Answer:
a = 10
T8 = 1280
Step-by-step explanation:
The nth term of a GP is expressed as;
Tn = ar^n-1
Forth term T4 = ar^3
first term = a
If the ratio of the fourth to the first term of a geometric sequence is ⅛ then;
ar^3/a = 1/8
r^3 = 1/8
r = ∛1/8
r = 1/2
If the first term exceed the second by 5, then;
a = 5 + T2
a = 5 + ar
a = 5 + a(1/2)
a-1/2a = 5
1/2 a 5
a = 10
Hence the first term is 10
T8 = ar^7
T10 = 10(1/2)^7
T10 = 10(128)
T10 = 1280
Hence the 8th term is 1280
1. Carla has some stickers. Kezia had 4 times as many as Carla but gave 5 to her sister and now she had 7. How many stickers does Carla have?
Answer:
2
Step-by-step explanation:
hope it helps god blessss
3
7+5=12
add 5 that she gave to her sister and divide it by 4 since she had 4x more than Carla
2 numbers have a product of 50 and also have a sum of 14 what are the two numbers x •x and x+x
Answer:
32 and 18
Step-by-step explanation:
This is a question of simultaneous equation.
Let's say the two numbers are x and y.
ATQ,
x+y =50 ——I
x-y=14——II
On adding I and II,
We get 2x=64
Implying x=32
Putting the value of x in equation I,
32+y=50
y=50–32
=18.
The answer is 32 and 18
A contractor is planning the acquisition of bulldozers needed for a new project in a remote area. From prior experience with this equipment he estimates that there is a 60% chance that each bulldozer will be operational for at least six months. If he purchases four bulldozers, it is desired to calculate the probabilities that exactly: 0, 1, 2, 3, and 4 bulldozers will be operational at the end of six months. Please document the following information:
a. Count the number of possible outcomes of the status of each bulldozer at the end of six months:
b. List the five events listed above as a function of the status of each bulldozer at the end of six months documented in 1.); and
c. Calculate the probabilities of these events assuming that the status of each bulldozer is statistically independent of the status of the rest of bulldozers.
Answer:
0.0256 ; 0.1536 ; 0.3456 ; 0.3456 ; 0.1296
Step-by-step explanation:
P, that each bulldozer will be operational for atleast 6 months = 0.6
p = 0.6 ; q = 1 - p = 1 - 0.6 = 0.4
Number of bulldozers purchased, n = 4
Probability that :
Exactly 0 bulldozer will be operational at the end of 6 months :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 0) = 4C0 * 0.6^0 * 0.4^4
P(x = 0) = 1 * 1 * 0.0256
P(x = 0) = 0.0256
Probability that :
Exactly 1 bulldozer will be operational at the end of 6 months :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 1) = 4C1 * 0.6^1 * 0.4^3
P(x = 1) = 4 * 0.6 * 0.064
P(x = 1) = 0.1536
Probability that :
Exactly 2 bulldozer will be operational at the end of 6 months :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 2) = 4C2 * 0.6^2 * 0.4^2
P(x = 2) = 6 * 0.36 * 0.16
P(x = 2) = 0.3456
Probability that :
Exactly 3 bulldozer will be operational at the end of 6 months :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 3) = 4C3 * 0.6^3 * 0.4^1
P(x = 3) = 4 * 0.216 * 0.4
P(x = 3) = 0.3456
Probability that :
Exactly 4 bulldozer will be operational at the end of 6 months :
P(x = x) = nCx * p^x * q^(n-x)
P(x = 4) = 4C4 * 0.6^4 * 0.4^0
P(x = 1) = 1 * 0.1296 * 1
P(x = 1) = 0.1296
The value of a car decreases by 20 percent per year. Mr. Sing purchases a $22,000 automobile. What is the value of the car at the end of the second year?$14,080$17,600$19,800$26,400
Answer:
$14,080
Step-by Step Explanation:
Answer:
$14,080
Step-by-step explanation:
Hope this helps.
Antonio eats 1 slice of pizza in 3 minutes. How long will it take Antonio to eat 4 slices?
Answer:
12
4*3
That's the answer
Sujan bought 16 pens for Rs256. how much would he have to pay for one pen he buys next time?
Step-by-step explanation:
.......................
Answer:
Rs 16
Step-by-step explanation:
Amount of money paid for 16 pens = Rs 256
Amount of money paid for 1 pen =
[tex] \frac{256}{16} = \frac{128}{8} \\ = \frac{64}{4} = \frac{32}{2} \\ = \frac{16}{1} \\ [/tex]
Therefore, amount paid for one pen is Rs 16
Sylvia had a small box. She filled it with 64 triangle pattern blocks. She said "The volume of this box is 64 cubic units." Do you agree with Sylvia? Why or why not?
Answer:
I do not agree with Sylvia
Step-by-step explanation:
Given
1 small box
64 triangle pattern blocks
Required
Is she right?
From the question, we understand that she fills the box with 64 blocks.
For the fact that she did this; it does not mean that the volume of the small box is 64 cubic units (even if she filled the box completely and the triangle pattern blocks are identical)
The reason for this is that, the volume of each box may not be 1 cubic unit.
So, first she needs to determine the volume of each pattern block, then multiply by 64. If the result is 64, then the volume of the box is 64 cubic units.
Since, it is not stated, we will not make any assumptions.
Hence, I do not agree with Sylvia.
Select all equations for which -3 is a solution.
2x3 = -27
0 -2 =9
O ? = 9
O 3 = 27
O x2 = -9
O (-2)2 = 9
Answer:
look it up
Step-by-step explanation:
Jamal reads for 1/2 hour on Monday and 1/3 hour on Tuesday.how much more did he read on Monday than on Tuesday?
Answer:
1/6 hour, or 10 minutes
Step-by-step explanation:
This is a subtraction problem.
1/2 - 1/3 =
We need a common denominator for 2 and 3. We can use 6.
= 1/2 * 3/3 - 1/3 * 2/2
= 3/6 - 2/6
= 1/6
Answer: 1/6 hours, or 10 minutes
Estimate 9/16 to the lowest terms
Answer:
9/16
is already in the simplest form. It can be written as 0.5625 in decimal form (rounded to 6 decimal places).
Step-by-step explanation:
which expression is equivalent to (5m) ^3
Answer:
5m•5m•5m
Step-by-step explanation:
so you multiply the factor by itself as many times as the exponent says so if the factor is 5m you would multiply it by the exponent which in this case is 3
5m.5m.5m and 125m³ is the equivalent expressions of the expression (5m)³.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (5m)³
We have to find the equivalent expression of (5m)³
Equivalent expressions are expressions that work the same even though they look different
(5m)³ can be written as 5m.5m.5m
The value of five cube is one hundred twenty five.
125m³
Hence, 5m.5m.5m and 125m³ is the equivalent expressions of the expression (5m)³.
To learn more on Expressions click:
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y=2x-1
y=1/2x+4
find the solution to the system equations
Answer:
x=10/3 y=17/3
Step-by-step explanation:
Use substitution to solve your equation. Plug in y=2x-1 into y=1/2x+4. This makes (2x-1)=1/2x+4. Simplify this to get 3/2x-1=4. Simplify it again to get 3/2x=5. No one likes fractions so multiply both sides by 2 to get 3x=10. Simplify this and get x=10/3. Plus 10/3 into one of the equations. You can pick anyone but I picked y=2x-1. Because you know x=10/3, you put y=2(10/3)-1. Simplify this and get y=20/3-1. Convert 1 into a fraction and get y=20/3-3/3. Simplify this and get y=17/3.
Therefore,
x=10/3 y=17/3
Hoped this helps you
Write the equation of the line in slope intercept from that: Has a slope of m= −2 and goes through (1, 2). please help
Answer:
y=-2x+4
Step-by-step explanation:
Jared bought a 15-pound bag of turkey for
Thanksgiving. His family ate 6 pounds of
the food on the morning of Thanksgiving
and 4% for dinner. Jared decided to use 2
of the remaining turkey to make
sandwiches for lunch. How much turkey, in
pounds, did Jared use to make
sandwiches?
Answer:
6 jared used six pounds
Step-by-step explanation:
you have it aubtexact what he used the first night and then divide by 4percwnt
Three different accounts are described below.order the accounts according to their values after 10 years ,from greatest to least
Answer:
3.You deposit $1000 in an account that earns 9% annual interest compounded semiannually.
1. You deposit $950 in an account that earns 9% annual interest compounded daily.
2. You deposit $1000 in an account that earns 8% annual interest compounded daily.
4. You deposit $1000 in an account that earns 10% simple interest.
Step-by-step explanation:
P.S - The exact question is -
To find - Three different accounts are described below. Order the accounts
according to their values after 10 years, from greatest to least.
1. You deposit $950 in an account that earns 9% annual
interest compounded daily.
2. You deposit $1000 in an account that earns 8% annual
interest compounded daily.
3.You deposit $1000 in an account that earns 9% annual
interest compounded semiannually.
4. You deposit $1000 in an account that earns 10% simple interest.
Proof -
1.)
Value after 10 years = 950( 1 + 0.09)¹⁰
= 950 ( 1.09)¹⁰
= 950(2.37) = 2248.995
⇒Value after 10 years = 2248.995
2.)
Value after 10 years = 1000( 1 + 0.08)¹⁰
= 1000 ( 1.08)¹⁰
= 1000(2.159) = 2158.925
⇒Value after 10 years = 2158.925
3.)
As it is compounded semiannually , so time period is doubles and rate goes half.
Value after 10 years = 1000( 1 + 0.045)²⁽¹⁰⁾
= 1000 ( 1.045)²⁰
= 1000(2.412) = 2411.714
⇒Value after 10 years = 2411.714
4.)
Value after 10 years = 1000×[tex]\frac{10}{100}[/tex]×10 = 1000
∴ we get
2411.714 > 2248.995 > 2158.925 > 1000
⇒ 3.) > 1.) > 2.) > 4.)
So,
3.You deposit $1000 in an account that earns 9% annual interest compounded semiannually.
1. You deposit $950 in an account that earns 9% annual interest compounded daily.
2. You deposit $1000 in an account that earns 8% annual interest compounded daily.
4. You deposit $1000 in an account that earns 10% simple interest.
-9.4 - 1.4b = b + 0.2
a) no solution
b) -6.7
c) 2.1
d) -4
Answer:
d) -4
Step-by-step explanation:
-9.4 - 2.4b = 0.2
-2.4b = 9.6
b = -4
good luck, i hope this helps :)
What is the percent of increase from 5,000 to 7,000?
Answer:
40%
Step-by-step explanation:
ONLY 1% PEOPLE CAN ANSWER THIS QUESTION CORRECTLY 100 points also brainliest
Simplify
(8 x 5) x b
3
Also is this formula true or false?
Answer:40b simplified
Step-by-step explanation:
Please help me if u don’t I will get a bad grade‼️
Given:
The equation is
[tex]\dfrac{1}{3}x=\dfrac{1}{5}[/tex]
To find:
The coefficient and reciprocal.
Solution:
We have,
[tex]\dfrac{1}{3}x=\dfrac{1}{5}[/tex]
Here, [tex]\dfrac{1}{3}[/tex] is multiplied with x.
So, the coefficient of x is [tex]\dfrac{1}{3}[/tex].
To find the reciprocal, we need to interchange numerator and denominator of a fraction.
So, the reciprocal of [tex]\dfrac{1}{3}[/tex] is [tex]\dfrac{3}{1}=3[/tex]
Therefore, the reciprocal is 3.
Can someone answer
q^8÷q^2
Answer:
q^6
Step-by-step explanation:
Exact distance between (-1,-9) and (5,-5)
[tex]2 \sqrt{13} [/tex]
that is your answer
Pls helllp!!!
Find the hourly wage: $80 for 9 hours.
O $8.89
O $17.78
O $71
O $10.12
A company manufacturing computer chips finds that 8% of all chips manufactured are defective. In an effort to decrease the percentage of defective chips, management decides to provide additional training to those employees hired within the last year. After training was implemented, a sample of 450 chips revealed only 27 defects. A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate. Which of the following statement is true about this hypothesis test?
A. It is a two tailed test about a proportion.
B. It is a one tailed test about a mean.
C. It is a one tailed test about a proportion.
D. It is a two tailed test about a mean.
E. None of the above.
Answer:
A. It is a two tailed test about a proportion
Step-by-step explanation:
We are given;
Population proportion; p= 8% = 0.08
Sample size; n = 450
Defective ones in the sample = 27
Sample proportion; p^ = 27/450 = 0.06
Let's define the hypotheses.
Null Hypothesis; H0: p = 0.08
Alternative hypothesis;Ha: p ≠ 0.08
≠ is used for the alternative hypothesis because we can't really ascertain if the training was going to make things worse.
Thus, this is a two tailed hypothesis test about a proportion.
Subtract. (12+8i)−(7+4i) Enter your answer in the box.
Answer:
5+12i
Step-by-step explanation:
So 12-7 = 5 and 8i+4i=12i and that equals 5+12i
A contractor purchases 3 dozen pairs of padded work gloves for $42.48. He incorrectly calculates the unit price as $14.16 per pair for the expense report. What is the correct unit price? What is the error?
Answer:
1.18
Step-by-step explanation:
$1.17
Step-by-step explanation:
He divided the total cost by 3 not 3 dozen (36).
A line has a gradient of -2
A line that is parallel to this will have a gradient of ...
Given:
A line has a gradient of -2
A line that is parallel to this will have a gradient of ..... .
To find:
The missing value.
Solution:
Gradient of a line is also known as slope of the line.
We know that the slopes of the parallel lines are equal.
A line has a gradient of -2. So, the slopes of all the lines which are parallel to this line have a gradient of -2.
Therefore, the missing value is -2.
For the following pair of functions, find (f+g)(x) and (f-g)(x).
f(x)= 4x2 + 7x-5 and g(x)= - 9x² + 4x - 13
(f+g)(x) = 0
(Simplify your answer. Type in descending order.)
(f-g)(x) =
(Simplify your answer. Type in descending order.)
Given:
The functions are
[tex]f(x)=4x^2+7x-5[/tex]
[tex]g(x)=-9x^2+4x-13[/tex]
To find:
The functions [tex](f+g)(x)[/tex] and [tex](f-g)(x)[/tex].
Solution:
We know that,
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=4x^2+7x-5-9x^2+4x-13[/tex]
[tex](f+g)(x)=(4x^2-9x^2)+(7x+4x)+(-5-13)[/tex]
[tex](f+g)(x)=-5x^2+11x-18[/tex]
And,
[tex](f-g)(x)=f(x)-g(x)[/tex]
[tex](f-g)(x)=(4x^2+7x-5)-(-9x^2+4x-13)[/tex]
[tex](f+g)(x)=4x^2+7x-5+9x^2-4x+13[/tex]
[tex](f+g)(x)=(4x^2+9x^2)+(7x-4x)+(-5+13)[/tex]
[tex](f-g)(x)=13x^2+3x+8[/tex]
Therefore, the required functions are [tex](f+g)(x)=-5x^2+11x-18[/tex]
and [tex](f-g)(x)=13x^2+3x+8[/tex].
Throwing a ball describes what kind of graph.
Answer:
parabola
Step-by-step explanation:
The path followed by a ball can be modeled by a graph.
Throwing a ball is a parabola or quadratic graph.
When a ball is thrown, the path it follows can be represented by:
[tex]\mathbf{f(x) = ax^2 + bx + c}[/tex]
or
[tex]\mathbf{f(x) = a(x - h)^2 + k}[/tex]
The above equations are functions of a parabola or quadratic graph.
Hence, throwing a ball is a parabola or quadratic graph.
Read more about graphs at:
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In the measurement of the length of a cylinder, the main scale reading of a vernier caliper is 2.8 cm, the vernier reading is 4, and the least count of the vernier is 0.01 cm. Find the reading of the length of the cylinder.
Answer:
the reading of the length of the cylinder is 2.84 cm
Step-by-step explanation:
Given the data in the question;
the main scale reading = 2.8 cm
the Vernier reading = 4
the least count of the Vernier = 0.01 cm
the reading of the length of the cylinder = ?
To determine the reading of the length of the cylinder, we simply say;
Reading length = main scale reading + ( Vernier reading × least count )
so we substitute in our given values
Reading length = 2.8 cm + ( 4 × 0.01 cm )
Reading length = 2.8 cm + 0.04 cm
Reading length = 2.84 cm
Therefore, the reading of the length of the cylinder is 2.84 cm
If Danny earned $1,000 on a 4 year investment at a rate of 6%, how much was his original investment?
Answer:
$4,166,67
Step-by-step explanation:
