What is happening to this graph when the x values are between -1 and 1
What are the zeros of the function?
f(t)=t^2−13t+36
Enter your answers in the boxes.
what is 100 . 23/25 x 3/16
whatcis 72/90 reduced
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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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.
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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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.
Write an explicit formula for the sequence 4,-1,-6,-11,-16 then find a14
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.
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 .
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 0.074¯¯¯¯¯ expressed as a fraction?
△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!
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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The Treasury Department auctioned $15 billion in 3-month bills in denominations of $10,000 at a discount rate of 3.750%.
What would be the effective rate of interest? (Use calendar year. Do not round intermediate calculations. Round your answer to the nearest hundredth percent.)
NEED HELP The value of x is
.
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.
Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i.
The first three iterates of the function f(z) = 2z + (3 - 2i) with z0 = 5i are 3 + 8i, 9 + 14i, and 21 + 26i after consecutive substitutions. The first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Explanation:To find the first three iterates of the function f(z) = 2z + (3 - 2i) with the initial value z0 = 5i, we perform successive substitutions into the function.
First iterate (f1): Substitute z0 into f(z)Second iterate (f2): Substitute f1 into f(z)Third iterate (f3): Substitute f2 into f(z)Thus, the first three iterates of the function are 3 + 8i, 9 + 14i, and 21 + 26i.
Final answer:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, substitute the initial value into the function to get the first iterate. Then, substitute the first result back into the function to find the second iterate. Finally, substitute the second result back into the function to find the third iterate.
Explanation:
To find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i, we substitute the initial value into the function:
f(z0) = 2(5i) + (3 - 2i) = 10i + 3 - 2i = 3 + 8i.
Then, we substitute the result back into the function to find the second iterate:
f(3 + 8i) = 2(3 + 8i) + (3 - 2i) = 6 + 16i + 3 - 2i = 9 + 14i.
Finally, we substitute the second result back into the function to find the third iterate:
f(9 + 14i) = 2(9 + 14i) + (3 - 2i) = 18 + 28i + 3 - 2i = 21 + 26i.
Sam counted Out Loud by 6's Jorge counted Out Loud by 8s what are the first three numbers both Sam and George said
Leo bought 6 chew toys for his new puppy each chew toy cost $4 how much did Leo spend for the chew toys
How would you write this equation in terms of sin and cos as well as simplify it from there?
(1+cotx)(1-cotx)-csc^2 x
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.
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
turn 1/8 into a percent
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%.
An acute angle θ is in a right triangle with cos θ =2/3 . What is the value of sec θ?
Final answer:
The secant of an angle is the reciprocal of its cosine. Given cos θ = 2/3 for an acute angle in a right triangle, the sec θ equals 3/2.
Explanation:
In the context of trigonometry, the secant (sec) of an angle is the reciprocal of the cosine (cos) of that angle.
Given that cos θ = 2/3 for an acute angle in a right triangle, we can find the value of sec θ by taking the reciprocal of the cosine value. Hence, the value of sec θ is simply the reciprocal of 2/3, which is 3/2.
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.
There were 48 blue, 48 green and 48 yellow crayons. Also there were 72 red crayons and 120 colored pictures. What is the largest number of identical sets can be made of these crayons and pictures?
24 is the largest number of identical sets can be made of these crayons and pictures
What is Number system?A number system is defined as a system of writing to express numbers.
To find out the largest number of identical sets that can be made, we need to determine the common factors of the total number of crayons and pictures.
The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, and since all three colors have the same number of crayons, we can say that there are 48 x 3 = 144 crayons in total.
The prime factorization of 72 is 2 x 2 x 2 x 3 x 3, and the prime factorization of 120 is 2 x 2 x 2 x 3 x 5.
The common factors of 144, 72, and 120 are 2 x 2 x 2 x 3 = 24. This means that we can make 24 identical sets.
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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: