity.
For f(x) = (2x² + 4x + 4)/x³;
lim x→∞ (2x² + 4x + 4) / x³ = 0
lim x→-∞ (2x² + 4x + 4) / x³ = 0
f(x) approaches zero as x approaches positive or negative infinity.
For g(x) = (2x² + 4x + 4)/x²;
lim x→∞ (2x² + 4x + 4) / x² = ∞
lim x→-∞ (2x² + 4x + 4) / x² = ∞
g(x) approaches infinity as x approaches positive or negative infinity.
For h(x) = (2x² + 4x + 4)/x
lim x→∞ (2x² + 4x + 4) / x = ∞
lim x→-∞ (2x² + 4x + 4) / x = -∞
h(x) approaches infinity as x approaches positive infinity, and negative infinity as well, but with a negative sign.
Learn more about limit of functions here: https://brainly.com/question/23935467
#SPJ1
in triangle QRS, the measure of angle RSQ is 48.2 degrees, and the SQR is 75 degrees. what is the QRS?
The measure of angle QRS in triangle QRS is 56.8 degrees.
To find the measure of angle QRS in triangle QRS, we can use the fact that the sum of the measures of the angles in a triangle is always 180 degrees.
We know that:
- The measure of angle RSQ is 48.2 degrees
- The measure of angle SQR is 75 degrees
Let x be the measure of angle QRS. Then, we can write:
RSQ + SQR + QRS = 180
Substituting the known values, we get:
48.2 + 75 + x = 180
Simplifying and solving for x, we get:
x = 180 - 48.2 - 75x = 56.8
Therefore, the measure of angle QRS in triangle QRS is 56.8 degrees.
for similar questions on Triangle
https://brainly.com/question/1058720
#SPJ11
Haley is returning from a business trip. Her empty suitcase has a mass of 5.1 kg. Her clothes have a combined mass of 14.8 kg. Haley also wants to pack 4 gifts, each with a mass of 870 g. The airline restriction for a suitcase is a limit of 22.7 kg. Can Haley bring everything home in her suitcase? If not, how many gifts can she pack? Explain.
From the calculation, she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.
What can she pack?We know that we have to consider the restriction that the airline has placed. We have been told that the luggage that have to be packed in this case would have to be less than 22.7 kg.
We would now have to look at all the things that Haley would need to pack so as to determine what can be packed and what can not be packed.
Total luggage that she has to pack;
Mass of empty suitcase + mass of her clothes + mass of 4 gifts
Total luggage = 5.1 Kg + 14.8 Kg + 4(0.87) = 23.38 Kg
This implies that she can't carry all but she can carry her suitcase with clothes in it and three out of the four gift items.
Learn more about luggage:https://brainly.com/question/31082914
#SPJ1
5) Stacy ran 8 miles. She
recorded how long it took her to run each mile in minutes. How many times did Stacy run her fastest mile?
Answer:
1?
Step-by-step explanation:
9 1/4 is the longest distance
2 times
Step-by-step explanation:According to the chart, the mile that she ran the fastest was [tex]9 \frac{1}{2}[/tex] miles. 1 dot equals 1 minute so her fastest mile was [tex]9 \frac{1}{2}[/tex].
I hoped this helped if not please tell me what I did wrong ૮ ˶ᵔ ᵕ ᵔ˶ ა
please see attached doc
The cosine value is given as follows:
[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]
How to obtain the cosine value?The tangent value is given as follows:
[tex]\tan{\theta} = -\frac{\sqrt{7}}{4}[/tex]
First we must obtain the secant value, according to the identity presented as follows:
[tex]\sec^2{\theta} = 1 + \tan^{2}{\theta}[/tex]
Replacing the tangent into the expression, we have that:
[tex]\sec^2{\theta} = 1 + \frac{7}{16}[/tex]
[tex]\sec^2{\theta} = \frac{23}{16}[/tex]
[tex]\sec{\theta} = \frac{\sqrt{23}}{4}[/tex]
The secant is positive, as the angle is in the fourth quadrant, where the cosine is positive.
The cosine is then given as follows:
[tex]\cos{\theta} = \frac{1}{\sec{\theta}}[/tex]
[tex]\cos{\theta} = \frac{4}{\sqrt{23}} \times \frac{\sqrt{23}}{\sqrt{23}}[/tex]
[tex]\cos{\theta} = \frac{4\sqrt{23}}{23}[/tex]
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
I need the answer to the problem
Determine if the table below represents a linear function. If so, what's the rate of change?  Question 9 options: A) Yes; rate of change = 4 B) No; it's a non-linear function. C) Yes; rate of change = 3 D) Yes; rate of change = 2
The given table represents a linear function with a constant rate of change of 2. Option D is the right answer.
