Answer:
A. [tex]\frac{9}{10}[/tex]
B. 1
C. [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{30}[/tex] or [tex]\frac{1}{15}[/tex]
E. [tex]\frac{12}{70}[/tex] or [tex]\frac{6}{35}[/tex]
F. [tex]\frac{6}{90}[/tex] or [tex]\frac{1}{15}[/tex]
G. [tex]\frac{9}{32}[/tex]
H. [tex]\frac{4}{15}[/tex]
Answer:
Step-by-step explanation:
Reducing the given expressions to the lowest terms:
A. 3/10 + 6/10:
B. 1/3 + 1/4 + 1/6:
C. 5/6-3/6:
D. 2/3-6/10:
E. 4/10*3/7:
F. 1/6*6/15:
G. 1/8 divided by 4/9:
H. 1/5 divided by 3/4:
Given: g(x) = square root x-4 and h(x) = 2x - 8 What are the restrictions on the domain of g of h. x greater than or equal to
Answer:
Step-by-step explanation:
x-4 greater or equal 0
x greater or equal 4
Answer:
The actual answer is x is greater than or equal to 6 (i used the answer that was on here and got it wrong so here is the correct answer!!)
just did the test on edg 2021
Show all work to solve 3x^2 – 5x – 2 = 0.
Answer:
Step-by-step explanation:
3x2−5x−2=0
For this equation: a=3, b=-5, c=-2
3x2+−5x+−2=0
Step 1: Use quadratic formula with a=3, b=-5, c=-2.
x= (−b±√b2−4ac )2a
x= (−(−5)±√(−5)2−4(3)(−2) )/2(3)
x= (5±√49 )/6
x=2 or x= −1 /3
Answer:
x=2 or x= −1/ 3
The solutions to the equation are x = -1/3 and x = 2.
Here are the steps on how to solve [tex]3x^{2}[/tex] – 5x – 2 = 0:
First, we need to factor the polynomial. The factors of 3 are 1, 3, and the factors of -2 are -1, 2. The coefficient on the x term is -5, so we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Next, we set each factor equal to 0 and solve for x.
(3x + 1)(x - 2) = 0
3x + 1 = 0
3x = -1
x = -1/3
x - 2 = 0
x = 2
Therefore, the solutions to the equation [tex]3x^{2}[/tex] – 5x – 2 = 0 are x = -1/3 and x = 2.
Here is the explanation for each of the steps:
Step 1: In order to factor the polynomial, we need to find two numbers that add up to -5 and multiply to -2. The two numbers -1 and 2 satisfy both conditions, so the factored polynomial is (3x + 1)(x - 2).
Step 2: We set each factor equal to 0 and solve for x. When we set 3x + 1 equal to 0, we get x = -1/3. When we set x - 2 equal to 0, we get x = 2. Therefore, the solutions to the equation are x = -1/3 and x = 2.
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Which equation can be used to find the area of the rectangle? A. A=9+4 B. A=1/2 (9)(4) C. A=9+9+4+4 D. A=(9)(4)
Answer:
D. A=(9)(4)
Step-by-step explanation:
area= length x width = 9x4
A restaurant has a main location and a traveling food truck. The first matrix A shows the number of managers and associates employed. The second matrix B shows the average annual cost of salary and benefits (in thousands of dollars). Complete parts (a) through (c) below.
Managers Associates
Restaurant 5 25 = A
Food Truck 1 4
Salary Benefits
Managers 41 6 = B
Associates 20 2
a. Find the matrix product AB .
b. Explain what AB represents.
c. According to matrix AB , what is the total cost of salaries for all employees (managers and associates) at the restaurant? What is the total cost of benefits for all employees at the food truck?
Answer:
A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]
Step-by-step explanation:
Given A= [tex]\left[\begin{array}{cc}5&25\\1&4\end{array}\right] \left[\begin{array}{cc}41&6\\20&2\end{array}\right][/tex] = B
Finding A*B means multiplying the first row with the first column and first row with the second column would give the first row elements. The second ro0w elements are obtained by multiplying the second row with the 1st column and second row with the second column.
so A*B= [tex]\left[\begin{array}{cc}5*41+ 25*20&5*6 + 25*2\\ 1*41+4*20 & 1*6+ 4*2\end{array}\right][/tex]
Now multiply and add the separate elements of the matrix A*B=
[tex]\left[\begin{array}{cc}205+500&30+50\\41+80&6+8\end{array}\right][/tex]
A*B= [tex]\left[\begin{array}{cc}705&80\\121&14 \end{array}\right][/tex]
b. The 1st element of the 1st row shows the salaries of the managers and 2nd element of the 1st row the salaries of associates at the restaurant . The second row 1 st element shows the benefits of the managers and 2nd element the benefits of the associates at the food truck.
c. The total cost of salaries for all employees (managers and associates) at the restaurant = 705 + 80 = 785
Total cost of benefits for all employees at the food truck= 121 + 14= 135
HELP ASAP! The number of entertainment websites in 1995 wass 54. By 2004 there were 793 entertainment website..
