Answer:
[tex]\large\boxed{the\ radius\ R=\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The formula of a volume of a sphere:
[tex]V=\dfrac{4}{3}\pi R^3[/tex]
We have
[tex]V=\dfrac{1}{6}\pi[/tex]
Substitute:
[tex]\dfrac{4}{3}\pi R^3=\dfrac{1}{6}\pi[/tex] divide both sides by π
[tex]\dfrac{4}{3}R^3=\dfrac{1}{6}[/tex] multiply both sides by 3
[tex]3\!\!\!\!\diagup^1\cdot\dfrac{4}{3\!\!\!\!\diagup_1}R^3=3\!\!\!\!\diagup^1\cdot\dfrac{1}{6\!\!\!\!\diagup_2}[/tex]
[tex]4R^3=\dfrac{1}{2}[/tex] divide both sides by 4
[tex]R^3=\dfrac{1}{2}:4\\\\R^3=\dfrac{1}{2}\cdot\dfrac{1}{4}\\\\R^3=\dfrac{1}{8}\to R=\sqrt[3]{\dfrac{1}{8}}\\\\R=\dfrac{\sqrt1}{\sqrt8}\\\\R=\dfrac{1}{2}[/tex]
What are the ratios for sin A and cos A? The diagram is not drawn to scale.
Answer:
sinA=15/17 and cosA=8/17
Step-by-step explanation:
sine is opposite side over hypotenuse and cosine is adjacent side over hypotenuse
Answer:
sin A = [tex]\frac{15} {17} [/tex] and cos A =[tex] \frac{8}{17}[/tex]
Step-by-step explanation:
We are given a right angled triangle and we are to determine the ratios for sin A and cos A.
Sin is the ratio of perpendicular/hypotenuse while cos is the ratio of base/hypotenuse.
With respect to angle A, base = 8, perpendicular = 15 and hypotenuse = 17.
Therefore, [tex]sin A = \frac{15}{17}[/tex] and [tex]cos A = \frac{8}{17}[/tex].
PLEASE ANSWER RIGHT AWAY
Answer:
The 3rd sequence could not be described by the following recursive definition tn+1 = tn + 6
Step-by-step explanation:
* Lets revise the recursive formula
1. Determine if the sequence is arithmetic (Do you add, or subtract, the
same amount from one term to the next?)
2. Find the common difference. (The number you add or subtract.)
3. Create a recursive formula by stating the first term, and then stating
the formula to be the previous term plus the common difference.
a1 = first term;
an+1= an + d
- Where:
# a1 = the first term in the sequence
# an = the nth term in the sequence
# an+1 = the term after the nth term
# n = the term number
# d = the common difference.
* Now lets solve the problem
∵ tn+1 = tn + 6
∴ d = 6 ⇒ common difference
- The 1st sequence 5 , 11 , 17 , 23 , 29 , .... has common difference 6
- The 2nd sequence 0 , 6 , 12 , 18 , 24 , .... has common difference 6
- The 3rd sequence 6 , 9 , 12 , 15 , 18 , .... has common difference 3
∴ This sequence could not be described by the following recursive
definition tn+1 = tn + 6
* The 3rd sequence could not be described by the following recursive
definition tn+1 = tn + 6
A grocer wishes to blend two different coffee brands in order to make a blend of 400 pounds to sell at $3.00 a pound. If he uses a brand of coffee worth $2.70 a pound with another brand worth $3.20 a pound, how many pounds of each does he use?
Step-by-step explanation:
Let's say x is the amount of $2.70/lb coffee and y is the amount of $3.20/lb coffee.
The total amount is:
x + y = 400
The total worth is:
2.70x + 3.20y = 3.00×400
2.7x + 3.2y = 1200
Solving the system of equations through substitution:
x = 400 - y
2.7 (400 - y) + 3.2y = 1200
1080 - 2.7y + 3.2y = 1200
0.5y = 120
y = 240
x = 160
The grocer uses 160 pounds of the $2.70/lb coffee and 240 pounds of the $3.20/lb coffee.
By solving a system of equations, we will see that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.
How to find the system of equations?First, we need to define the variables, we can use:
x = pounds of the $2.70 coffee used.y = pounds of the $3.20 coffee used.We know that they make 400 pounds of the mixture, then:
x + y = 400
We also know that the price of the mixture is $3.00 per pound, then we will have that:
x*$2.70 + y*$3.20 = 400*$3.00
So the system of equations is:
x + y = 400
x*$2.70 + y*$3.20 = 400*$3.00
To solve this, we isolate one of the variables in one of the equations. For example, I will isolate x on the first equation:
x = 400 - y
Now we can replace that on the other equation to get:
(400 - y)*$2.70 + y*$3.20 = 400*$3.00
And solve this for y.
400*$2.70 - y*$2.70 + y*$3.20 = 400*$3.00
y*$0.50 = 400*$3.00 - 400*$2.70 = 400*$0.30
y = ( 400*$0.30)/$0.50 = 240
Then we have:
x = 400 - y = 400 - 240 = 160
This means that they used 240 pounds of the $3.20 coffee and 160 pounds of the $2.70 coffee.
If you want to learn more about systems of equations, you can read:
https://brainly.com/question/13729904
what are the coordinates of the midpoint between (3,-7) and (-5,2)?
Step-by-step explanation:
3- -5 equals 8. 8/2 equals 4. 4 plus -5=-1. so the x coordinate=-1.
2- -7=5. 5/2=2.5. 2.5+-5=2.5. so the y coordinate= 2.5. so the full set of coordinates= -1,-2.5
What is the equation for f-1(x)? Help needed 10 points math 3!!!
ANSWER
A.
[tex] {f}^{ - 1} (x) = 4x - 3[/tex]
EXPLANATION
Given
[tex]f(x) = \frac{x + 3}{4} [/tex]
Let
[tex]y= \frac{x + 3}{4} [/tex]
Interchange x and y
[tex]x= \frac{y + 3}{4} [/tex]
Solve for y,
[tex]4x = y + 3[/tex]
y=4x-3
This implies that,
[tex] {f}^{ - 1} (x) = 4x - 3[/tex]
is y=4/5 proportional
Just by itself? No it is not.
Name the polynomial based on its degree and number of terms
X to the 2nd power +2-4x
Answer:
Second degree trinomial.
Step-by-step explanation:
Help! Will mark you the brainiest
Answer:
+14.9%
Step-by-step explanation:
From 74 to 85 hours is a positive change of 11 (an increase).
Calculate 11/74: It is 0.1486.
Multiplying this by 100% yields 14.9%.
The increase from 74 hours to 85 hours is 14.9% in magnitude.
Answer:
From 74 hours to 85 hours is approximately 15%. It is an increase.
Step-by-step explanation:
Subtract 85-74 and it'll be 11. From there, divide 11 by 74 and you'll get 0.1486... . Move the decimal place two space to the right and round the 8 to the nearest whole number. Since 8 is greater than 5, you will then round it to 15%.
a flagpole casts a shallow that is 40 feet long
Check the picture below.
If 9999 = 4, 8888 = 8, 1816 = 6, 1212 = 0, then 1919=??
Answer:
2
Step-by-step explanation:
9999 = 4, so each 9 has a value of 1.
8888 = 8, so each 8 has a value of 2.
1212 = 0, so each 1 and 2 has a value of 0.
1816 = 6, so 6 has a value of 4.
Therefore, 1919 = 0 + 1 + 0 + 1 = 2.
50 POINTS
Triangle ABC and triangle CDE are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of CE?
A)
6 − 2
9 − 3
=
8 − 6
12 − 9
B)
6 − 2
9 − 3
=
12 − 6
8 − 9
C)
8 − 6
9 − 3
=
6 − 2
12 − 9
D)
9 − 3
6 − 2
=
8 − 6
12 − 9
Answer:
B
Step-by-step explanation:
3,2
9,6
(6-2)/(9-3)
Answer:
The answer is B
Step-by-step explanation:
6-2
9-3
=
12-6
8-9
what is the distance between the points (-6, 7) and (-1, 1) ? Round to the nearest whole number
Answer:
7.8 rounded to the nearest whole number would be 8.
Step-by-step explanation:
-6 would be x1
7 would be y1
-1 would be x2
1 would be y2
Take these numbers and plug them into the distance formula:
[tex]\sqrt{(x2-x1)^{2} + (y2-y1)^2}[/tex]
[tex]\sqrt{(-1 - -6)^2 + (1-7)^2} \\\sqrt{(5)^2 + (6)^2\\\} \\\sqrt{25 + 36} \\\sqrt{61} = 7.81[/tex]
find each sum of difference. (6x^2+3x+1)-(2x^2-4x+5)
Subtract the like terms:
6x^2 - 2x^2 = 4x^2
3x - -4x = 3x+4x = 7x
1 - 5 = -4
Now combine them to get the final answer:
4x^2 + 7x - 4
you have a $20 bill. If you buy 24 pensa and 12 pencils, you will get $1.40 change. If you buy 12 pens and 24 pencils, you will get 4.40 change. How much does each pen and each pencil cost
Answer:
The cost of a pen is $0.60 and the cost of a pencil is $0.35
Step-by-step explanation:
Let
x-----> the cost of a pen
y----> the cost of a pencil
we know that
24x+12y=20-1.40
24x+12y=18.60 -----> equation A
12x+24y=20-4.40
12x+24y=15.60 -----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
The solution is the point (0.60,0.35)
see the attached figure
therefore
The cost of a pen is $0.60
The cost of a pencil is $0.35
5. Kalen is trying to find the average of three measurements. The measurements are 13.8, 15.64, and 22.51. He adds the
numbers and divides by three. The result on the calculator shows 17.3167. Where should Kalen round? Explain.
he should round to the hundredths place so 17.32
Answer:
Karen should round to hundredth place.
Step-by-step explanation:
We are given that Kalen is trying to find the average of three measurements.
The measurements are 13.8, 15.64, and 22.51.
Now we are given that He adds the numbers and divides by three. The result on the calculator shows 17.3167
Now we are asked Where should Kalen round the final answer.
Since the values in the given data is upto hundredth place
So, we are supposed to round the final answer to hundredth place.
So, final answer after round off = 17.32
Hence Karen should round to hundredth place.
Which of the following expressions is not equivalent to -4.5x-8
A. (8)(-4.5)
B. 8x4.5
C. -8x -4.5
D. (4.5)(8)
ANSWER
A. (8)(-4.5)
EXPLANATION
The given expression is
[tex] - 4.5 \times - 8[/tex]
We evaluate this to obtain:
[tex]- 4.5 \times - 8 = 36[/tex]
For option A
[tex](8) \times - 4.5 = - 36[/tex]
For option B
[tex]8 \times 4.5 = 36[/tex]
For option C,
[tex] - 8 \times - 4.5 = 36[/tex]
For option D
[tex](4.5)(8) = 36[/tex]
The odd one is option A.
The correct answer is A.
A because it would become negative while the rest become positive.
How much interest does a $482 investment earn at 5% over 3 years?
Answer: $72.30
Step-by-step explanation:
[tex]I=P*r*t[/tex]
P is the principal amount, $482.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 3 years
The answer you're looking for is $72.30. To find this answer multiply $482 by 0.05 (five percent). From there you'll get 24.1, then multiply that by 3 (three years), and you'll get $72.30/ Hope that helps! :)
What is the sum of the polynomials? (6x + 7 + x2) + (2x2 - 3)
Answer:
3x^2+6x+4 is the answer :D
The sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.
What is polynomial?Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have given polynomials:
= (6x + 7 + x²) + (2x² - 3)
To add the polynomials, we must add the like terms:
= 3x² + 6x +4
Thus, the sum of the polynomials (6x + 7 + x²) + (2x² - 3) is 3x² + 6x +4 after adding the like terms.
Learn more about Polynomial here:
brainly.com/question/17822016
#SPJ2
Find the 25th term of the sequence -1, 2, 5, 8
Answer:
71
Step-by-step explanation:
This is an arithmetic sequence with n th term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here d = 2 - (- 1) = 5 - 2 = 8 - 5 = 3 and a₁ = - 1, so
[tex]a_{25}[/tex] = - 1 + (24 × 3) = - 1 + 72 = 71
The price of a computer was decreased by 30% to £147. What was the price before the decrease?
Answer:
£210
Step-by-step explanation:
A decrease of 30% represents 70% of the original cost.
100% represents the original cost
Divide the price by 70 to find 1% then multiply by 100 for original cost
original cost = [tex]\frac{147}{70}[/tex] × 100 = 2.1 × 100 = £210
Answer:
210
Step-by-step explanation:
let original price =x
x×70÷100=147
x=147×100÷70=210
whats an exponent and how is it used an mathematics
Answer: a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression
Step-by-step explanation:
for example
10 x 10 = 100
to simplify this you put a small 2 on the top right corner of the number 10
Final answer:
An exponent, or a power, is mathematical shorthand for repeated multiplications. It is used to multiply a number by itself a certain number of times.
Explanation:
An exponent, or a power, is mathematical shorthand for repeated multiplications. For example, the exponent "2" means to multiply the base for that exponent by itself (in the example here, the base is "5").
5² = 5 x 5 = 25
The exponent is "2" and the base is the number "5." This expression (multiplying a number by itself) is also called a square. Any number raised to the power of 2 is being squared. Any number raised to the power of 3 is being cubed.
Can you help me answer this
Answer:
Step-by-step explanation:
so wa
Find the solution:
16x-18=2y
4x+9=y
x=____
y=____
Answer:
[tex]x=\frac{9}{2}[/tex] and [tex]y=27[/tex]
Step-by-step explanation:
A system of linear equations is a set of (linear) equations that have more than one unknown. The unknowns appear in several of the equations, but not necessarily in all of them. What these equations do is relate the unknowns to each other.
We need to find the solution of the follow equations:
[tex]16x-18=2y[/tex] and [tex]4x+9=y[/tex]
First, we divided by 2 the equation [tex]16x-18=2y[/tex]
We obtain [tex]8x-9=y[/tex]
Equating both equations
[tex]8x-9=4x+9[/tex]
Let's clear x
[tex]8x-4x=9+9\\4x=18\\x=\frac{18}{4} \\x=\frac{9}{2}[/tex]
Substituting the value of x in the second equation
[tex]4(\frac{9}{2}) +9=y\\y=\frac{36}{2} +9=18+9\\y=27[/tex]
.
which expression is equivalent to the product 2x(x+2) (x-3)? A. 12x to the third - 12x ) B. 2x to the third - 4x squared - 6) C. 2x to the third - 2x squared -10x ) D. 2x to the third - 2x squared -12x
Answer:
Option 4 is the correct option.
Step-by-step explanation:
We need to solve the expression 2x(x+2)(x-3)
Multiplying the terms with each other we get,
[tex]2x(x+2)(x-3)\\=2x(x^2 -3x+2x-6)\\=2x(x^2 -x -6)\\=2x^3 -2x^2 -12x[/tex]
Option 4 is the correct option.
A decagon has angles that measure 156°, 135°, 147°, 160°, 116°, 150°, 150.2°, 119.2°, 146.6°, and z. What is z?
bearing in mind that the sum of all interior angles in a polygon is
180(n - 2) n = number of sides in the polygon
a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.
[tex]\bf 156+135+147+160+116+150+150.2+119.2+146.6+z=1440 \\\\\\ 1280+z=1440\implies z=1440-1280\implies z=160[/tex]
Final answer:
The angle z in the decagon is calculated by subtracting the sum of the given angles from the total interior angle sum of a decagon, which is 1440°. The measure of angle z is 159.8°.
Explanation:
In geometry, the sum of the interior angles of an n-sided polygon is given by the formula (n - 2) × 180°. For a decagon, which is a 10-sided polygon, this sum is (10 - 2) × 180° = 8 × 180° = 1440°. To find the measure of the unknown angle z in the decagon with the given angle measurements, we can subtract the sum of the known angles from this total.
First, let's add up the given angles: 156° + 135° + 147° + 160° + 116° + 150° + 150.2° + 119.2° + 146.6° = 1280.2°. Now, subtract that sum from the total sum of the angles for a decagon: 1440° - 1280.2° = 159.8°. Therefore, the measure of angle z is 159.8°.
Given f(x) = 6x + 9 and g(x) = X^4, choose
the expression for (fºg)(x).
Answer:
(fºg)(x) = [tex]6x^{4}+9[/tex]
Step-by-step explanation:
We have been given the following two functions;
f(x) = 6x + 9
g(x) = X^4,
We are then required to determine the expression for (fºg)(x). (fºg)(x) denotes a composite function f[g(x)] which is obtained by
substitute g(x) in place of x in f(x)
(fºg)(x) = 6[g(x)] + 9
(fºg)(x) = 6X^4 + 9
find the surface area of a cone with 9 in radius and 13 in height
[tex]\bf \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=9\\ h=13 \end{cases}\implies SA=\pi (9)\sqrt{9^2+13^2}+\pi (9)^2 \\\\\\ SA=9\pi \sqrt{250}+81\pi \implies SA=9\pi (\sqrt{250}+9)\implies SA\approx 701.53[/tex]
Simplify the expression below -3(10x + 4y) + 6(6x − 2y)
Answer:
6x - 24y
Explanation:
Expand -3(10x + 4y): -30x - 12y
= [tex]\bold{-30x-12y+6\left(6x-2y\right)}[/tex]
Simplify [tex]\bold{-30x-12y+6\left(6x-2y\right): \ 6x-24y}[/tex]
= 6x - 24y
Mordancy.
For this case we must simplify the following expression:
[tex]-3 (10x + 4y) +6 (6x-2y)[/tex]
We apply distributive property to the terms of the parenthesis, taking into account that:
[tex]- * - = \\- * + = -[/tex]
So, we have:
[tex]-30x-12y + 36x-12y =[/tex]
We add similar terms:
[tex]-30x-12y + 36x-12y =[/tex]
Equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:
[tex]6x-24y[/tex]
ANswer:
[tex]6x-24y[/tex]
The table shows the results of a survey on people’s favorite fruit. What percent of the people chose strawberry as their favorite fruit? Round to the nearest tenth percent.
Favorite Fruit
Number of People
Apple
17
Orange
10
Banana
17
Pear
3
Strawberry
15
Question 13 options:
27.4%
20.8%
24.2%
16.1%
Answer:
24.2%
Explanation:
The percentage of people choosing strawberry can be calculated as follows:
[tex]Percentage = \frac{PeopleChoosingStrawberry}{TotalNumberOfSurveyedPeople} * 100[/tex]
We have:
Number of people choosing strawberry = 15 people
Total number of surveyed people = 17 + 10 + 17 + 3 + 15 = 62 people
Substitute in the above rule to get the percentage as follows:
[tex]Percentage = \frac{15}{62}*100 = 24.19 = 24.2[/tex]%
Hope this helps :)
15 ft
7 ft
144
20 ft
III. Solve.
(10) A bedroom is 15 ft long and 12 ft wide.
How much will it cost to carpet the room
if carpeting costs $22 per square yard?
(1 yd = 3 ft)
......... ANSW
...........
It will cost $440 to carpet the room.
To find the cost of carpeting the room, we need to calculate the area of the room in square yards.
First, let's convert the dimensions of the room from feet to yards:
15 ft = 5 yd (since 1 yd = 3 ft, 15 ft = 5 yd)
12 ft = 4 yd
Next, calculate the area of the room in square yards:
Area = Length x Width = 5 yd x 4 yd = 20 square yards
Finally, multiply the area by the cost per square yard:
Cost = Area x Price
= 20 x $22/square yard
= $440
Complete question
A bedroom is 15 ft long and 12 ft wide. How much will it cost to carpet the room if carpeting costs $22 per square yard?