Answer:
[tex]-\infty < x < \infty[/tex]
Step-by-step explanation:
Given
[tex]f(x) = (-\frac{5}{6}) \cdot (\frac{3}{5})^x[/tex]
Required
The domain
There are no undefined points such as denominator of x or square roots.
Hence, the domain is:
[tex]-\infty < x < \infty[/tex]
19. The sum of a number m and a number n, multiplied by ninety-one 20. Forty-one times the difference when six is subtracted from a num- bera 21. A number r divided by the difference between eighty-three and ten 22. The total of a number p and twelve, divided by eighteen 23. The product of a number c and three more than the sum of nine and twelve 24. The sum of a number y and ten, divided by the difference when a number x is decreased by five. I need to convert all of them into expressions. PLEASE HELP.
Answer:
Step-by-step explanation:
19.
The numbers are m and n
Sum of m and n = m + n
Sum is multiplied by 91 = 91 x ( m + n )
20.
Let the number be = m
Six subtracted from the number = m - 6
41 times the difference = 41 x ( m - 6)
21.
Let the number be = r
Difference between 83 and 10 = 83 - 10 = 73
[tex]The \ number\ divided \ by\ the \ difference \ = \frac{r}{73}[/tex]
22.
Total of p and 23 = p + 12
[tex]Total \ divided \ by \ 18 = \frac{p + 12 }{18}[/tex]
23.
The product of c and 3 = 3c
Sum of 9 and 12 = 21
Product is more than Sum = 3c + 21
24.
Sum of y and 10 = y + 10
Number x decreased by 5 = x - 5
[tex]Sum \ divided \ by \ difference = \frac{ y + 10 }{x - 5}[/tex]
A professor is interested in whether or not college students have a preference (indicated by a satisfaction score) for reading a textbook that has a layout of one column or layout of two columns. In the above experiment, what is the dependent variable
Answer:
Satisfaction score
Step-by-step explanation:
The dependent variable may be described as the variable which is being measured in a research experiment. In the scenario described above, the dependent variable is the satisfaction score which is used to measure preference for a one or two column textbook. The dependent variable can also seen as the variable which we would like to predict, also called the predicted variable . The predicted variable here is the satisfaction score.
10=−4x+3x^2 solve
please help!
Answer:
-1.28 AND 2.61
Step-by-step explanation:
[tex]10= -4x+3x^2\\ 3x^2 -4x - 10 = 0\\\\[/tex]
use quadratic formula
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
Solution/X-Intercepts: -1.28 AND 2.61
The parametric equations for the paths of two projectiles are given. At what rate is the distance between the two objects changing at the given value of t? (Round your answer to two decimal places.) x1 = 10 cos(2t), y1 = 6 sin(2t) First object x2 = 4 cos(t), y2 = 4 sin(t) Second object t = π/2
Answer:
- [tex]\frac{4}{\sqrt{29} }[/tex]
Step-by-step explanation:
The equations for the 1st object :
x₁ = 10 cos(2t), and y₁ = 6 sin(2t)
2nd object :
x₂ = 4 cos(t), y₂ = 4 sin(t)
Determine rate at which distance between objects will continue to change
solution Attached below
Distance( D ) = [tex]\sqrt{(10cos2(t) - 4cos(t))^2 + (6sin2(t) -4sin(t))^2}[/tex]
hence; dD/dt = - [tex]\frac{4}{\sqrt{29} }[/tex]
A 27% solution ( 27mg per 100 mL of solution) is given intravenously. Suppose a total of 1,36 L of the solution is given over a 10 -hour period. Complete parts (a) through (c) below.
a. What is the flow rate in units of mL/hr?
nothing mL/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
What is the flow rate in per hour?
nothing mg/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
b. If each mL contains 13 drops (the drop factor is expressed as gtt/mL), what is the flow rate in units of 13gtt/hr?
nothing gtt/hr (Type an integer or decimal rounded to the nearest thousandth as needed.)
c. During the 10 -hour period, how much is delivered?
nothing mg (Type an integer or decimal rounded to the nearest thousandth as needed.)
Answer:
Step-by-step explanation:
a.
(1.36 L)/(10 hr) = (0.136 L)/(hr)
Flow rate = (0.136 L)/(hr) × (1000 mL)/L = (136 mL)/(hr)
136 mL × (27 mg)/(100 mL) = 36.72 mg
Delivery rate = (36.72 mg)/(hr)
b.
(136 mL)/(hr) × (13 gtt)/(mL) = (1868 gtt)/(hr)
c.
10 hr × (36.72 mg)/)hr) = 367.2 mg
Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt)
Answer:
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Step-by-step explanation:
Given
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]P(1) = 2[/tex]
Required
The solution
We have:
[tex]\frac{dP}{dt} = \sqrt{Pt[/tex]
[tex]\frac{dP}{dt} = (Pt)^\frac{1}{2}[/tex]
Split
[tex]\frac{dP}{dt} = P^\frac{1}{2} * t^\frac{1}{2}[/tex]
Divide both sides by [tex]P^\frac{1}{2}[/tex]
[tex]\frac{dP}{ P^\frac{1}{2}*dt} = t^\frac{1}{2}[/tex]
Multiply both sides by dt
[tex]\frac{dP}{ P^\frac{1}{2}} = t^\frac{1}{2} \cdot dt[/tex]
Integrate
[tex]\int \frac{dP}{ P^\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Rewrite as:
[tex]\int dP \cdot P^\frac{-1}{2} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the left hand side
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]\frac{P^{\frac{-1}{2}+1}}{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
[tex]2P^{\frac{1}{2}} = \int t^\frac{1}{2} \cdot dt[/tex]
Integrate the right hand side
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2} +1 } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{t^{\frac{3}{2}}}{\frac{3}{2} } + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex] ---- (1)
To solve for c, we first make c the subject
[tex]c = 2P^{\frac{1}{2}} - \frac{2}{3}t^\frac{3}{2}[/tex]
[tex]P(1) = 2[/tex] means
[tex]t = 1; P =2[/tex]
So:
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1^\frac{3}{2}[/tex]
[tex]c = 2*2^{\frac{1}{2}} - \frac{2}{3}*1[/tex]
[tex]c = 2\sqrt 2 - \frac{2}{3}[/tex]
So, we have:
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + c[/tex]
[tex]2P^{\frac{1}{2}} = \frac{2}{3}t^\frac{3}{2} + 2\sqrt 2 - \frac{2}{3}[/tex]
Divide through by 2
[tex]P^{\frac{1}{2}} = \frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3}[/tex]
Square both sides
[tex]P = (\frac{1}{3}t^\frac{3}{2} + \sqrt 2 - \frac{1}{3})^2[/tex]
Find the area of
1.Table
Length = 123cm
Width = 82cm
Height = 76cm
2.Living room
Length = 422cm
Width = 278cm
Height = 253cm
3. Door
Length = 87cm
Width = 2.3cm
Height = 208cm
Answer:
1. 766,536cm^3
2. 29,680,948cm^3
3. 41,620.8cm^3
Step-by-step explanation:
1. 123×82 = 10,086 10,086×76 = 766,536
2. 422×278 = 117,316 117,316×253 = 29,680,948
3. 87×2.3 = 200.1 200.1×208 = 41,620.8
Hope this helps! :)
x(x-y) - y( x- y) simplify
Step-by-step explanation:
x²-xy-xy+y²
x²+2xy+y²
hope it helps
Which of the following is not true regarding the flow of information from the adjusted trial balance on the end-of-period spreadsheet?
The correct statement about the flow of information from the adjusted trial balance on the end-of-period spreadsheet is A. The revenue and expense account balances flow into the income statement.
What is an Adjusted Trial Balance?This refers to the general ledger balance after some changes have been done an account balance such as accrued expenses, depreciation, etc.
Therefore, we can see that from the complete information, the statement that is false about the adjusted trial balance on the end-of-period spreadsheet is option A because the revenue and expense account balances does not flow into the income statement.
The other options from the complete text are:
a. The revenue and expense account balances flow into the income statement.b. The asset and liability account balances flow into the retained earnings statement.c. The revenue and expense account balances flow into the retained earnings statement.d. The retained earnings and dividends account balances flow into the balance sheet.
Read more about adjusted trial balance here:
https://brainly.com/question/14476257
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An urn contains 2 small pink balls, 7 small purple balls, and 6 small white balls.
Three balls are selected, one after the other, without replacement.
Find the probability that all three balls are purple
Express your answer as a decimal, rounded to the nearest hundredth.
Answer:
The probability is P = 0.08
Step-by-step explanation:
We have:
2 pink balls
7 purple balls
6 white balls
So the total number of balls is just:
2 + 7 + 6 = 15
We want to find the probability of randomly picking 3 purple balls (without replacement).
For the first pick:
Here all the balls have the same probability of being drawn from the urn, so the probability of getting a purple one is equal to the quotient between the number of purple balls (7) and the total number of balls (15)
p₁ = 7/15
Second:
Same as before, notice that because the balls are not replaced, now there are 6 purple balls in the urn, and a total of 14 balls, so in this case the probability is:
p₂ = 6/14
third:
Same as before, this time there are 5 purple balls in the urn and 13 balls in total, so here the probability is:
p₃ = 5/13
The joint probability (the probability of these 3 events happening) is equal to the product between the individual probabilities, so we have:
P = p₁*p₂*p₃ = (7/15)*(6/14)*(5/13) = 0.08
The function f is defined by the following rule. f(x) = 5x+1 Complete the function table.
Answer:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x + 1[/tex]
Required
Complete the table (see attachment)
When x = -5
[tex]f(-5) = 5 * -5 + 1 = -24[/tex]
When x = -1
[tex]f(-1) = 5 * -1 + 1 = -4[/tex]
When x = 2
[tex]f(2) = 5 * 2 + 1 = 11[/tex]
When x = 3
[tex]f(3) = 5 * 3 + 1 = 16[/tex]
When x = 4
[tex]f(4) = 5 * 4 + 1 = 21[/tex]
So, the table is:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
For each of the following, assume that the two samples are obtained from populations with the same mean, and calculate how much difference should be expected, on average, between the two sample means. Each sample has n =4 scores with s^2 = 68 for the first sample and s^2 = 76 for the second. (Note: Because the two samples are the same size, the pooled variance is equal to the average of the two sample variances).
a) 4.24.
b) 0.24.
c) 8.48.
d) 6.00.
Next, each sample has n=16 scores with s^2 = 68 for the first sample and s^2 = 76 for the second.
a) 0.12.
b) 2.12.
c) 4.24.
d) 3.00.
Answer:
d)6.00
d)3.00
Step-by-step explanation:
We are given that
n=4 scores
[tex]S^2_1=68[/tex]
[tex]S^2_2=76[/tex]
We have to find the difference should be expected, on average, between the two sample means.
[tex]S_{M_1-M_2}=\sqrt{\frac{S^2_1}{n_1}+\frac{S^2_2}{n_2}}[/tex]
[tex]n_1=n_2=4[/tex]
Using the formula
[tex]S_{M_1-M_2}=\sqrt{\frac{68}{4}+\frac{76}{4}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68+76}{4}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{36}=6[/tex]
Option d is correct.
Now, replace n by 16
[tex]n_1=n_2=16[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68}{16}+\frac{76}{16}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{\frac{68+76}{16}}[/tex]
[tex]S_{M_1-M_2}=\sqrt{9}=3[/tex]
Option d is correct.
Please help me >_< will give out brainliest
====================================================
Explanation:
We have an octagon because there are n = 8 sides. The diagram below shows one way to number the sides so you can count them efficiently (without missing any or double counting any).
----------------
Plug n = 8 into the formula below
S = 180(n-2)
S = 180(8-2)
S = 180(6)
S = 1080
The 8 interior angles add up to 1080 degrees.
Select the correct answer. What is the range of the function shown on the graph above?
A. -8
B.-2y <-7
C. -7 Sy < -2
D. -9
Answer: The answer would be D
Step-by-step explanation:
Last softball season, Pamela had 46 hits, a combination of singles (1 base), doubles (2 bases), and triples (3 bases). These 46 hits totaled 66 bases, and she had 4 times as many singles as doubles. How many doubles did she have?
Answer:
She had 8 doubles.
Step-by-step explanation:
This question is solved by a system of equations.
I am going to say that:
x is the number of singles.
y is the number of doubles
z is the number of triples.
46 hits
This means that [tex]x + y + z = 46[/tex]
46 hits totaled 66 bases
This means that:
[tex]x + 2y + 3z = 66[/tex]
4 times as many singles as doubles
This means that [tex]x = 4y[/tex]
So
[tex]x + 2y + 3z = 66[/tex]
[tex]4y + 2y + 3z = 66[/tex]
[tex]6y + 3z = 66[/tex]
And
[tex]x + y + z = 46[/tex]
[tex]4y + y + z = 46[/tex]
[tex]5y + z = 46 \rightarrow z = 46 - 5y[/tex]
Then
[tex]6y + 3z = 66[/tex]
[tex]6y + 3(46 - 5y) = 66[/tex]
[tex]6y + 138 - 15y = 66[/tex]
[tex]9y = 72[/tex]
[tex]y = \frac{72}{9}[/tex]
[tex]y = 8[/tex]
She had 8 doubles.
ABCD is a square of side 12 cm. It is formed from two rectangles AEGD and
EBCG. H is a point on AD and F is a point on BC.
Find the area of EFGH.
Answer:72 [tex]cm^{2}[/tex]
Solution 1:
Step 1: Find EF use Pythagorean theorem
[tex]EF^{2} = EB^{2} + BF^{2}[/tex]
[tex]EF^{2} = 6^{2} + 6^{2}[/tex]
EF = [tex]\sqrt{6^{2} + 6^{2} }[/tex] = 6[tex]\sqrt{2}[/tex] cm
Step 2: The area of EFGH = [tex]EF^{2}[/tex]= [tex](6\sqrt{2} )^{2}[/tex] = 72
Solution 2: See that the area of EFGH is equal [tex]\frac{1}{2}[/tex] the area of ABCD
The area of ABCD = 12x12 = 144
Thus, the area of EFGH = 144: 2 = 72:)
Have a nice day!
The sum of the first ten terms of an arithmetic progression consisting of
positive integer terms is equal to the sum of the 20th, 21st and 22nd term.
If the first term is less than 20, find how many terms are required to give
a sum of 960.
Answer: [tex]n=13[/tex]
Step-by-step explanation:
Given
Sum of the first 10 terms is equal to sum of 20, 21, and 22 term
[tex]\Rightarrow \dfrac{10}{2}[2a+(10-1)d]=[a+19d]+[a+20d]+[a+21d]\\\\\Rightarrow 5[2a+9d]=3a+60d\\\Rightarrow 10a+45d=3a+60d\\\Rightarrow 7a=15d[/tex]
No of terms to give a sum of 960
[tex]\Rightarrow 960=\dfrac{n}{2}[2a+(n-1)d]\\\\\Rightarrow 1920=n[2a+(n-1)\cdot \dfrac{7}{15}a]\\\\\Rightarrow 28,800=n[30a+7a(n-1)]\\\\\Rightarrow a=\dfrac{28,800}{n[30+7n-7]}\\\\\Rightarrow a=\dfrac{28,800}{n[23+7n]}[/tex]
Value of first term is less than 20
[tex]\therefore \dfrac{28,800}{n[23+7n]}<20\\\\\Rightarrow 28,800<20n[23+7n]\\\Rightarrow 0<460n+140n^2-28,800\\\Rightarrow 140n^2+460n-28,800>0\\\\\Rightarrow n>12.79\\\\\text{For integer value }\\\Rightarrow n=13[/tex]
Answer:
15
Step-by-step explanation:
In the previous answer halfway through they used the equation: 960 = (n÷2)×(2a+(n-1)×(7a÷15))
Using this equation we can substitute an number to replace n, the higher the number is the smaller a would be.
When we substitute 15 into a, then it leaves us with the answer to be a = 15 which is a positive integer and also is smaller than 20, this then let’s us know that 15 is how many terms can be summed up to make 960.
To double check this answer you can find that d = 7 by changing the a into 15 in the formula 7a/15 (found in the previous answer.
Then in the expression: (n÷2)×(2a+(n-1)×d)
substitute:
n = 14 (must be an even number for the equation to work)
a = 15
d = 7
This will give you an answer of 847, but this is only 14 terms as we changed n into 14. To add the final term you need to complete the following equation: 847+(a+(n-1)×d)
substituting:
n = 15
a = 15
d = 7
This will give you the answer of 960, again proving that it takes 15 terms to sum together to make the number 960.
I hope this has helped you.
P.S. Everything in the previous solution was right apart from the start of the last section and the answer
Write the range of the function using interval notation.
Given:
The graph of a function.
To find:
The range of the given function using interval notation.
Solution:
Range: The set of y-values or output values are known as range.
From the given graph, it is clear that the function is defined for [tex]0<x<4[/tex] and the values of the functions lie between -2 and 2, where -2 is excluded and 2 is included.
Range [tex]=\{y|-2<y\leq 2\}[/tex]
The interval notation is:
Range [tex]=(-2,2][/tex]
Therefore, the range of the given function is (-2,2].
Christian and Tanae both leave Disneyland at the same time. Christian travels north at 65 mph. Tanae travels south at 55 mph. How long will it take them to be 540 miles apart? Which of the following equations would you use to solve this word problem?
65t + 55(t − 1) = 540.
65t + 55t = 540.
65t + 55(t + 1) = 540.
None of these choices are correct.
Answer:
Step-by-step explanation:
B looks like it would work.
You add speeds * time when you are travelling in opposite directions.
I don't know why you would add or subtract 1 as in A and C
120 * t = 540
t = 540/120
t = 4.5 hours.
So after 4.5 hours they are 540 miles apart.
Answer:
b
Step-by-step explanation:
15. The area of a triangle is 72 in the base is 12 in. Find the height.
Answer:
[tex]hright =12[/tex]
Step-by-step explanation:
----------------------------------------
The formula to find the area of a triangle is [tex]A=\frac{1}{2}bh[/tex] where [tex]b[/tex] stands for the base and [tex]h[/tex] stands for the height.
But we already know the area and the base. So to find the height, let's substitute 72 for [tex]A[/tex] and 12 for [tex]b[/tex], and solve.
[tex]72=\frac{1}{2}(12)(h)[/tex]
[tex]72=6h[/tex]
Here, divide both sides by 6
[tex]12=h[/tex]
--------------------
Hope this is helpful.
Answer:
height = 12
Step-by-step explanation:
.............
What is the standard form equation of the quadratic function shown in this graph?
Answer:
A is the equation in standard form
Step-by-step explanation:
-8(9r - 1) - 9(-8r+2)
Simplest form
Answer:
-10
Step-by-step explanation:
Step-by-step explanation:
-8(9r-1)-9(-8r+2)-72r+8-72r-18-72r-72r+8-18-144r-10-(144r+10)hope it helps
stay safe healthy and happy...Let f(x)
2x + 8, g(x) = x2 + 2x – 8, and h(x) = 3x – 6.
Perform the indicated operation. (Simplify as far as possible.)
(h · f)(3) =
Answer:
36
Step-by-step explanation:
(h · f)(x) = h(f(x))
h(f(x)) = h(2x+8)
h(f(x))= 3(2x+8) - 6
h(f(x)) = 6x + 24 - 6
h(f(x))= 6x + 18
If x = 3
h(f(x))= 6(3) + 18
h(f(x))= 18 + 18
h(f(x))= 36
Hence (h · f)(3) = 36
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
The probability of this event is represented by a value of 1.
Step-by-step explanation:
Probability of a certain event:
The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
This means that the probability of this event is represented by a value of 1.
HELP
-5(2m-3)-4<81
I need the steps also well
Answer:
m>-7
Step-by-step explanation:
expand
-10m+15-4<81
-10m+11<81
collect like terms
-10m<81-11
-10m<70
m>-7
Which represents can be used to determine the slope of the linear function graphed below
Which answers describe the shape below? Check all that apply.
A. Square
B. Quadrilateral
C. Rhombus
D. Trapezoid
E. Rectangle
F. Parallelogram
Answer:
b and f
Step-by-step explanation:
Consider random samples of size 1200 from a population with proportion 0.65 . Find the standard error of the distribution of sample proportions. Round your answer for the standard error to three decimal places.
Answer:
The standard error of the distribution of sample proportions is of 0.014.
Step-by-step explanation:
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]
Consider random samples of size 1200 from a population with proportion 0.65 .
This means that [tex]n = 1200, p = 0.65[/tex]
Find the standard error of the distribution of sample proportions.
This is s. So
[tex]s = \sqrt{\frac{0.65*0.35}{1200}} = 0.014[/tex]
The standard error of the distribution of sample proportions is of 0.014.
If you have 3/8 of one pie, what does the denominator tells you ?
Step-by-step explanation:
There was originally 8 pieces of pie.
Answer:
if you have 3/8 of one pie, the denominator tells you that the pie was divided into 8 piece.
If the cutoff Z score on the comparison distribution is 2.33 and the sample value has a score of 2.35 on the comparison distribution, the correct decision is to:____.
A) fail to reject the null hypothesis.
B) reject the null hypothesis.
C) accept the researc hypothesis.
D) reject the research hypothesis.
Answer:
B) reject the null hypothesis.
Step-by-step explanation:
