Answer:
$4
Step-by-step explanation:
10x = 8(x+1)
2x = 8
x = 4
Answer:
40 dollars
Step-by-step explanation:
We can say
x=amount each friend has to pay
Then, the price of the gift would be 10x because there are 10 friends and each pays x dollars. But since two friends dropped out, it will now become 8x. Also, each of the 8 friends has to pay an extra dollar to go back to the original amount, so 8x+8 is also the price of the gift. We set these two expressions equal to each other (because they both represent the price of the gift) so
10x=8x+8. Using the subtraction property of equality (which says if a=b, then a-c=b-c) we subtract 8x from both sides to get
2x=8. Using the division property of equality (which says if a=b, then a/c=b/c) we divide by 2 on both sides to get x=4. But the question asked how much money they planned to collect, or what was the price of the gift, which is 10x, 10*4=40, 40 dollars.
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]
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.
Plz help ASAP :))))
David is planning a party outside. He googles the weather for that particular day and it says there is a 58% chance of rain. Is it likely to rain or not likely to rain?
A:likely
B:Not likely
Answer:
It would be A:likely
Step-by-step explanation:
let's take rounding decimals for example; when you 5.86 and you were rounding to the nearest tenth it would be 5.9. That is because the 6 is greater than 5, so for the weather the highest the percentage it can be is 100% and 50% is half and since it is more than half then it would be more likely.
what is 300 times 500
Answer:
150000
Step-by-step explanation:
Answer:
150,000
Step-by-step explanation:
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
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.
Learn more about Math Problems here:https://brainly.com/question/32830508
#SPJ2
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
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.
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:
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
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
What is the length and width of a rectangle given by the trinomial r squared - 6r- 55? Use factoring
The length of the rectangle is 11 units
The width of the rectangle is 5 units.
Explanation:
The equation of the trinomial is [tex]r^{2}-6 r-55[/tex]
We need to find the length and the width of the rectangle.
The length and width of the rectangle can be determined by factoring the trinomial [tex]r^{2}-6 r-55=0[/tex]
Factoring using the quadratic formula, we have,
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
where [tex]a=1, b=-6[/tex] and [tex]c=-55[/tex]
Substituting these in the above formula, we have,
[tex]r=\frac{-(-6) \pm \sqrt{(-6)^{2}-4 \cdot 1(-55)}}{2 \cdot 1}[/tex]
[tex]r=\frac{6\pm \sqrt{36+220}}{2}[/tex]
[tex]r=\frac{6\pm \sqrt{256}}{2}[/tex]
[tex]r=\frac{6\pm 16}{2}[/tex]
Hence, the two roots of the trinomial are
[tex]r=\frac{6+ 16}{2}[/tex] and [tex]r=\frac{6- 16}{2}[/tex]
Solving [tex]r=\frac{6+ 16}{2}[/tex] , we get,
[tex]r=\frac{22}{2}[/tex]
[tex]r=11[/tex]
Solving [tex]r=\frac{6- 16}{2}[/tex] , we get,
[tex]r=\frac{-10}{2}[/tex]
[tex]r=-5[/tex]
Thus, the solutions of the trinomial are 11 and -5
Since, the length of the rectangle is larger than the width, the length of the rectangle is 11 units.
Also, the width of the rectangle cannot be negative.
Thus, ignoring the negative sign, we have, [tex]r=5[/tex]
Hence, the width of the rectangle is 5 units.
the 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?
Answer:
[tex]\large \boxed{2}[/tex]
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.
[tex]\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}[/tex]
Check:
[tex]\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}[/tex]
It checks.
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
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.
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]
Learn more about volume
https://brainly.com/question/26402559
#SPJ2
What is the difference of the two polynomials?
(92+8)–(22+3)
Answer:
75
Step-by-step explanation:
(92+8)-(22+3)
Add the terms inside of the parentheses because of PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction)
(100)-(25)
Then subtract 25 from 100
75
Can this be simplified?
Answer:
0.2+sqrt3/10
Step-by-step explanation:
Ⓗⓘ ⓣⓗⓔⓡⓔ
Well, if I'm reading it correctly, it could be simplified to (1/5)+(sqrt3/10) or 0.2+sqrt3/10.
(っ◔◡◔)っ ♥ Hope this helped, have a great day! ♥
˜”*°•.˜”*°• ~Star •°*”˜.•°*”˜
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)
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]
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!
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.
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:
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!
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≤).
what is c- 1/2 + 16=36
Answer:
20 1/2
Step-by-step explanation:
its 20 and a half because 16+20=36 and you just need to add a half to 20 since your taking it away
Answer:
c=20.5 or 41/2
Step-by-step explanation:
c- 1/2 + 16=36
Make C the subject
c=36-16+1/2
c=20+1/2
Using LCM
c=(40+1)/2
c=41/2
c=20.5
To check if we are correct, we substitute c with 41/2. and then both sides of the equation must be equal
c- 1/2 + 16=36
41/2-1/2+16=36
20+16=36
36=36
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.