Approximately, what was the rate of change for the number of the websites for this time period??
=============================================================
How I got that answer:
We have gone from 54 websites to 793 websites. This is a change of 793-54 = 739 new websites. This is over a timespan of 2004-1995 = 9 years.
Since we have 739 new websites over the course of 9 years, this means the rate of change is 739/9 = 82.1111... where the '1's go on forever. Rounding to the nearest whole number gets us roughly 82 websites a year.
----------
You could use the slope formula to get the job done. This is because the slope represents the rise over run
slope = rise/run
The rise is how much the number of websites have gone up or down. The run is the amount of time that has passed by. So slope = rise/run = 739/9 = 82.111...
In a more written out way, the steps would be
slope = rise/run
slope = (y2-y1)/(x2-x1)
slope = (793 - 54)/(2004 - 1995)
slope = 739/9
slope = 82.111....
Erika has 3 pieces of ribbon. Each piece is 25 yards long. She needs to cut pieces that are 22 inches long. What is the greatest number of 22 inch pieces she can cut from the 3 pieces of ribbon
Answer:
She can cut 122 pieces.
Step-by-step explanation:
She has 3 pieces of ribbon that are 25 yds long. In total, she has 75 yds, which is equal to 2700 in. Erika needs 22 in. pieces, so just divide 2700 by 22 to get your number.
2700/22 ≈ 122.72
State the domain and range of the following functions f(x) =1/x+3 g(x) =sqrt x+6
Answer:
For the function [tex]f(x)=\frac{1}{x} +3[/tex]. The domain is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex] and the range is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].
For the function [tex]g(x) =\sqrt{x+6}[/tex]. The domain is [tex]\left[-6, \infty\right)[/tex] and the range is [tex]\left[0, \infty\right)[/tex].
Step-by-step explanation:
The domain of a function is the set of input or argument values for which the function is real and defined.
The range of a function is the complete set of all possible resulting values of the dependent variable, after we have substituted the domain.
[tex]f(x)=\frac{1}{x} +3[/tex] is a rational function. A rational function is a function that is expressed as the quotient of two polynomials.
Rational functions are defined for all real numbers except those which result in a denominator that is equal to zero (i.e., division by zero).
The domain of the function is [tex]\left(-\infty \:,\:0\right)\cup \left(0,\:\infty \:\right)[/tex].
The range of the function is [tex]\left(-\infty, 3\right) \cup \left(3, \infty\right)[/tex].
[tex]g(x) =\sqrt{x+6}[/tex] is a square root function.
Square root functions are defined for all real numbers except those which result in a negative expression below the square root.
The expression below the square root in [tex]g(x) =\sqrt{x+6}[/tex] is [tex]x+6[/tex]. We want that to be greater than or equal to zero.
[tex]x+6\geq 0\\x\ge \:-6[/tex]
The domain of the function is [tex]\left[-6, \infty\right)[/tex].
The range of the function is [tex]\left[0, \infty\right)[/tex].
The ratio of boys to girls in Jamal's class is 3:2. If four more girls join the class, there will be the same number of boys and girls. What is the number of boys in the class?
Answer:
12 boys
Step-by-step explanation:
From the above question:
Number of boys = 3
Number of girls = 2
Boys: Girls
3:2
Let :
a = boys
b = girls
Hence, a : b = 3 : 2
a/b = 3/2
Cross Multiply
2a = 3b .......... Equation 1
a = 3b/2
If four more girls join the class, there will be the same number of boys and girls
Hence,
a: b + 4 = 3 : 3
a/b + 4 = 3/3
Cross Multiply
3a = 3(b + 4)
3a = 3b + 12 ........ Equation (2)
From Equation 1: a = 3b/2
Substitute 3b/2 for a in Equation 2 we have:
3a = 3b + 12 .........Equation 2
3(3b/2) = 3b + 12
9b/2 = 3b + 12
Cross Multiply
9b = 2(3b + 12)
9b= 6b + 24
9b - 6b = 24
3b = 24
b = 8
Substitute 8 for b in Equation 1
a = 3b/2
a = 3 × 8/2
a = 24/2
a = 12
Therefore, the number of boys in the class is 12
by how much is 25% of #25 greater than 15% of #15
Answer:
4
Step-by-step explanation:
25% of 25
0.25 × 25 = 6.25
15% of 15
0.15 × 15 = 2.25
Find the difference.
6.25 - 2.25
= 4
[tex]\frac{d}{7}[/tex] + –59 = –50
d = _______
A tablet contains 0.5 mg of medication. A patient receives 5 tablets a day. How many mg patient receive per day?
Answer:
2.5 mg
Step-by-step explanation:
.5 x 5 = 2.5
The graph represents function 1 and the equation represents function 2: A graph with numbers 0 to 4 on the x-axis and y-axis at increments of 1. A horizontal straight line is drawn joining the ordered pairs 0, 3 and 4, 3. Function 2 y = 5x + 1 How much more is the rate of change of function 2 than the rate of change of function 1? PLEASE ANSWER SOON I NEED IT BAD WHO EVER ANSWERS FIRST GETS VOTE FOR BRAINLYIEST
Answer:
Rate of change of function 1: ZERO
Rate of change of function 2: TWO
The rate of change of function 2 is 2 more than the rate of change of function 1.
Step-by-step explanation:
Hope this helps and please mark as brainiest!
Answer:
The answer is 2.
Step-by-step explanation:
ope Equation
fy
What is the equation of the line in point-slope form?
4
= {(x + 4)
Oy+4=;
O y-4 = 2(x + 4)
N
Oy - 0 = 2(x-4)
Oy - 4 = 2(x -0)
4
-2.
2.
Answer:
A
Step-by-step explanation:
For point-slope form, you need a point and the slope.
y - y₁ = m(x - x₁)
Looking at the graph, the points you have are (4, 0) and (-4, -4). You can use these points to find the slope. Divide the difference of the y's by the difference of the x's/
-4 - 0 = -4
-4 - 4 = -8
-4/-8 = 1/2
The slope is 1/2. This cancels out choices C and D.
With the point (-4, -4), A is the answer.
the equation of the line in slope-intercept form is:
y = (1/2)x - 2
What is the Linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
From the graph, two points on the line are (-4, -4) and (4,0),
The formula for the slope of a line is:
m = (y₂ - y₁) / (x₁ - x₁)
where (x₁, y₁) and (x₂, y₂) are two points on the line.
Using the given points (-4, -4) and (4, 0), we can calculate the slope:
m = (0 - (-4)) / (4 - (-4))
m = 4 / 8
m = 1/2
Now that we know the slope, we can use the slope-intercept form of a line, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the y-intercept, we can use one of the given points on the line. Let's use the point (-4, -4):
y = mx + b
-4 = (1/2)(-4) + b
-4 = -2 + b
b = -2
Therefore, the slope-intercept form of the line is y = (1/2)x - 2.
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The half-life of radium-226 is 1590 years. If a sample contains 400 mg how many mg will remain after 4000 years?
Answer:
69.9 mg
Step-by-step explanation:
A = A₀ (½)^(t / T)
where A is the final amount,
A₀ is the initial amount,
t is time,
and T is the half life.
A = 400 (½)^(4000 / 1590)
A = 69.9 mg
76% is between which of the following two numbers?
Hey there!
You haven't provided any answer options but here's how you would solve a problem like this.
To find the number in between two numbers, you add it up and divide it by two!
So, what's between 1 and 3? Well you do 1+3 is 4 then divide by 2 you get 2!
100 and 580? You add them to get 680 then divide by two you get 340!
In between 0.57 and 0.69? Adding gives you 1.26 and then divide by two and we have 0.63!
And with percents, let's do 45% and 67%. You add you get 112% and then divide by two you have 56%!
So, with your answer options just add them up and divide by two and see which one gives you 76%!
I hope that this helps!
What is the point-slope form of a line with slope 3/2 that contains the point
(-1,2)?
A. y+2 = (x - 1)
B. y-2 = {(x-1)
C. y-2 = = {(x+1)
D. y+2= {(x+1)
Answer:
y - 2 = (3/2)(x + 1)
Step-by-step explanation:
Start with the point-slope formula y - k = m(x - h). With m = 3/2, h = -1 and k = 2, we get:
y - 2 = (3/2)(x + 1)
Does the following systems produce an infinite number of solutions 2y + x = 4 ; 2y = -x +4
Answer:
Yes.
Step-by-step explanation:
In the future, simply plug both equations into Desmos.
find the average rate of change if the function f(x)=x^2+4x from x1=2 to x2=3
Replace x with 2 and solve:
2^2 + 4(2) = 4 + 8 = 12
Replace x with 3 and solve:
3^2 + 4(3) = 9 + 12 = 21
The difference between the two answers is : 21 -12 = 9
The difference between the two inputs is 3-2 = 1
The rate of change is the change in the answers I’ve the change in the inputs:
Rate of change = 9/1 = 9
if it takes four men to dig a land in 6 days.how many days will it take 6 men to build that same land.
