Answer: The correct option is (b) [tex]-4\leq y\leq 2.[/tex]
Step-by-step explanation: We are given to select the correct range of the following function
[tex]y=3\cos x-1.[/tex]
We know that the range of the cosine function is from - 1 to 1.
That is,
[tex]-1\leq \cos x\leq 1\\\\\Rightarrow -(1)\times 3\leq 3\times \cos x\leq 3\times 1\\\\\Rightarrow -3\leq 3\cos x\leq 3\\\\\Rightarrow -3-1\leq 3\cos x-1\leq 3-1\\\\\Rightarrow -4\leq 3\cos x-1\leq 2\\\\\Rightarrow -4\leq y\leq 2.[/tex]
Thus, the range of the given function is [tex]-4\leq y\leq 2.[/tex]
Option (b) is CORRECT.
Find the volume v of the described solid s. a right circular cone with height 7h and base radius 3r
The volume of a right circular cone with height 7h and base radius 3r is ⅔ 9r² h.
Explanation:The volume of a right circular cone can be calculated using the formula V = ⅔ ² h, where r is the radius of the base and h is the height of the cone.
In this case, the height of the cone is 7h and the base radius is 3r.Plugging in the values, we have V = ⅔ (3r)² (7h) = ⅔ 9r² h.
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Sigma Notation: Need Help!!
Problem 1:
Evaluate the summation of 3 times negative 2 to the n minus 1 power, from n equals 1 to 5.
Choices:
A.-93
B.-33
C.33
D.93,
Final answer:
To solve the sigma notation problem, we individually calculate each term for n from 1 to 5 and sum them up, resulting in a total value of 33. Thus, the correct answer is C.33.
Explanation:
The problem involves evaluating a series using sigma notation. Specifically, we're looking at the summation of 3 × (-2)n-1, with n going from 1 to 5.
To find the solution, we need to calculate each term separately for each value of n, and then sum all of the calculated terms together.
For n=1: [tex]3 \times (-2)^{1-1[/tex] = 3 × 1 = 3For n=2: [tex]3 \times (-2)^{2-1[/tex] = 3 × (-2) = -6For n=3: [tex]3 \times (-2)^{3-1[/tex] = 3 × 4 = 12For n=4: [tex]3 \times(-2)^{4-1[/tex] = 3 × (-8) = -24For n=5: [tex]3 \times (-2)^{5-1[/tex] = 3 × 16 = 48Adding these values together: 3 - 6 + 12 - 24 + 48 = 33.
So the correct answer to the summation is 33, which corresponds to choice C.
The area of a regular octagon is 35 cm2. What is the area of a regular octagon with sides five times as long?
A. 625 cm2
B. 875 cm2
C. 175 cm2
D. 245 cm2
Answer with Step-by-step explanation:
Area of octagon=2(1+√2)a²
Where a is the length of the side of the octagon
Area=35 cm²
Let a' be the length of side of new octagon
a'=5a
Area=2(1+√2)a'²
=25×2(1+√2)a²
=25×35 cm²
= 875 cm²
Hence, correct option is:
B. 875 cm²
What is the quotient of -3/8 and -1/3
Answer:
its actually a
Step-by-step explanation:
Randy drove 540 miles in three times the time it took Andy to travel 135 miles Andy’s speed was slower than Randy’s by 15 miles per hour what were the rate and time of each?
I really need help please!!!
Let's assume
Randy's speed =x mph
we have
Andy’s speed was slower than Randy’s by 15 miles per hour
so,
Andy's speed =x-15
Randy drove 540 miles
so, we can find time taken by Randy
time = distance / speed
so, we get
[tex]t_R=\frac{540}{x}[/tex]
we can find time taken by Andy
time = distance / speed
so, we get
[tex]t_A=\frac{135}{x-15}[/tex]
Randy drove 540 miles in three times the time it took Andy to travel 135 miles
so,
[tex]t_R=3t_A[/tex]
we can plug it
[tex]\frac{540}{x}=3*\frac{135}{x-15}[/tex]
now, we can solve for x
[tex]540\left(x-15\right)=405x[/tex]
[tex]135x=8100[/tex]
[tex]x=60[/tex]
so,
Calculation of rate:
Randy's speed is 60 mph
Andy's speed =x-15
Andy's speed =60-15=45mph
Calculation of time:
Randy's time is
[tex]t_R=\frac{540}{x}[/tex]
[tex]t_R=\frac{540}{60}[/tex]
[tex]t_R=9 hours[/tex]
Andy's time is
[tex]t_A=\frac{135}{x-15}[/tex]
[tex]t_A=\frac{135}{60-15}[/tex]
[tex]t_A=3 hours [/tex]
The junior class has 50 students. Twenty-five students take only french, 15 take only Latin, and 10 take both. If a student is chosen at random from the class, what is the probability that the student takes latin?
A.)1
B.)1/2
C.)
1/4
Answer: B ) [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given: The number of students in junior class n(S)= 50
The number of students take only Latin n(L-F)= 15
The number of students take only French n(F-L)=25
The number of students take both = n(F∩L)=10
The number of students take Latin n(L)=n(L-F)+n(F∩L)=15+10=25
Therefore, the probability that the student takes Latin is given by :-
[tex]\text{Probability(Latin)}=\frac{\text{number of students take latin}}{\text{Total students}}\\\\=\frac{25}{50}=\frac{1}{2}[/tex]
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what is the probability that a card picked at random from a 52-card deck of playing cards is a club or a jack?
[tex] |\Omega|=52\\
|A|=\underbrace{13}_{\text{clubs}}+\underbrace{4}_{\text{jacks}}-\underbrace{1}_{\text{jack of clubs}}=16\\\\
P(A)=\dfrac{16}{52}=\dfrac{4}{13}\approx31\% [/tex]
Answer:
A. 4/13
Step-by-step explanation:
4/13 in percent is 30%(30.7692308 percent)
For Plato Users
Which explanation justifies how the area of a sector of a circle is derived?
Determine the percent of the sector of the circle divided by the degrees in a circle. Then find the number of triangles within a circle. Divide the two numbers and multiply by the area of the circle.
The sector of a circle is a fractional part of the circle. Determine the fraction of the circle that the sector represents. Multiply this fraction by the area of the entire circle.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle.
Find how many sector pieces fit in a circle. Divide this number by the total degrees in a circle. Then multiply the quotient by the diameter of the circle.
The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle justifies how the area of a sector of a circle is derived
The explanation that justifies how the area of a sector of a circle is derived is:
"The sector of a circle represents a part of a whole circle. Determine how many sections of the sectors will fit in the circle. Multiply this number by 180 and then multiply it by the area of the circle."
This method involves finding the fraction of the circle that the sector represents by dividing the central angle of the sector by 360 degrees. Then, multiply this fraction by the area of the whole circle to get the area of the sector.
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Raj writes a polynomial expression in standard form using one variable, a, that has 4 terms and is degree 5.
Nicole writes a polynomial expression in standard form using one variable, a, that has 3 terms and is degree 2.
Raj and Nicole’s polynomial expressions are added to create a sum, written in standard form.
What can you determine about the degree of the sum?
The sum will be degree
.
What can you determine about the number of terms of the sum?
The maximum number of terms of the sum is
, but it could be less.
Answer:
the sum will be degree 5
the maximum number of terms of the sum is 6
Step-by-step explanation:
PLEASE CHECK THIS FOR ME
LET ME KNOW IF ITS CORRECT
What number should be placed in the box to help complete the division calculation?
Mark's father travels 463 miles every month for his job. How many miles does he travel in 8 months?
find the equation of the straight line passing throughthe point (3,5) which is perpendicular to the line y=3x+2
please explain
Graph the ordered pairs for y=4x+2 using x={-2,1,2}
The graph of the ordered pairs is a straight line graph with x,y values (-2, -6), (1, 6), and (2,10).