To determine if the table represents a linear function and calculate the rate of change, let's examine the given values:
x | y
-----------
1 | 3
2 | 5
3 | 7
4 | 9
By looking at the y-values, we can observe that for every increase of 1 in x, the corresponding y-value increases by 2. This indicates a constant rate of change, suggesting that the table represents a linear function.
To calculate the rate of change, we can use the formula:
[tex]\[\text{{Rate of Change}} = \frac{{\text{{Change in y}}}}{{\text{{Change in x}}}}\][/tex]
Taking any two points from the table, let's choose (1, 3) and (2, 5):
[tex]\[\text{{Rate of Change}} = \frac{{5 - 3}}{{2 - 1}} = \frac{2}{1} = 2\][/tex]
The table provided exhibits a linear function with a constant rate of change. As the x-values increase by 1 from [tex]1[/tex] to [tex]4[/tex], the corresponding y-values increase by [tex]2[/tex] from [tex]3[/tex] to [tex]9[/tex]. This consistent change in y for each unit change in x indicates a linear relationship between the variables.
The rate of change, also known as the slope of the function, is determined by the ratio of the change in y to the change in x. In this case, the rate of change is [tex]2[/tex], meaning that for every increase of [tex]1[/tex] in [tex]x[/tex], the y-value increases by 2.
Thus, the table represents a linear function with a rate of change of [tex]2[/tex].
Therefore, the correct answer is D) Yes; rate of change = [tex]2[/tex].
NOTE: The given question is incomplete. The complete question is:
Determine if the table below represents a linear function. If so, what's the rate of change?
options:
A) Yes; rate of change = 4
B) No; it's a non-linear function.
C) Yes; rate of change = 3
D) Yes; rate of change = 2
Table:
x | y
-----------
1 | 3
2 | 5
3 | 7
4 | 9
For more such questions on linear function: https://brainly.com/question/2248255
#SPJ11
The distance between home and
school is 4.5 miles.On a map it
shows the distance to be 9 cm.
What is the scale?
Answer:
1 mile : 2 cm
Step-by-step explanation:
ratio is 4.5 miles : 9
Which, if you want simplified, 1:2
Answer:
2 cm is 1 mile
or 1 cm is 1/2 mile
Step-by-step explanation:
We are going from 9 cm to 4.5 miles
9 cm * scale factor = 4.5 miles
scale factor = 4.5 miles / 9 cm
scale factor = 1/2 mile per cm
The scale is 2 cm is 1 mile
or 1 cm is 1/2 mile
(Score for Question of 15 pointS! 1. The data set shows the January 1 noon temperatures in degrees Fahrenheit for a particular city in each of the past 6 years. 28 34 27 42 52 15 Answer 15 27 28 34 42 52 (a) What is the five-number summary of the data set? 15,27,28,34,42,52 (b) What is the mean, X, of the data set? 33 (c) What is the sum of the squares of the differences between each data value and the mean? Use the table to organize your work. (x − x)² 15-33--18 27-33=-6 28-33=-5 34-33-1 42-33-9 52-33-19 (15-33)^2-324 (27-33)^-36 (28-33)=25 (34-33)^2=1 (42-33142-81 (52-33)^2-361 Sum:828
(d) What is the standard deviation of the data set? Use the sum from Part (c) and show your work.
pls need answer for (d) thanks!
Answer:
To many questions, and too many numbers
Step-by-step explanation:
You want to take out a $219,000 mortgage (home loan). The interest rate on the loan is 4.5%, and the loan is for 30 years. Your monthly payments are $1,109.64. How much will still be owed after making payments for 15 years? Round your answer to the nearest dollar.
After making payments for 15 years, the amount still owed on the mortgage would be approximately $145052.36.
To determine how much will still be owed after making payments for 15 years, we can use the formula for the remaining balance on a mortgage:
Remaining balance = P ((1 + r)ⁿ - (1 + r)ᵇ) / ((1 + r)ⁿ - 1)
where:
P = the initial loan amount (in this case, $219,000)
r = the monthly interest rate (which is the annual interest rate divided by 12)
n = the total number of monthly payments (which is 30 years times 12 months per year, or 360 months)
b = the number of monthly payments made so far (which is 15 years times 12 months per year, or 180 months)
First, we need to calculate the monthly interest rate:
r = 4.5% / 12 = 0.00375 = 0.375%
Next, we can plug in the values to get:
Remaining balance = $219,000 ((1 + 0.00375)³⁶⁰- (1 + 0.00375)¹⁸⁰) / ((1 + 0.00375)³⁶⁰ - 1)
= $145052.36
To learn more about loan calculations;
https://brainly.com/question/28244942
#SPJ1