Write an explicit formula for the sequence 4,-1,-6,-11,-16 then find a14
Assume the $12,000 Treasury bill, 7% for 15 weeks. Calculate the effective rate of interest. (Use calendar year. Round your answer to the nearest hundredth percent.)
Answer:
7.25%
Step-by-step explanation:
You want the effective rate of interest on a $12,000 Treasury bill with a nominal interest rate of 7% and maturity in 15 weeks.
InterestThe Treasury computes the selling price of the bill by subtracting the interest from the face value. The interest is computed as "ordinary interest" using a 360-day year. 15 weeks is 105 days.
I = Prt
I = $12000·0.07·(105/360) = $245
Then the cost of the bill is $12,000 -245 = $11,755.
RateUsing the formula for the maturity value with a 365-day year, we have ...
A = P(1 +rt)
12000 = 11755(1 +r(105/365))
Solving for r gives ...
[tex]r=\left(\dfrac{12000}{11755}-1\right)\cdot\left(\dfrac{365}{105}\right)\approx0.0724514\approx\boxed{7.25\%}[/tex]
The effective rate of interest is about 7.25%.
Find the area enclosed between f(x)=0.3x2+7 and g(x)=x from x=−4 to x=8.
To find the area enclosed between two functions, we calculate the definite integral of the absolute difference between the functions over the given interval. The area is equal to the integral of ∣f(x) - g(x)∣, split into two parts where g(x) ≥ f(x) and g(x) < f(x), then added together. The enclosed area for the given functions is 82.26 square units.
Explanation:To find the area enclosed between the functions f(x) = 0.3x^2+7 and g(x) = x from x = -4 to x = 8, we need to calculate the definite integral of the absolute difference between the two functions over the given interval.
The area is equal to the integral of ∣f(x) - g(x)∣ from x = -4 to x = 8. We can split the integral into two parts where g(x) ≥ f(x) and g(x) < f(x), then evaluate each separately. Finally, we add the two areas together.
After evaluating the integrals, we find that the area enclosed between the two functions is 82.26 square units.
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In response to very high demand, a basketball jersey has been marked up by 25% and is now selling for $95.00. How much was the jersey before the mark-up?
76 is the correct answer
The price of the jersey before the mark-up = $76
What is percentage?"A number that can be expressed as a fraction of 100."
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
A basketball jersey has been marked up by 25% and is now selling for $95.00
Let 'm' be the price of the jersey before the mark-up.
So, we get an equation,
⇒ m + (25 percent of m) = 95
25 percent of m
= [tex]\frac{25}{100}\times m[/tex]
= 0.25 m
so, the equation becomes,
⇒ m + 0.25 m = 95
⇒ 1.25 m = 95
⇒ m = 76
Therefore, the price of the jersey before the mark-up = $76
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In MNO NM=3 cm NO=4cm and MO=5 cm list the angels in order from smallest to largest
The triangle is a right triangle as the sides follow the Pythagorean theorem. The angles opposite the sides are 90° (largest), 53.13°, and 36.87° (smallest), listed from largest to smallest based on side lengths.
The student's question involves a triangle with sides of lengths 3 cm, 4 cm, and 5 cm and asks for the angles to be listed from smallest to largest. Since these side lengths satisfy the Pythagorean theorem (32 + 42 = 52), the triangle is a right triangle, with the right angle opposite the longest side, MO. Using the properties of a right triangle, we can determine that the smallest angle is opposite the shortest side, NM, and the next larger angle is opposite the intermediate side, NO.
To find the actual angle measurements, we would typically use trigonometric ratios such as sine, cosine, or tangent. However, since this is a 3-4-5 triangle, we already know that the angles are 90° for the right angle, and 36.87° and 53.13° for the other two angles, respectively. Thus, the angle opposite NM (3 cm) is the smallest, the angle opposite NO (4 cm) is larger, and the angle opposite MO (5 cm) is the largest, at 90 degrees.
The angle measurements in a right triangle will always follow this pattern based on the lengths of the sides, making it a straightforward matter to list them from smallest to largest.
The area of a rectangular field is 8624 yd^2. If the length of the field is 98 yards, what is its width
The width of the rectangular field is 88 yards.
Explanation:To find the width of the rectangular field, we can use the formula for the area of a rectangle: Area = length x width.
In this case, the area is given as 8624 yd² and the length is given as 98 yards. So, we can rearrange the formula to solve for the width: width = Area / length.
Plugging in the values, we have width = 8624 yd² / 98 yds. Dividing these values gives us the width of the field: width = 88 yards.