What are ordered pairs.
In geometry, Ordered pairs are the values of x and y on the coordinate plane. They are called ordered pairs because they are usually arrange in (x,y) axis.
For a linear equation, the graph is a straight line graph. From the information given:
y = 4x + 2
The slope of the line (m) = 4The y-intercept (b) = 2The points x-axis {-2, 1, 2} are marked on the graph and the corresponding y-values are {-6, 6, 10} respectively.
Why is circle 1 similar to circle 2?
Circle 1: center (2, 3) and radius 4
Circle 2: center (2, 3) and radius 12
Answer: The answer is given below.
Step-by-step explanation: The given circles are:
Circle 1: centre (2, 3) and radius 4
Circle 2: centre (2, 3) and radius 12.
The equations of circle 1 and circle 2 are respectively given as :
[tex](x-2)^2+(y-3)^2=4^2,\\\\(x-2)^2+(y-3)^2=12^2.[/tex]
These two circles are drawn on the graph as shown in the attached figure.
We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor
[tex]S=\dfrac{12}{4}=3.[/tex]
Thus, the two circles are similar.
There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag, without replacing the first one picked. The probability that both marbles will be yellow is 5 33 . How many YELLOW marbles are in the bag?
Answer:
B) 5
Step-by-step explanation:
The probability of picking yellow first is
x
12
. The probability of picking yellow second is
x-1
11
. This will give a solution of
x (x-1)
132
.
5
33
is equivalent to
20
132
. 5 and 4 are the only two consecutive numbers that when multiplied together equal 20. Therefore there are 5 yellow marbles in the bag.
Help. I need to explain if she’s right or not
To solve 5(2^x+4)=15, first divide each side by
Answer:5
Step-by-step explanation:
You are paid $8.50/hr at your part-time job. Your deductions are FICA (7.65%), federal tax withholding (9.15%), and state tax withholding (7.5%). Your travel expenses are $6.00 per day worked. You work 16 hours over a 4-day period of time. What is your net income after travel expenses?,
Why is the quotient of three divided by one-fifth different from the quotient of one-fifth divided by three?
The quotients are different because the order matters in division. When 3 is divided by 1/5 it becomes a multiplication problem with reciprocal of 1/5, yielding 15. However, when 1/5 is divided by 3, it becomes multiplication with reciprocal of 3 and yields 1/15.
Explanation:The reason that the quotient of three divided by one-fifth is different from the quotient of one-fifth divided by three is due to how division works in mathematics. To put it simply, the order of numbers in a division operation matters; it is not commutative like addition or multiplication.
When you divide 3 by 1/5, you're essentially asking, 'how many times does 1/5 fit into 3?'. Here, you're dealing with fractions and whole numbers. To perform the division, we multiply 3 by the reciprocal of 1/5, which is 5. The answer is 3 * 5 = 15.
But, when you divide 1/5 by 3, you're asking 'how many times does 3 fit into 1/5?'. Here, you need to multiply 1/5 by the reciprocal of 3, which is 1/3. The calculation is (1/5) * (1/3) = 1/15.
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What is the value of c such that x2 + 10x + c is a perfect square trinomial?
The value of c that makes x² + 10x + c a perfect square trinomial is c = 25.
What value of c makes the equation a perfect square trinomial?Given the equation in the question:
x² + 10x + c
A perfect square trinomial is of the form (ax² + bx + c), and it can be factored into (px + q)², where p and q are constants.
To find the value of c such that x² + 10x + c is a perfect square trinomial, we need to factor it as (px + q)².
Note that, the coefficient of x in the given trinomial is 10, so 2pq must equal 10.
Also, the coefficient of x² is 1, so p² must equal 1.
Hence, we have:
2pq = 10
p² = 1
From equation (2), we know that p could be either 1 or -1, after taking the square of both sides:
If p = 1, from equation (1) we have:
2pq = 10
2(1)q = 10
2q = 10
q = 10/2
q = 5
So, if p = 1 and q = 5, the perfect square trinomial is (x + 5)².
Let's expand to check:
(x + 5)² = x² + 10x + 25
Therefore, the value of c is 25.
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1. What is the simplest form of the radical expression? 4 fourth root of two x+ 6 fourth root of two x (1 point) 10fourth root of two x 10 fourth root of four x 20 fourth root of two x not possible to simplify,
Centered 7 meters above the ground, a Ferris wheel of radius 6 meters is rotating with angular speed 24 degrees per second.
a. Assuming that you begin at time t = 0 seconds at the lowest point on the wheel, find a formula that describes the distance h (in meters) from you to the ground after t seconds of riding.
b. At what times are you 10 meters above the ground? Please explain clearly how you got your solution.
simplify the expression. write the answer using scientific notation 4(6.2x10^11)
The correct answer is 2.48*10^12.
The supply and demand curves reflect data for a specific brand of sunglasses. Which circumstance best explains the shift of the demand curve from D to D1?
a. An ad campaign highlights the sustainable resources used to make the sunglasses.
b. Consumer reports indicate that the sunglasses break easily.
c. Fuel costs increase, making it more costly to produce the sunglasses.
d. Tax incentives encourage the producer to hire more workers.
Since there is a decrease in quantity and supply the answer would be Consumer reports indicate that the sunglasses break easily.
Answer "A" is definitely wrong
find the fraction
53*53−32*32/61*61−44*44
An unlabeled hierarchical diagram of various astronomical bodies is shown below. The labels A, B, C and D can be used to represent the galaxy, Mars, universe, moon, and solar system.
Part 1: Which four astronomical bodies would you choose to represent the four labels in the diagram?
Part 2: Explain why the hierarchical level D is different from the rest.
The four astronomical bodies represents here are A represents Universe, B represents Galaxy, C represents Solar System, and D represents Mars.
The hierarchical level D is different from the rest is because Mars is a planet and unlike all other astronomical bodies it does not hold other astronomical bodies with in it.
What are astronomical bodies?"Astronomical bodies are objects in space like sun, moon, planets, and stars. They form a part of the vast universe we live in and are very far from Earth."
What is Universe?"The universe includes all space, time, and their objects that also includes planets, stars, galaxies, and other forms of matter and energy."
What is Galaxy?"Galaxy is a vast collection of dust, gas, billions of stars with their solar systems that are all held together by gravity."
What is Solar System?"Solar System is a gravitationally bound system of eight planets, their moons in orbit round the sun with small bodies like comets, meteoroids, and asteroids."
What is Mars?"Mars is the fourth planet from the sun and the second smallest planet in the Solar System."
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what is the inverse of the function f(x) = 4x + 8 a. h(x) 1/4 x - 2
The inverse of the function will be, [tex]\rm y=\frac{1}{4} x-2[/tex]. Option A is correct. The function is obtained by rearranging the equation.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The given function is;
[tex]\rm f(x) = 4x + 8 \\\\ y=4x+8 \\\\[/tex]
After rearranging the equation, we get;
[tex]\rm x=4y+8 \\\\ y= \frac{1}{4} (x-8)\\\\ y=\frac{x}{4} -2\\\\ y=\frac{1}{4} x-2[/tex]
The inverse of the function will be, [tex]\rm y=\frac{1}{4} x-2[/tex].
Hence, option A is correct.
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1.Which explanation justifies how the area of a sector of a circle is derived?
Determine how many triangles can fit into a circle. Divide 360° by the number of triangles. Multiply the quotient by the area of the circle .
Calculate the area of the circle. Then, determine the central angle of the sector and divide this angle by 360° to get a fraction. Multiply the area of the circle by this fraction.
Determine the degree of the sector. Divide by 180° and then multiply it by the area of the triangle the sector is in.
Partition the circle into unit squares. Determine the area of the sector and multiply the area by the degree of the circle.