Answer:
3 years
Step-by-step explanation:
By simple interest formula:
[tex]i = \frac{prt}{100} \\ \\ 27 = \frac{225 \times 4 \times x}{100} \\ \\ x = \frac{27 \times 100}{900} \\ \\ x = \frac{2700}{900} \\ \\ x = 3 \: years[/tex]
10k4 ⋅ (−9k3) how to solve this
Answer:
The product of the terms in the given expression is -90k⁷
Step-by-step explanation:
10k⁴ · (-9k³)
When we multiply exponents, then we are going to add the exponential together. So, we will add 4 and 3 together which is 7. Since our base numbers are different, then we also multiply them together. So, we will multiply 10 by -9 which is -90.
-90k⁷
Ms. Perez’s biology class continued to grow sunflowers. During the second week, the average sunflower grew 2.2 inches. The table shows the difference from the average for four students.
Answer:
4/5=0.8
-1 1/2= -1.5
The greatest number is=1.3
Mia, Raj, Clara, Jacob
Answer:
4/5 is equal to 0.8
-11/2 is equal -1.5
The greatest number is 1.3
The students names Mia, Raj, Clara, Jacob
Step-by-step explanation:
I took the assignment. Hope this helps! :)
What is the solution to this equation?
Answer:
x = -7/2
Step-by-step explanation:
(1/4) ^ (x+1) = 32
Rewriting 32 as 2^5 and 1/4 and 2^-2
2^-2 ^ (x+1) = 2^5
We know that a^b^c = a^ ( b*c)
2 ^ (-2x-2) = 2 ^ 5
Since the bases are the same, the exponents have to be the same
-2x-2 = 5
Add 2 to each side
-2x = 7
Divide by -2
x = -7/2
Y varies jointly with x. Y=16 when x=4 and z=1/2. Find y when x=2 and z=1/4. Enter the value of y in the box. Picture attached, 15 points and I'll give Brainliest! Due in two hours.
Answer:
y = 4
Step-by-step explanation:
Given that y varies jointly with x and z then the equation relating them is
y = kxz ← k is the constant of variation
To find k use the condition y = 16 when x = 4 and z = [tex]\frac{1}{2}[/tex] , that is
16 = k × 4 × [tex]\frac{1}{2}[/tex] = 2k ( divide both sides by 2 )
8 = k
y = 8xz ← equation of variation
When x = 2 and z = [tex]\frac{1}{4}[/tex] , then
y = 8 × 2 × [tex]\frac{1}{4}[/tex] = 16 × [tex]\frac{1}{4}[/tex] = 4
if a+b+c=2 , ab+bc+ac= -1 and abc = -2 , then find the value of a^3 + b^3 + c^3
Answer: 8
Step-by-step explanation:
EQ1: a + b + c = 2 --> b + c = 2 - a
EQ2: ab + bc + ac = -1 --> b + c = (-1 - bc)/a
EQ3: abc = -2 --> bc = -2/a
Set EQ1 = EQ2 and substitute bc using EQ3 to solve for "a":
[tex]2-a=\dfrac{-1-bc}{a}\\\\\\\text{Clear the denominator:}\\a(2-a)=-1-bc\\\\\text{Substitute bc:}\\a(2-a)=-1-\dfrac{-2}{a}\\\\\\\text{Clear the denominator:}\\a^2(2-a)=-a+2\\\\\\\text{Simplify and set equal to 0:}\\2a^2-a^3=-a+2\\0=a^3-2a^2-a+2\\\\\text{Factor:}\\0=a^2(a-2)-1(a-2)\\0=(a^2-1)(a-2)\\\\\text{Solve for a:}\\a^2-1=0\qquad a-2=0\\a=\pm1}\qquad \qquad a=2[/tex]
Consider the solution a = 2 and plug it into EQ1 to solve for "b"
b + c = 2 - 2
b + c = 0
b = -c
Plug in a = 2, b = -c, and c = c into a³ + b³ + c³
2³ + (-c)³ + c³
= 8 - c³ + c³
= 8
15 and 17 pls.. 15 points!!!!
Step-by-step explanation:
15) 50 ÷ 2 = 25
17) Mean = 301, Mode = 40-50
(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35
(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65
(70+80) ÷ 2 = 75
• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540
55×10 = 550, 65×4 = 260, 75×2 = 150
Mean = (60+200+350+540+550+260+150) ÷ 7
= 2110 ÷ 7
= 301.4285....
= 301
Mode : the highest frequency
Answer:
15) 50 ÷ 2 = 25
17) Mean = 301, Mode = 40-50
(10+20) ÷ 2 = 15, (20+30) ÷ 2 = 25, (30+40) ÷ 2 = 35
(40+50) ÷ 2 = 45, (50+60) ÷ 2 = 55, (60+70) ÷ 2 = 65
(70+80) ÷ 2 = 75
• 15×4 = 60, 25×8 = 200, 35×10 = 350, 45×12 = 540
55×10 = 550, 65×4 = 260, 75×2 = 150
Mean = (60+200+350+540+550+260+150) ÷ 7
= 2110 ÷ 7
= 301.4285....
= 301
Mode : the highest frequency
hello please help ASAP thank you!
Answer:
I believe it is 1.
Step-by-step explanation:
1. because thats half
82, 77, 72, 67, 62 ....... The recursive pattern in the sequence above is latex-_ (be sure to show if it is positive or negative). The 4th term in the sequence is . An explicit formula that I can use to write for this sequence is latex-_ . The value of the 100th term is .
Answer:
a. It is a negative pattern
b. Fourth term is 67
c. Explicit formula is Tn = 87 - 5n where n is the number of the term.
d. The value of the 100th term is -413
Step-by-step explanation:
1.Firstly, we want to know if the pattern is positive or negative.
Looking at the pattern, we can see our first term as 82, second as 77, third as 72.
What this show is that the pattern is decreasing as we move on from one term to another. So we can say it is a negative recursive pattern.
2. We are asked which term is the 4th.
This is quite obvious from the spelt out pattern.
82 77 72 67
1....2......3.....4
67 is the fourth term.
3. We want an explicit formula for the sequence.
What this question is asking us is a formula such that we can use at any point in time to calculate the value of the term at that point.
Firstly we have the first term as 82.
We need the common difference.
Mathematically this is the second term minus the first term which is same as the third term minus the second term.
That would be; 77-82 = 72-77 = -5
Mathematically the nth term of an arithmetic sequence is;
Tn = a + (n-1) d
Where in this case a is 82 and d is -5
Substituting these values, we have;
Tn = 82 + (n-1)-5
Tn = 82 -5n + 5
Tn = 82 + 5 -5n
Tn = 87 -5n
Where Tn is the term we are looking for while n is the number of the term.
4. Value of the 100th term
Simply substitute the value of 100 for n in the explicit formula.
That would be;
87 -5(100) = 87-500 = -413
A lawn company advertises that they can spread 7,500 square feet of grass seed in 2 and a half hours. Find the number of square feet of grass seed that can be spread per hour.
Answer:
3000 square feet
Step-by-step explanation:
Divide 7,500 by 2.5:
7500/2.5
= 3000
So, 3000 square feet of grass seed can be spread per hour
Which expression represents the phrase “twice the quotient of 50 and a sum of a number y and 8
Answer:
2 * 50/(y + 8)
Step-by-step explanation:
"twice the quotient of 50 and a sum of a number y and 8"
y + 8
"twice the quotient of 50 and a sum of a number y and 8"
50/(y + 8)
"twice the quotient of 50 and a sum of a number y and 8"
2 * 50/(y + 8)
Answer:
2*50/ (8+y)
Step-by-step explanation:
twice the quotient of 50=2*50 divided by something
the sum of a number= y and 8
So... 2*50/ (8+y) is the answer
rewrite expression in the form k*z^n
Answer:
9z
Step-by-step explanation:
4th root of z = z^1/4
=> 3 * z^1/4
=> 3z^1/4
3z^1/4 * 3z^3/4
=> 3 x 3 x z^1/4 + 3/4
=> 9z^4/4
=> 9z^1
=> 9z
The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.
We are given:
= [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]
We need to write this in the form of :
= [tex]k~.~z^{n}[/tex]
What are exponents and powers?We use exponents and powers when we want to write very large numbers or very small numbers in a simplified manner.
Example:
8 = 2 x 2 x 2 = [tex]2^{3}[/tex].
Where 2 is the base and 3 is the exponents.
72 = 8 x 9 = [tex]2^{3} \times3^{2}[/tex].
Here we have two bases 2 and 3 and two exponents 3 and 2.
8 / 9 = [tex]\frac{2^{3} }{3^{2} }[/tex] = [tex]2^{3} \times3^{-2}[/tex].
Here the bases are 2 and 3 and exponents are 3 and -2.
We have
[tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex]
Here,
[tex]\sqrt[4]{z}[/tex] can be written as [tex]z^{\frac{1}{4} }[/tex].
[tex]z^{\frac{1}{4} }~.~z^{\frac{3}{4} }[/tex] can be written as :
[tex]z^{\frac{1}{4} +\frac{3}{4} }\\\\ z^{\frac{4}{4} } \\\\z^{1} = z[/tex]
Now we have,
3 x 3 x [tex]z^{\frac{1}{4} }[/tex] x [tex]z^{\frac{3}{4} }[/tex]
3 x 3 x z
[tex]3^{2}[/tex] x z
9 x [tex]z^{1}[/tex]
So, comparing with k . [tex]z^{n}[/tex]
we have,
k = 9 and n = 1.
The expression [tex]3\sqrt[4]{z}~.~3z^{\frac{3}{4} }[/tex] in the form k . [tex]z^{n}[/tex] is 9z.
Learn more about exponents and powers here:
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Given that a rectangle has a length of 5/2x + 10 with a width of 5/2x + 5, formulate an expression to represents the area of the rectangle.
Answer:
A = ²⁵/₄x² + ⁷⁵/₂x + 50Step-by-step explanation:
L = ⁵/₂x + 10
W = ⁵/₂x + 5
A = L•W
A = (⁵/₂x + 10)(⁵/₂x + 5)
A = ⁵/₂x•⁵/₂x + ⁵/₂x•5 + 10•⁵/₂x + 10•5
A = ²⁵/₄x² + ²⁵/₂x + ⁵⁰/₂x + 50
A = ²⁵/₄x² + ⁷⁵/₂x + 50
Or if yoy mean:
L = 5/(2x) + 10
W = 5/(2x) + 5
A = [5/(2x) + 10][5/(2x) + 5] = 25/(4x²) + 75/(2x) + 50
A washer and a dryer cost $600 combined. The cost of the washer is three times the cost of the dryer. What is the cost of the dryer?
Answer:150
Step-by-step explanation:
600/4=150 (150)3=450 450+150=600
Answer: 150 dollars
Step-by-step explanation: Because the dryer is equal to washer divided by 3 you can substitute Washer/3 in the equation
W+ W/3=600
multiply both sides by 3
3W+W=1800
4W=1800
Divide both sides by 4
The answer to W is 450 dollars which you then divide by three to get 150 dollars
Which interval notation represents the set of all numbers from -9 to 0, inclusive?
Answer:
[-9,0]
Step-by-step explanation:
You use brackets to indicate that the numbers, in this case -9 and 0, are included in the interval.
You use parentheses to indicate that the numbers are excluded from the interval.
Since we want to include the numbers in the interval, we use the brackets.
The answer is [-9,0]
Hope this helps!
4(-8x + 5) – (-33x – 26)
Answer:
1x+46 is the answer
Step-by-step explanation:
=4(-8x + 5) – (-33x – 26)
opening brackets to simplify
=-32x+20+33x+26
=-32x+33x+20+26
=1x+46 is the answer
hope it will help :)
Answer:
x+46
Step-by-step explanation:
4(-8x + 5) – (-33x – 26)
The first step is to distribute and simplify.
4 distributed to -8x will be -32x, and same thing goes with 5, which is 20.
-
The first part of the equation is -32x+20
Now, this is where it gets confusing.
If there is a sign before a pair of parentheses, you always put 1. In this case, it's -1 distributed to -33x and -26.
So, the second part of the expression will be +33x+26
The whole expression is
-32x + 20 + 33x + 26
add like terms, -32x+33x= x.
20+26=46.
The answer is x+46.
-6=-2+w solve the equation
Answer:
w = -4
Step-by-step explanation:
Answer:
w = -4
Step-by-step explanation:
[tex]-6=-2+w\\[/tex]
Switch sides
[tex]-2+w=-6[/tex]
Add 2 to both sides
[tex]-2+w+2=-6+2[/tex]
Simplify
[tex]w=-4[/tex]
what's 43 to the nearest hundred
Answer:
0
Step-by-step explanation:
43 rounded to nearest hundred is 0 because 43 is more closer to 0 than to 100.
3) Walt and 23 of his friends are going on a month-long
camping trip. Bags of marshmallows come with about 38
marshmallows per bag. They decide to bring 12 bags of
marshmallows to the trip. How many marshmallows will
each person get if they each eat the same number of
marshmallows and eat all of the marshmallows at camp?
Answer:
19 marshmallows per person.
Step-by-step explanation:
So, 38 marshmallows per bag and 12 bags were brought.
38 x 12 = 456
Walt and 23 of his friends - 24 people
456/24 = 19 marshmallows
why is -15/3 classified as an integer and not a rational number, even though it is a fraction.?
Answer:
see below
Step-by-step explanation:
Can we simplify the number
-15/3 simplifies to -5, which is an integer
We categorize the number to its smallest category and integer contains less than rational
If m∠XWZ = 90, what is x?
Right angle X W Z is divided into 2 acute angles labeled 5 x plus 5 degrees and 2 x plus 8 degrees.
Answer: x=11
Step-by-step explanation:
If m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
Given,
m∠XWZ = 90.
Right angle ∠XWZ is divided into 2 acute angles labeled as:
- 5x + 5 degrees
- 2x + 8 degrees.
We need to find the value of x.
What is an acute angle?An acute angle means angles that are less than 90 degrees.
If an angle is divided, the sum of the divided angles must be equal to the angle divided.
Find the right angle.
m∠XWZ = 90
Find the acute angles that are being divided.
= 5x + 5° and 2x + 8°
Find x.
Since m∠XWZ is divided we have,
90° = 5x + 5° + 2x + 8°
Now,
Add the like terms.
90 = 7x + 13
Subtract 13 on both sides.
90 - 13 = 7x
77 = 7x
Divide both sides by 7.
11 = x
x = 11
We can crosscheck the angles:
90° = 5x + 5° + 2x + 8°
90 = 5x11 + 5 + 2x11 + 8
90 = 55 + 5 + 22 + 8
90 = 60 + 30
90 = 90
Thus if m∠XWZ = 90 and is divided into 2 acute angles labeled 5x+5 degrees and 2x+8 degrees then the value of x is 11.
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18 cans of soda cost $6.48. What is the cost per can in dollars? Please help, I'm in a hurry
Answer:
36 cents
Step-by-step explanation:
In order to figure out how much one can cost you need to do 6.48/18 which then gets you 33 cents, the cost of one can.
A company needs two loads of sand to make an indoor beach area when employee picnic one load of sand weigh 4 tons and the other load Waze 7500 pounds what is the total weight of sand in pounds
Answer:
15500 pounds
Step-by-step explanation:
The weight of one load is 4 tons and the weight of other load is 7500 pounds.
We know that, 1 ton = 2000 pounds
4 tons = 8000 pounds
Total weight = 8000 pounds + 7500 pounds
Total weight = 15500 pounds
So, the total weight of sand is 15500 pounds.
You want to put a logo on each cell phone holder you make. Sew-on logos cost 2.30 for 10. Stick-on logos cost 9.40 for 100. Divide the cost by the number of logos for both types
Answer:
[tex]Rate = \$0.23[/tex] and [tex]Rate = \$0.094[/tex]
Step-by-step explanation:
Given
Sew-on logos
Cost = $2.30
Units = 10
Stick-on logos
Cost = $9.40
Units = 100
Required
Divide cost by units, in both cases
When we divide cost by units, it gives the unit rate.
i.e.
[tex]Rate = \frac{Cost}{Units}[/tex]
FOR SEW-ON LOGOS
Substitute $2.30 for Cost and 10 for Units
[tex]Rate = \frac{\$2.30}{10}[/tex]
[tex]Rate = \$0.23[/tex]
FOR STICK-ON LOGOS
Substitute $9.40 for Cost and 100 for Units
[tex]Rate = \frac{\$9.40}{100}[/tex]
[tex]Rate = \$0.094[/tex]
Hence, the solution is
[tex]Rate = \$0.23[/tex] and [tex]Rate = \$0.094[/tex]
Evaluate: 20/ 5·2^-3
Step-by-step explanation:
[tex] = \frac{20}{5} . {2}^{ - 3} [/tex]
[tex] = 4. \frac{1}{ {2}^{3} } [/tex]
[tex] = \frac{4}{2 \times 2 \times 2} [/tex]
[tex] = \frac{4}{8} [/tex]
[tex] = \frac{1}{2} [/tex]
Please answer for me way to hard for me its pre algera
Answer:
It probably has to deal with a joke or som10.
Step-by-step explanation:
Answer:
1. I
2. R
3. R
4. I
5. W
6. I
7. W
8. I
Step-by-step explanation:
Find the value of x in the equation below. 12+x = 16.7
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 4.7}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{12 + x = 16.7}[/tex]
Move 12 to right hand side and change it's sign
[tex] \dashrightarrow{ \sf{x = 16.7 - 12}}[/tex]
Subtract 12 from 16.7
[tex] \dashrightarrow{ \sf{4.7}}[/tex]
Hope I helped!
Best regards!
Answer:
[tex]\huge\boxed{\sf x = 4.7}[/tex]
Step-by-step explanation:
12 + x = 16.7
Subtracting 12 to both sides
x = 16.7 - 12
x = 4.7
Two functions represent the composite function h(x) = (x – 1)³ + 10 so that h(x) = (g compose f)(x). Given f(x) = x + a and g(x) = x³ + b, what values of a and b would make the composition true? a = b =
Answer:
a = -1 and
b = 10
Step-by-step explanation:
Given:
h(x) = (x – 1)³ + 10
h(x) = (g compose f)(x).
f(x) = x + a and
g(x) = x³ + b
To find:
The values of a and b = ?
Solution:
First of all, let us have a look at the composite functions.
(g compose f)(x) means we replace the value of [tex]x[/tex] with [tex]f(x)[/tex] in the function [tex]g(x)[/tex].
We know that:
[tex]g(x) =x^3+b[/tex] and
[tex]f(x) = x + a[/tex]
Let us find (g compose f)(x) by replacing [tex]x[/tex] with [tex]x+a[/tex]
[tex](g\ compose\ f)(x) = (x+a)^3+b[/tex]
Also, h(x) = (g compose f)(x) = (x – 1)³ + 10
Therefore,
[tex](x - 1)^3 + 10 = (x+a)^3+b[/tex]
Comparing the corresponding elements of the above expressions:
we get a = -1 and
b = 10
Answer:
a: -1
b: 10
edge 2020
ns
What personal qualities do you think Rudolph displayed to help her challenge people's
expectations?
pok
Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function l(x)=10/x. Suppose the width of the rectangle increases 1 unit while the area remains constant. Which graph models the length of the new rectangle
Answer: answer is C
Step-by-step explanation:
The question asks us to find the a graph which represents the width of the rectangle increasing by 1 unit while the area remains constant. The best graph to model this, would be answer choice C
Help Plzzz.........
Answer:
£7448
Step-by-step explanation:
Simple interest (I) is calculated as
I = [tex]\frac{PRT}{100}[/tex]
P is principle ( amount invested), R is rate of interest and T is time in years.
Here P = £5600, R = 11 and T = 3 , thus
I = [tex]\frac{5600(11)3)}{100}[/tex] = £1648
Value after 3 years = £5600 + £1848 = £7448