Consider the proof. Given: In △ABC, BD ⊥ AC Prove: the formula for the law of cosines, a2 = b2 + c2 – 2bccos(A) Statement Reason 1. In △ABC, BD ⊥ AC 1. given 2. In △ADB, c2 = x2 + h2 2. Pythagorean thm. 3. In △BDC, a2 = (b – x)2 + h2 3. Pythagorean thm. 4. a2 = b2 – 2bx + x2 + h2 4. prop. of multiplication 5. a2 = b2 – 2bx + c2 5. substitution 6. In △ADB, cos(A) = 6. def. cosine 7. ccos(A) = x 7. mult. prop. of equality 8. a2 = b2 – 2bccos(A) + c2 8. ? 9. a2 = b2 + c2 – 2bccos(A) 9. commutative property What is the missing reason in Step 8?
Solution: The missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].
Explanation:
The given steps are used to prove the formula for law of cosines.
From step 5 it is noticed that our equation is
[tex]a^2=b^2-2bx+c^2[/tex] ..... (1)
From step 7 it is noticed that the value of [tex]x[/tex] is [tex]c\cos (A)[/tex].
So by substituting [tex]c\cos (A)[/tex] for [tex]x[/tex] in equation (1) we get the equation of step 8, i.e.,
[tex]a^2=b^2-2bc\cos (A)+c^2[/tex]
Hence, the missing reason in Step 8 is substitution of [tex]x=c\cos (A)[/tex].
The missing reason in Step 8 of the proof for the Law of Cosines is substitution, where x is replaced with cc cos(A) in the expression.
Explanation:The missing reason in Step 8 of the proof that shows how the Law of Cosines is derived, a2 = b2 + c2 – 2bc cos(A), is the substitution property. In Step 7, we established that c cos(A) is equal to x. Thus, for Step 8, when we replace x with cc cos(A) in the expression b2 – 2bx + c2, we effectively utilize substitution to arrive at the expression a2 = b2 – 2bccos(A) + c2.
What is 0.074¯¯¯¯¯ expressed as a fraction?
25 Points to answer this question. What are the roots of the equation? x2+24=14x Enter your answers in the boxes. x1= x2=
The roots of the Given quadratic equation are x₁ = -2 and x₂ = -12.
What is a Quadratic equation?ax²+bx+c=0, with a not, equal to 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.
Given a quadratic equation, x² + 24 = 14 x
Simplifying the equation using the factorization method,
=> x² + 24 = 14 x
=> x² +14 x +24 = 0
factorize the "x term"
=> x² +12x + 2x +24 = 0
=> x(x +12)+2(x + 12) = 0
=>(x + 2)(x + 12) = 0
x = -2, -12
thus,
the value of x will be either -12 or -2
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Your parents have decided to buy a new Toyota 4Runner for 25,635. According to the dealer, the car will depreciate in value approximately $3,000 per year. Write and solve a linear equation to find how many years it will be until the car is worth $3,135
jude earns $54 interest each year on an investment. his principal was $1800. what is jude's interest rate?
Jude's interest rate will be 3% for the principal of $1800 on an investment.
What is the simple interest?Simple interest is defined as interest paid on the original principal and calculated with the following formula:
S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.
To find Jude's interest rate, we need to set up an equation using the information given. Let R be the interest rate.
The interest earned is equal to the principal times the interest rate, so the equation is:
Interest = Principal × Rate
Substituting the given values, we have:
54 = 1800 × R
Dividing both sides by 1800 gives:
R = 54 / 1800
R = 0.03, or 3%.
Therefore, for an investment of $1800, the interest rate will be 3%.
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What is happening to this graph when the x values are between -1 and 1
Create the quadratic function that contains the points (0, -2), (1, 0) and (3, 10). Show all of your work for full credit
what is 100 . 23/25 x 3/16
not sure what this question is asking...
A toll bridge charges $1.00 for passenger cars and $2.50 for other vehicles. suppose that during daytime hours, 60% of all vehicles are passenger cars. if 25 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? hint: let ???? = the number of passenger cars out of 25. start by identifying the type of discrete random variable ???? is. then, create a linear function of ???? to represent the toll revenue. finally, find the expected value of the function that represents the toll revenue.
WILL MARK BRAINLIEST FOR CORRECT ANSWER Which statements about the opposite of −12 are true? Select each correct answer. −12 and its opposite are located the same distance from zero on a number line. The opposite of the opposite of −12 is −12 . −12 and its opposite are on located on the same side of zero on a number line. The opposite of −12 is −1 1/2 .
Leo bought 6 chew toys for his new puppy each chew toy cost $4 how much did Leo spend for the chew toys
How many 1/2 foot pieces can be cut from 6 foot ribbon?
You withdrew $36.25 from your checking account. Now your balance is -$14.75. Write and solve an equation to find the amount of money in your account before you withdrew the money?
Three consecutive odd integers whose sum is 243
Final answer:
The three consecutive odd integers whose sum is 243 are 79, 81, and 83. The integers were found using the algebraic expression for consecutive odd numbers and solving for the sum equal to 243.
Explanation:
To find three consecutive odd integers whose sum is 243, we can represent the first of these integers as 'n', the second as 'n + 2', and the third as 'n + 4', since each consecutive odd integer is 2 more than the previous one. The equation we would use to portray their sum is:
n + (n + 2) + (n + 4) = 243
Simplifying the equation, we combine like terms:
3n + 6 = 243
Next, we subtract 6 from both sides to isolate the 3n term:
3n = 243 - 6
3n = 237
Now we divide by 3 to solve for n:
n = 237 / 3
n = 79
The first odd integer is 79, the second odd integer is 79 + 2 = 81, and the third odd integer is 79 + 4 = 83.
Therefore, the three consecutive odd integers are 79, 81, and 83.
For the weight of the box that she measured, Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds. What was the greatest possible error for her actual measurement? 0.5 pounds 1 pound 24 pounds 24.5 pounds
Answer:
Option A - 0.5 pounds
Step-by-step explanation:
Given : Beatriz determined the margin of error as 23.5 pounds to 24.5 pounds.
To find : What was the greatest possible error for her actual measurement?
Solution :
To find the margin of error first we find the median of the given numbers.
Median of 23.5 and 24.5
[tex]M=\frac{23.5+24.5}{2}=\frac{48}{2}=24[/tex]
So, the Greatest possible error is 24.5-24 = 0.5 pounds
Therefore, option A is correct.
Grass can grow up to six inches in a week depending on temperature, humidity, and time of year. At this rate , how tall will grass grow in 24 days?
Grass can grow up to six inches in a week depending on temperature, humidity, and time of year
We have to calculate how tall will grass grow in 24 days
we know there are seven days in a week
so in one day grass can grow up to 6/7 inches
therefore we could say that grass can grow up to 24*6/7 inches
so the answer is 20.57 inches
so in 24 days grass can grow up to 20.57 inches
Grass can grow approximately 20.58 inches in 24 days.
Explanation:To calculate the height that grass will grow in 24 days, we need to find out how much it grows in 1 week, and then multiply that by the number of weeks in 24 days. If grass can grow up to six inches in a week, we can calculate the height it will grow in 24 days as follows:
Calculate the number of weeks in 24 days: 24 days ÷ 7 days/week = 3.43 weeks (rounded to the nearest hundredth).Multiply the growth per week (6 inches) by the number of weeks: 6 inches/week × 3.43 weeks = 20.58 inches.Therefore, grass will grow approximately 20.58 inches in 24 days.
What is the value of x?
Enter your answer in the box.
x =
Two intersection lines. Angle formed at the top is labeled 2 x plus 2 degrees. Angle formed at the bottom is labeled 3 x minus 52 degrees.
Diagram is in the attachment below
△BCD is a right triangle. The length of the hypotenuse is 20 centimeters. The length of one of the legs is 15 centimeters. What is the length of the other leg? Enter your answer, as a decimal rounded to the nearest tenth, in the box
Answer:
13.2 cm
Step-by-step explanation:
b = [tex]\sqrt{c^{2} - a\\^{2} }[/tex]
b = [tex]\sqrt{20^{2} - 15\\^{2} }[/tex]
b = [tex]\sqrt{400-225\\} \\[/tex]
b = [tex]\sqrt{175}[/tex]
b = 13.228
b= 13.2 cm
:) good luck on the rest!
What are the zeros of the function?
f(t)=t^2−13t+36
Enter your answers in the boxes.
You purchased merchandise from a suppler and failed to pay the invoice amount $310 by the last day of the credit period, August 12. Calculate the total amount you must pay on October 15 if the suppler charges 18% interest on past-due accounts.
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. r = 2.7 meters, s = 4.32 meters
a. 1.6 radians
b. 0.37 radians
c. 3.5 radians
d. 1.35 radians
Answer:
The correct option is a.
Step-by-step explanation:
Given information: radius r =2.7 meters, arc length s = 4.32 meters.
The formula of arc length is
[tex]s=r\theta[/tex]
where, r is radius and θ is central angle in radians.
Using the above formula we get
[tex]4.32=2.7\times \theta[/tex]
Divide both sides by 2.7.
[tex]\frac{4.32}{2.7}=\theta[/tex]
[tex]1.6=\theta[/tex]
The value of the central angle is 1.6 radians. Therefore option a is correct.
what is the measure ?
What is the standard deviation for the data set?
212, 249, 212, 248, 239, 212, 216, 234, 248
Express your answer as a decimal to the nearest tenth.
Enter your answer in the box.
What is the standard deviation for the data set?
212, 249, 212, 248, 239, 212, 216, 234, 248Answer:16.9
Step-by-step explanation: