Answer:
x = 10
Step-by-step explanation:
[tex]x = 3 \times 2 + 4[/tex]
[tex]x = 6 + 4[/tex]
[tex]x = 10[/tex]
Bill invested $4000 at 6%
compounded annually. Find the
accumulated amount at the end of
12 years.
Answer:
$ 8048.79Step-by-step explanation:
P = $4000t = 12 yearsr = 6% = 0.06Formula:
A = P(1 + r)^tThe total amount:
A = 4000*(1 + 0.06)^12 = 8048.79We have to find the,
Accumulated amount at end of 12 years.
The formula we use,
→ A = P(1+r)^t
It is given that,
→ P = $4000
→ t = 12 years
Then r will be,
→ 6%
→ 6/100
→ 0.06
Then the total amount is,
→ P(1+r)^t
→ 4000 × (1 + 0.06)^12
→ 8048.79
Thus, $ 8048.79 is the amount.
13) What is 4 1/2 subtracted from 5.33?
A. 0.43
B. 0.53
C. 0.83
D. 1.08
Given:
[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33.
To find:
The value for the given statement.
Solution:
[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33 can be written as:
[tex]5.33-4\dfrac{1}{2}[/tex]
On simplification, we get
[tex]=5.33-\dfrac{8+1}{2}[/tex]
[tex]=5.33-\dfrac{9}{2}[/tex]
[tex]=5.33-4.5[/tex]
[tex]=0.83[/tex]
Therefore, the correct option is C.
The quadratic equation [tex]x^2+3x+50 = 0[/tex] has roots r and s. Find a quadratic question whose roots are r^2 and s^2.
According to the question, our quadratic equation is :
\begin{gathered} \bf {x}^{2} - ( {r}^{2} + {s}^{2} )x + {r}^{2} {s}^{2} = 0 \\ \bf \implies \: {x}^{2} - ( - 91)x + {(rs)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + {(50)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + 2500 = 0\end{gathered}
x
2
−(r
2
+s
2
)x+r
2
s
2
=0
⟹x
2
−(−91)x+(rs)
2
=0
⟹x
2
+91x+(50)
2
=0
⟹x
2
+91x+2500=0
Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.
Answer:
4 e
Step-by-step explanation:
dz6dxrx xrrx6 xz33x4xr4x xrx
this khan academy problem confuses me... (5/3)^3= can anyone help me solve it?
Answer:
4.629
Step-by-step explanation:
(5/3)³5×5×5/3×3×3125/274.629.Hope it is helpful to you
The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 10 in-state applicants results in a SAT scoring mean of 1173 with a standard deviation of 38. A random sample of 15 out-of-state applicants results in a SAT scoring mean of 1076 with a standard deviation of 57. Using this data, find the 95% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Find the margin of error to be used in constructing the confidence interva.
Answer:
jebtucky
Step-by-step explanation:
yes yee yee yee eyetegevw
Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%
Answer:
x = 50
y = 50
Step-by-step explanation:
[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]
.12(100-y) + .38y = 25
x = 50
y = 50
Solve 8x + c = k for x
Answer:
x = 1/8(k-c)
Step-by-step explanation:
8x + c = k
Subtract c from each side
8x +c-c = k-c
8x = k-c
Divide each side by 8
8x/8 = (k-c)/8
x = 1/8(k-c)
Answer:
x-1/8(k-c)
Step-by-step explanation:
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 47 states. What is the probability that she selects the route of three specific capitals?
Answer:
1 / 97290
Step-by-step explanation:
The number of ways of selecting 3 specific route capitals from 47 states can be obtained thus :
Probability = required outcome / Total possible outcomes
Total possible outcomes = 47P3
Recall :
nPr = n! / (n-r)!
47P3 = 47! / (47-3)! = 47! / 44! = 97290
Hence, probability of selecting route if 3 specific capitals is = 1 / 97290
Which graph represents y = RootIndex 3 StartRoot x + 6 EndRoot minus 3? in a test plese help fast
Answer:
Graph (a)
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x+ 6} -3[/tex]
Required
The graph
First, calculate y, when x = 0
[tex]y = \sqrt[3]{0+ 6} -3[/tex]
[tex]y = \sqrt[3]{6} -3[/tex]
[tex]y = -1.183[/tex]
The above value of y implies that the graph is below the origin when x = 0. Hence, (c) and (d) are incorrect because they are above the origin
Also, only the first graph passes through point (0,-1.183). Hence, graph (a) is correct
Answer:
the answer is A
Step-by-step explanation:
Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202
Answer:
Kindly check explanation
Step-by-step explanation:
Rounding each number to 4 significant figures and expressing in standard notation :
(a) 102.53070,
Since the number starts with a non-zero, the 4 digits are counted from the left ;
102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2
(b) 656.980,
Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.
656.980 = 657.0 (4 significant figures) = 6.57 * 10^2
(c) 0.008543210,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3
(d) 0.000257870,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4
(e) -0.0357202,
Since number starts at 0 ; the first significant figure is the first non - zero digit ;
-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2
The time it takes a customer service complaint to be settled at a small department store is normally distributed with a mean of 10 minutes and a standard deviation of 3 minutes. Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
Answer:
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 10 minutes and a standard deviation of 3 minutes
This means that [tex]\mu = 10, \sigma = 3[/tex]
Find the probability that a randomly selected complaint takes more than 15 minutes to be settled.
This is 1 subtracted by the p-value of Z when X = 15, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 10}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
0.0475 = 4.75% probability that a randomly selected complaint takes more than 15 minutes to be settled.
whats the next two terms in order are p+q, p , p-q
Answer:
p - 2q and p - 3q
Step-by-step explanation:
A Series is given to us and we need to find the next two terms of the series . The given series to us is ,
[tex]\rm\implies Series = p+q , p , p - q [/tex]
Note that when we subtract the consecutive terms we get the common difference as "-q" .
[tex]\rm\implies Common\ Difference = p - (p + q )= p - p - q =\boxed{\rm q}[/tex]
Therefore the series is Arithmetic Series .
Arithmetic Series:- The series in which a common number is added to obtain the next term of series .
And here the Common difference is -q .
Fourth term :-
[tex]\rm\implies 4th \ term = p - q - q = \boxed{\blue{\rm p - 2q}}[/tex]
Fifth term :-
[tex]\rm\implies 4th \ term = p - 2q - q = \boxed{\blue{\rm p - 3q}}[/tex]
Therefore the next two terms are ( p - 2q) and ( p - 3q ) .
I need all the help I can get. please assist.
4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx
5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx
Answer:
4(a).
Expression of dy/dx :
[tex]{ \tt{ \frac{dy}{dx} = - 2(3 - 2x) {}^{2} + 24}}[/tex]
5(a).
[tex]{ \tt{ \frac{dy}{dx} = 54 - 2(2x - 7) {}^{2} }}[/tex]
How do I figure this question out
Answer:
Orthocenter would be in the middle of the shape.
Step-by-step explanation:
B.
Simplify: (w^3)^8 * (w^5)^5
Answer:
(w^3)^8 * (w^5)^5 = w^49
Step-by-step explanation:
(w^24) * (w^25)
using exponent rule
w^24 • w^25 = w^24+25
w^49
Answer:
Step-by-step explanation:
(W^24)*(W^25)
W^24+25
=W^49
Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2
Answer:
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
Step-by-step explanation:
We have the mean during the interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
Lost-time accidents occur in a company at a mean rate of 0.8 per day.
This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.
10 days:
This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]
What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]
[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]
[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]
So
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]
0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.
find the slope of the line passing through the points (-4, -7) and (4, 3)
Answer:
5/4
Step-by-step explanation:
Use the slope formula which is y2-y1/x2-x1.
1. Plug the given values into the equation: 3-(-7)/4-(-4)=5/4
A Food Marketing Institute found that 34% of households spend more than $125 a week on groceries. Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population. What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31
Answer:
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Assume the population proportion is 0.34 and a simple random sample of 124 households is selected from the population.
This means that [tex]p = 0.34, n = 124[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.34[/tex]
[tex]s = \sqrt{\frac{0.34*0.66}{124}} = 0.0425[/tex]
What is the probability that the sample proportion of households spending more than $125 a week is less than 0.31?
This is the p-value of Z when X = 0.31, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.31 - 0.34}{0.0425}[/tex]
[tex]Z = -0.705[/tex]
[tex]Z = -0.705[/tex] has a p-value of 0.2405.
0.2405 = 24.05% probability that the sample proportion of households spending more than $125 a week is less than 0.31.
two sides of a triangle measure 5 in and 12 in what could be the length of the third side
Answer:
b
Step-by-step explanation:
What is the greatest common factor of 16ab3 + 4a2b + 8ab ?
Answer:
2ab(3b^2+2a+4)
Step-by-step explanation:
6ab^3 + 4a^2b + 8ab
2*3*a*b*b^2 +2*2*a*a*b +2*2*2*a*b
Factor out the common terms
2ab( 3*b^2 +2*a +2*2)
2ab(3b^2+2a+4)
4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?
Answer:
12
Step-by-step explanation:
how did the tempicher change if at first it increased by 5% and then increased by 20 percent
Answer:
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
Step-by-step explanation:
Take a number, x.
Now increase it by 5%.
1.05x
Now increase it by 20%.
1.2 * 1.05x = 1.26x
1.26x = 126% of x = 100% of x + 26% of x
100% of x is the same as x, so it is the same as the original x.
The increase is 26% of the original number.
Increasing a number by 5% and then by 20% is the same as increasing the original number by 26%.
A graph of 2 functions is shown below. graph of function f of x equals negative 11 by 3 multiplied by x plus 11 by 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 Which of the following is a solution for f(x) = g(x)? (2 points) x = −2 x = 1 x = 0 x = −1
9514 1404 393
Answer:
(b) x = 1
Step-by-step explanation:
A graph shows the solution to f(x) = g(x) is x = 1.
__
We want to solve ...
g(x) -f(x) = 0
x^3 +2x^2 -x -2 -(-11/3x +11/3) = 0
x^2(x +2) -1(x +2) +11/3(x -1) = 0 . . . . . factor first terms by grouping
(x^2 -1)(x +2) +11/3(x -1) = 0 . . . . . . the difference of squares can be factored
(x -1)(x +1)(x +2) +(x -1)(11/3) = 0 . . . . we see (x-1) is a common factor
(x -1)(x^2 +3x +2 +11/3) = 0
The zero product rule tells us this will be true when x-1 = 0, or x = 1.
__
The discriminant of the quadratic factor is ...
b^2 -4ac = 3^2 -4(1)(17/3) = 9 -68/3 = -41/3
This is less than zero, so any other solutions are complex.
A box contains 16 large marbles and 18 small marbles. Each marble is either green or white. 9 of the large marbles are green, and 3 of the small marbles are white. If a marble is randomly selected from the box, what is the probability that it is small or green
Answer:
[tex]P(S&G) =0.7941[/tex]
Step-by-step explanation:
From the question we are told that:
Sample size [tex]n=16+18=>34[/tex]
N0 of Large [tex]L=16[/tex]
N0 of Small [tex]S=18[/tex]
N0 large Green [tex]L_g=9[/tex]
N0 of small White [tex]S_w=3[/tex]
Therefore
Number of green marbles [tex]N0(G)=9+(18-3)[/tex]
Number of green marbles [tex]N0(G)=24[/tex]
Generally the Number of both small and green Marble is
[tex]N0 of (S&G)= 18 - 3 = 15[/tex]
Generally the probability that it is small or green P(S&G) is mathematically given by
[tex]P(S&G) = \frac{(18 + 24 - 15)}{(18 + 16)}[/tex]
[tex]P(S&G) =0.7941[/tex]
Zoe has 4 pounds of strawberries to make pies. How many ounces of strawberries Is this?
64 oz.
60 oz.
68 oz.
72 oz.
Work Shown:
1 pound = 16 ounces
4*(1 pound) = 4*(16 ounces)
4 pounds = 64 ounces
1. What is the theoretical probability that the family has two dogs or two cats?
2.
Describe how to use two coins to simulate which two pets the family has.
3. Flip both coins 50 times and record your data in a table
like the one below.
Frequency
Result
Heads, Heads
Heads, Tails
Tails. Heads
Tails. Tails
Total
50
4
Based on your data, what is the experimental probability that the family has two dogs or
two cats?
5
If the family has three pets, what is the theoretical probability that they have three dogs or
three cats?
How could you change the simulation to generate data for three pets
6
let dogs be heads. Let cats be tails. A coin has two sides, in which you are flipping two of them. Note that there can be the possible outcomes
h-h, h-t, t-h, t-t.
How this affects the possibility of two dogs & two cats. Note that there are 1/2 a chance of getting those two (with the others being one of each), which means that out of 4 chances, 2 are allowed.
2/4 = 1/2
50% is your answer
Heads represents cats and tails represents dogs. There is two coins because we are checking the probability of two pets. You have to do the experiment to get your set of data, once you get your set of data, you will be able to divide it into the probability for cats or dogs. To change the simulation to generate data for 3 pets, simply add a new coin and category for the new pet.
Hope this helps you out!
Calculate the product below and give your answer in scientific notation.
(3.3 x 10-4) (8.0 x 109) = ?
Show Calculator
Answer:
25288
Step-by-step explanation:
shown in the picture
22
20
14
22
29
20
Mean
Mode
Medium
Range
Answer:
mean=21.17
mode=20,22
median=3.5
range=15
Step-by-step explanation: MEAN=sum of all observations/ no. of observations
mean=22+20+14+22+29+20/6
mean=127/6
mean=21.17
MODE= most frequent observations
mode=22,20
MEDIAN=1/2(n/2+n+2/2)
=1/2(6/2+6+2/2)
=1/2(3+4)
=1/2(7)
=7/2
=3.5
RANGE=X max -X min
=29-14
=15
PLEASE HELPPPPPPP #1
Answer:
is the second answer 2x+1/x-1
