Answer:
A) Table:
Value of the sofa in dollars:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B) Multiply successively by 0.70
C) [tex]1,500(0.7)^t[/tex]: see the tests below
Explanation:
A) Find the missing values for the table shown
Although the table was not provided with the question, you can create a complete table from the supplied information.
Table: value of the sofa
Year Value
0 $1,500
1 A
2 B
3 C
4 D
Then, determine the missing values, i.e. A, B, C, and D
Notice that 30% is 0.30 and a reduction in the value is determined by mutiplying the starting value by 1 - 0.3 = 0.7.
A = $1,500 × 0.7 = $1,050.00B = $1,050 × 0.7 = $735.00C = $735 × 0.7 = $514.50D = $514.50 × 0.7 = $360.15Thus, once completed the table would be:
Year Value
0 $1,500
1 $1,050
2 $735
3 $514.50
4 $360.15
B. Explain how you found each of the missing values in the table.
I multiplied successively by 0.70 which is the constant decaying rate of the function.
C. Write an expression in the form [tex]a(b)^t[/tex] that represents the value of the sofa in dollars t years after Carlos purchased it. Then test your expression for t = 0, 1, 2, 3, and 4.
a is the purchasing value of the sofa or the value when t = 0: 1,500b is the decaying rate: 1 - 30% = 1 - 0.3 = 0.7Thus, the expression is:
[tex]1,500(0.7)^t[/tex]Test it for t = 0, 1, 2, 3, and 4:
1,500(0.7)⁰ = 1,500(1) = 1,500 [tex]\checkmark[/tex]1,500(0.7)¹ = 1500(0.7) = 1,050 [tex]\checkmark[/tex]1,500(0.7)² = 1,500(0.49) = 735 [tex]\checkmark[/tex]1,500(0.7)³ = 1500(0.343) = 514.5 [tex]\checkmark[/tex]1,500(0.7)⁴ = 1,500(0.2401) = 360.15 [tex]\checkmark[/tex]Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7 ?
The average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]
To find the average value of a function f(x) on a closed interval [a, b], we use the formula:
[tex]\[ \text{Average value} = \frac{1}{b - a} \int_{a}^{b} f(x) \, dx \]In this case, the function \( f(x) = 3x \sin(x) \) and the closed interval is \( 1 \leq x \leq 7 \).So, the average value of \( f(x) \) on the interval \( 1 \leq x \leq 7 \) is:\[ \text{Average value} = \frac{1}{7 - 1} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]
[tex]\[ \text{Average value} = \frac{1}{6} \int_{1}^{7} 3x \sin(x) \, dx \][/tex]
Now, we need to compute the integral. We can do this using integration by parts:
[tex]Let \( u = 3x \) and \( dv = \sin(x) \, dx \).Then, \( du = 3 \, dx \) and \( v = -\cos(x) \).Using the integration by parts formula:\[ \int u \, dv = uv - \int v \, du \]\[ \int_{1}^{7} 3x \sin(x) \, dx = \left[ -3x \cos(x) \right]_{1}^{7} - \int_{1}^{7} (-\cos(x)) \cdot 3 \, dx \][/tex]
[tex]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \int_{1}^{7} \cos(x) \, dx \]\[ = \left[ -3x \cos(x) \right]_{1}^{7} + 3 \left[ \sin(x) \right]_{1}^{7} \]\[ = \left[ -21 \cos(7) + 3 \sin(7) \right] - \left[ -3 \cos(1) + 3 \sin(1) \right] \][/tex]
Now, let's compute these values:
[tex]\[ \text{Average value} = \frac{1}{6} \left[ \left( -21 \cos(7) + 3 \sin(7) \right) - \left( -3 \cos(1) + 3 \sin(1) \right) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-21 \times 0.7539 + 3 \times 0.6560) - (-3 \times 0.5403 + 3 \times 0.8415) \right] \]\[ \text{Average value} = \frac{1}{6} \left[ (-15.8359 + 1.9680) - (-1.6209 + 2.5245) \right] \][/tex]
[tex]\[ \text{Average value} = \frac{1}{6} \left[ -13.8679 + 4.1454 \right] \]\[ \text{Average value} = \frac{1}{6} \times (-9.7225) \]\[ \text{Average value} \approx -1.6204 \][/tex]
So, the average value of f(x) = 3x sin(x) on the interval [tex]\( 1 \leq x \leq 7 \) is approximately \( -1.6204 \).[/tex]
The average value of [tex]\(f(x) = 3x \sin(x)\)[/tex] on the interval [tex]\(1 \leq x \leq 7\)[/tex] is approximately 1.879.
To find the average value of [tex]\( f(x) = 3x \sin(x) \)[/tex]on the closed interval [tex]\( 1 \leq x \leq 7 \)[/tex], we can use the formula for the average value of a function on a closed interval [a, b] :
[tex]\[ \text{Average value} = \frac{1}{b - a} \int_a^b f(x) \, dx \][/tex]
In this case, a = 1 and b = 7, so:
[tex]\[ \text{Average value} = \frac{1}{7 - 1} \int_1^7 3x \sin(x) \, dx \][/tex]
Now, we need to evaluate the integral:
[tex]\[ \int_1^7 3x \sin(x) \, dx \][/tex]
This integral can be evaluated using integration by parts or by using a software tool. After evaluation, we find that the average value is approximately 1.879.
So, the correct answer is 1.879.
Complete Question:
Let f be the function given by f(x)=3xsinx. What is the average value of f on the closed interval 1≤x≤7 ?
−14.764
−2.461
1.879
8.161
Finding the value of x
Use the given diagram to help answer the question.
Sam found a tent in his garage, and he needs to find
the center height. The sides are both 5 feet long, and
the bottom is 6 feet wide. What is the center height of
Sam's tent, to the nearest tenth?
X 3 feet
O
4 feet
5 feet
5 feet
5.5 feet
7.8 feet
6 feet
Intro
V Done
Answer:
4ft
Step-by-step explanation:
A) This is a Pythagorean Triple.
B) 3^2 +x^2=5^2
9+x^2=25
x^2=16
x=4
Answer:
It is 4
Step-by-step explanation:
d(1) = 1 / 12
d(n) = d(n – 1)*(-6)
What is the 4th term in the sequence?
Answer:
D(4) = -18
Step-by-step explanation:
D(n) = D(n – 1)(-6)
D(1) = 1/12
D(2) = D(2 – 1)(-6)
D(2) = D(1)(-6)
D(2) = 1/12 * (-6)
D(2) = -6/12
D(2) = -1/2
D(3) = D(3 – 1)(-6)
D(3) = D(2)(-6)
D(3) = -1/2 * (-6)
D(3) = 6/2
D(3) = 3
D(4) = D(4 – 1)(-6)
D(4) = D(3)(-6)
D(4) = 3 * (-6)
D(4) = -18
Answer:
D(4) = -18
Step-by-step explanation:
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A spherical ball of wax with a radius of 8 inches is melted and poured into a container shaped like a rectangular prism with a 14 inch x 16 inch base. What is the height of the melted wax in the new shape?
Answer:
9.57 inch
Step-by-step explanation:
(4/3)×pi×8³ = 14×16×h
h = (4/3)×pi×8³ ÷ (14×16)
h = 64pi/21 inch
Or, 9.57 inch (3 sf)
You have 42,784 grams of a radioactive kind of curium. If its half-life is 18 years, how much will be left after 72 years?
Answer:
2,674.14 g
Step-by-step explanation:
Recall that the formula for radioactive decay is
N = N₀ e^(-λt)
where,
N is the amount left at time t
N₀ is the initial amount when t=0, (given as 42,784 g)
λ = coefficient of radioactive decay
= 0.693 ÷ Half Life
= 0.693 ÷ 18
= 0.0385
t = time elapsed (given as 72 years)
e = exponential constant ( approx 2.7183)
If we substitute these into our equation:
N = N₀ e^(-λt)
= (42,787) (2.7183)^[(-0.0385)(72)]
= (42,787) (2.7183)^(-2.7726)
= (42,787) (0.0625)
= 2,674.14 g
Final answer:
After 72 years, which corresponds to 4 half-lives of the curium with a half-life of 18 years, the remaining amount of a 42,784 gram sample would be 2,674 grams, as it halves every 18 years.
Explanation:
The question asks how much of a radioactive sample of curium, with an initial mass of 42,784 grams and a half-life of 18 years, will remain after 72 years. To answer this, we apply the concept of radioactive decay, which follows a geometric sequence where the quantity of a radioactive substance halves every half-life period.
In this scenario, 72 years consist of 4 half-lives (since 72 ÷ 18 = 4). Therefore, after each half-life, the mass of the curium would be reduced by half. Following the sequence:
After 18 years, half of the 42,784 grams would remain, which is 21,392 grams.
After 36 years, half of that would remain, becoming 10,696 grams.
After 54 years, again half of that would remain, so 5,348 grams.
Finally, after 72 years, halving once more, we would be left with 2,674 grams.
The amount of curium remaining after 72 years is 2,674 grams.
47%
a) The ratio 20 minutes to 1 hour can be written in the form 1: n.
Find the value of n. n =
Answer:
1hr=60minutes
ATQ,20 minutes/60 minutes=1/n
1/3=1/n
so the value of n is 3...
Step-by-step explanation: Hope i helped please give brainliest!
simply 11a+7+10a+3+12a+9 by combining like terms
Answer: 33a+19
Step-by-step explanation:
11a+7+10a+3+12a+9
Collect like terms.
(11a+10a+12a)+(7+3+9)
Simplify.
33a+19
Answer:
33a+9
Step-by-step explanation:
11a+10a+12a= 33a
7+3+9= 19
LMNP is a rectangle. Find the value of x and the length of each diagonal.
LN = 6x + 1 and MP = 9x-5
Final answer:
To find the value of x, set the two expressions for the lengths of the sides of the rectangle equal to each other and solve. The value of x is 2. To find the length of each diagonal, use the Pythagorean Theorem with the lengths of the sides of the rectangle. The length of each diagonal is 13 * sqrt(2).
Explanation:
To find the value of x, we can set the two expressions for the lengths of the sides of the rectangle equal to each other, since opposite sides of a rectangle are congruent. So, we have:
6x + 1 = 9x - 5
To solve for x, we can subtract 9x from both sides and add 5 to both sides:
1 + 5 = 9x - 6x
6 = 3x
x = 2
Therefore, the value of x is 2. To find the length of each diagonal, we can use the Pythagorean Theorem. The diagonal of a rectangle acts as the hypotenuse of a right triangle formed by the sides of the rectangle. In this case, the length of one side is 6x + 1, and the length of the other side is 9x - 5. So, the length of each diagonal is:
d = sqrt((6x + 1)^2 + (9x - 5)^2)
d = sqrt((6(2) + 1)^2 + (9(2) - 5)^2)
d = sqrt(13^2 + 13^2)
d = sqrt(2 * 13^2)
d = 13 * sqrt(2)
what must be the length of ZY in order for ZY to be tangent to circle X at point Y?
To determine the length of ZY for it to be a tangent to circle X at point Y, we must know additional measurements, such as the radius of the circle, because a tangent is perpendicular to the radius at the point of tangency.
Explanation:To determine the length of ZY so that it is tangent to circle X at point Y, we need to apply properties of tangents to a circle. A tangent to a circle forms a right angle with the radius at the point of tangency. Therefore, in a right-angled triangle, with the radius XY being one side and ZY being the hypotenuse, we could use the Pythagorean theorem if we know the length of the radius and any other segment connected to the radius or tangent.
Without further information, such as the length of radius XY or any other segment, it's not possible to calculate the exact length of ZY. However, the essential condition is that radius XY must be perpendicular to the tangent ZY at point Y for ZY to be a proper tangent.
How do you solve and graph inequalities
Well, there can be three different steps.
Rearrange the equation so "y" is on the left and everything else on the right.
Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>)
Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).
Solve by finding square roots.
5x² - 400
-13.5
-$2.52
-2/2, 2/2
-2/3,283
Answer:
See explanation
Step-by-step explanation:
Let the given equation be:
[tex]5 {x}^{2} - 400 = 0[/tex]
This implies that:
[tex]5 {x}^{2} = 400[/tex]
Divide through by 5 to get;
[tex] {x}^{2} = 80[/tex]
Take square root to obtain:
[tex]x = \pm \sqrt{80} [/tex]
This implies that
[tex]x = \pm4 \sqrt{5} [/tex]
[tex]x = - 4 \sqrt{5} \: or \: x = 4 \sqrt{5} [/tex]
Which values are solutions to the inequality below? Check all that apply.
Answer:
b,d
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given that
x²>18
So, let take the square root of both sides
Then,
√x²>√18
x> ± 4.24
So it is either
x>4.24 or x<-4.24
Either of the two will gives a square higher than 18. You should note that the square of any number is always positive.
The applicable answer are
A. 5
Because
5²=25 which is greater than 18
D. 8
Because
8²= 64 which is greater than 18
F. -18
Because
(-18)²=-18×-18=324 which is greater than 18.
Note : -×-=+
Solve for x.
8/15
15/8
24/5
Answer:15/8
Step-by-step explanation:
Answer:
15/8
Step-by-step explanation:
Cross multiply, 8x=15. Divide by 15 on both sides, 15/8 is your answer.
1 3/4 - 2 + -4 3/4
What is the answer
Answer:
[tex]\frac{-19}{2}[/tex]
Step-by-step explanation:
[tex]\frac{5}{4}[/tex] + [tex]\frac{-43}{4}[/tex] = [tex]\frac{-19}{2}[/tex]
Help ASAP I’ll give you brainliest
Answer:
-2/3
[tex]\sqrt50[/tex]
-1
-2.3145
Step-by-step explanation:
Answer:
-2/3
\sqrt50
-1
-2.3145
Step-by-step explanation:
please brainlist!
what integer represents a loss of $20
In math, a loss of $20 is represented by the negative integer -20. The negative in front of the 20 represents the loss or decrement.
Explanation:In mathematics, integers are whole numbers that can be either positive, negative, or zero. When we talk about a loss or decrement of something, it's universally symbolized with a negative integer.
In case of a loss of $20, it is represented as -20, where the negative sign indicates the loss or subtraction of money.
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It takes half of a yard of ribbon to make a bow. How many bows
can be made with 5 yards of ribbon?
Answer:
10 bows
Step-by-step explanation:
Each bow is 0.5 yards and you have 5 yards of ribbon. In equation form (where x = number of bows), that looks like: 0.5 * x = 5. Solve for x and you'll get x = 10.
This mathematics problem can be solved by multiplication. Since each bow requires half a yard of ribbon, each yard can produce two bows. Therefore, five yards of ribbon can produce 10 bows.
Explanation:The question requires us to determine how many bows we can make with a given number of yards of ribbon. Since it takes half a yard of ribbon to make a bow, you can fit two bows in a single yard. To find how many bows can be made with 5 yards, you can perform multiplication.
To do this, you would multiply the number of yards by 2, since each yard can create two bows: 5 yards × 2 = 10 bows. So, you can make 10 bows out of 5 yards of ribbon.
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The length of a room is 2 feet more then the width. If the area of the room is 120 ft what is the length and the width of the room
Simplify 5a-2(-3a +b).
Steps to solve:
5a - 2(-3a + b)
~Distribute
5a + (-2 * -3a) + (-2 * b)
~Simplify
5a + 6a - 2b
~Simplify
11a - 2b
Best of Luck!
PLS HELP
What is the volume of the right rectangular prism shown?
A. 8 un3
B. 20 un3
C. 24 un3
D. 12 un3
The volume of the given rectangular prism is option C. [tex]24 un^{3}[/tex].
Step-by-step explanation:
Step 1:
The dimensions of the given rectangular prism are 4 units × 3 units × 2 units.
So we take the length equals 4 units, the width is equal to 3 units and the height is 2 units.
Step 2:
The volume of this rectangular prism is calculated by multiplying the given prism's length, its width, and its height.
The Volume of the given rectangular prism = [tex]( Length) (Width) (Height) = (4units) (3units) (2 units) = 24 unit^{3} .[/tex]
So the given right rectangular prism's volume is [tex]24 unit^{3}[/tex] which is option C.
What is the exact circumference of the circle?
A. 10 feet
B. 20 feet
C. 40 feet
D. 60 feet
Answer:
60ft
Step-by-step explanation:
you havent multiplied it by [tex]\pi[/tex] yet do it would just be the radius multiplied by two so it would be 60, becuase the radius is 30.
C= 2[tex]\pi[/tex]r
when Sami showed her mother her shape picture. Mrs. Harper decided she would glue the pieces
on a white mounting board and frame the puzzle so Sami could hang it in her room. The mounting
board is 12 inches by 15 inches and there will be a colored mat on top of the mounting board that
Trames the letter S, which will be placed in the center of the mat and board. The mat is 1.5 inches
on all sides.
zin
1. What is the area of each square?
Answer:
[tex]2.25\ in^{2}[/tex]
Step-by-step explanation:
Area of a square is given by
[tex]A=b*b=b^{2}[/tex]
Where A is area and b is the length of any side. This question has only one thing that is square in shape, the mat hence the question directly requires its area.
Given that the mat has square shape and has dimensions of 1.5 in each then the area will be
A=1.5*1.5=2.25 square inches
Therefore, the area is 2.25 square inches.
Answer:
Step-by-step explanation:
Stefan spent a third of his weekly allowance on clothes. To earn more money his parents let him wash the car for $5. Write and solve a two-step equation to determine his weekly allowance if he ended with $29. *Hint: start with: b/.... +....... =.......
Answer:
$36
Step-by-step explanation:
The amount spent on cloths is 1/3
The amount earned from washing the car is $5
Amount at the end of the week is $29
Let the amount earned that week be x
Then amount spent on cloths = 1/3x
so the equation is
x- 1/3 x+$5=$29
2/3 x=29-5
2/3 x= 24
x=(24*3)/2= $36
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts? A 2/9 pie B. 4/9 pie C. 1 1/4 pies D. 2 1/4 pies
Answer:
D. 2 1/4
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
9 pies/4 friends =
9/4 = 2 1/4
D
what is 300 times 500
Answer:
150000
Step-by-step explanation:
Answer:
150,000
Step-by-step explanation:
If 3x−y=12, what is the value of 8x 2y?
A) 212
B) 44
C) 82
D) The value cannot be determined from the information given.
Answer:
D
Step-by-step explanation:
To find two unknowns, you need atleast two different equations.
Last questions for my last 15 pts.
Step-by-step explanation:
[tex] {6}^{2} - 10 \\ = 36 - 10 \\ = 26 \\ so \: kurt \: forgot \: to \: write \: units \: place \: \\ number \: 6 \: after \: 2.[/tex]
The large sphere has a diameter of 12 feet. What is the volume of the shaded figure? Express the answer in terms of π.
252π ft3
261π ft3
288π ft3
324π ft3
Answer:
The Answer is A. 252π ft3
Step-by-step explanation:
Hence volume of shaded sphere is [tex]113.09734ft^{2}[/tex]
What is Volume?
Volume refers to part inside 3 d figure which tell how much space it occupies.
How to solve?
Given two concentric spheres one with D=12 ⇒ R= 6 feet other with r=3feet.
volume of shaded part[tex]=\frac{4}{3} \pi R^{3}-\frac{4}{3} \pi r^{3}[/tex]
[tex]=\frac{4}{3} \pi (R-r)^{3}[/tex]
[tex]=\frac{4}{3} \pi 3^{3}[/tex]=[tex]113.09734[/tex][tex]ft^{2}[/tex]
Hence volume of shaded sphere is [tex]113.09734ft^{2}[/tex]
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If it takes 8 hours for Sanya to build a fence, and it takes 6 hours for Sean to build the same fence, how long will it take them working together?
Answer:
3 3/7 hours
Step-by-step explanation:
(8×6)/(8+6) = 48/14 = 3 3/7 hours
What is the volume of a cone with the height of 5.5 and a radius of 4
Answer:
29.33π cm³ or 92.10 cm³
Step-by-step explanation:
To find the volume of a cone with height 5.5 and radius 4, we will simply use the formula;
volume of a cone = [tex]\frac{1}{3}[/tex] π r² h
h = 5.5 and r= 4, we will simply plug in these values into our formula
volume of a cone = [tex]\frac{1}{3}[/tex] × π × (4)² (5.5)
= [tex]\frac{1}{3}[/tex] ×π × 16 × 5.5
=88π / 3
=29.33π
volume of cone = 29.33π
But π= 3.14
plugging in π=3.14, we have;
volume of cone = 29.33(3.14)=29.10
Answer:
88/3
Step-by-step explanation:
i just did the assignment