Answer:
4 daysSolution,
____________________________
Men ------------------------------ Days
4 ------------------------> 66 ------------------------> X (suppose)_____________________________
In case of indirect proportion,
4/6= 6/X
or, 6*X= 6*4 ( cross multiplication)
or, 6x= 24
or, 6x/6= 24/6 ( dividing both sides by 6)
x= 4 days
Hope this helps...
Good luck on your assignment..
Answer:
[tex]\boxed{4 days}[/tex]
Step-by-step explanation:
M1 = 4
D1 = 6
M2 = 6
D2 = x (we've to find this)
Since, it is an inverse proportion (more man takes less days for the work to complete and vice versa), so we'll write it in the form of
M1 : M2 = D2 : D1
4 : 6 = x : 6
Product of Means = Product of Extremes
=> 6x = 4*6
=> 6x = 24
Dividing both sides by 6
=> x = 4 days
I NEED HELP FAST, THANKS! :)
Answer:
33 units²
Step-by-step explanation:
A (graphing) calculator shows you that f(4) ≈ 8, and f(8) ≈ 8.5. The curve is almost a straight line between, so the area is approximately ...
A = (1/2)(8 + 8.5)(4) = 33
__
If you do the integration, it gets a bit messy.
[tex]\displaystyle\dfrac{5}{7}\int_4^8{x^{2/7}}\,dx+\dfrac{1}{2}\int_4^8{x^{4/9}}\,dx+\int_4^8{6}\,dx\\\\=\left.\left(\dfrac{5}{9}x^{9/7}+\dfrac{9}{26}x^{13/9}+6x\right)\right|_4^8\approx 33.16[/tex]
The appropriate answer choice is 33 square units.
Find the percent of increase. Original Price: $200 Retail Price: $250
Answer:
The percent of increase is 25%
Step-by-step explanation:
Percentage increase = increase in price/original price × 100 = ($250 - $200)/$200 × 100 = $50/$200 × 100 = 25%
pls pls help me help me help me
Answer:
2
Step-by-step explanation:
Answer:
I hope it will help you....
. The client was hoping for a likability score of at least 5.2. Use your sample mean and standard deviation identified in the answer to question 1 to complete the following table for the margins of error and confidence intervals at different confidence levels. Note: No further calculations are needed for the sample mean. (6 points: 2 points for each completed row) Confidence Level | Margin of error | Center interval | upper interval | Lower interval 68 95 99.7
Answer:
The 68% confidence interval is (6.3, 6.7).
The 95% confidence interval is (6.1, 6.9).
The 99.7% confidence interval is (5.9, 7.1).
Step-by-step explanation:
The Central Limit Theorem states that if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n ≥ 30) from the population with replacement, then the distribution of the sample-means will be approximately normally distributed.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\bar x[/tex]
And the standard deviation of the sample means (also known as the standard error)is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}} \ \text{or}\ \frac{s}{\sqrt{n}}[/tex]
The information provided is:
[tex]n=400\\\\\bar x=6.5\\\\s=4[/tex]
As n = 400 > 30, the sampling distribution of the sample-means will be approximately normally distributed.
(a)
Compute the 68% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.9945\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.1989\\\\=(6.3011, 6.6989)\\\\\approx (6.3, 6.7)[/tex]
The 68% confidence interval is (6.3, 6.7).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.7-6.3}{2}=0.20[/tex]
(b)
Compute the 95% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 1.96\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(6.108, 6.892)\\\\\approx (6.1, 6.9)[/tex]
The 95% confidence interval is (6.1, 6.9).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{6.9-6.1}{2}=0.40[/tex]
(c)
Compute the 99.7% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot \frac{s}{\sqrt{n}}[/tex]
[tex]=6.5\pm 0.594\cdot \frac{4}{\sqrt{400}}\\\\=6.5\pm 0.392\\\\=(5.906, 7.094)\\\\\approx (5.9, 7.1)[/tex]
The 99.7% confidence interval is (5.9, 7.1).
The margin of error is:
[tex]MOE=\frac{UL-LL}{2}=\frac{7.1-5.9}{2}=0.55[/tex]
How do you write 0.0683 in scientific notation? ____× 10^____
Answer:
It's written as
[tex]6.83 \times {10}^{ - 2} [/tex]
Hope this helps you
Answer:
6.83 × 10 -2
hopefully this helped :3
I NEED HELP PLEASE, THANKS! :)
A music concert is organized at a memorial auditorium. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows. Find the number of people that can be accommodated in the sixteenth row. (Show work)
Answer: 136
Step-by-step explanation:
An= A1+(n-1)d
A1=16, d=8, and n=16
A16= 16 +(16-1)(8)
A16= 16(15)(8)
A16= 16+120
A16=136
Hey there! :)
Answer:
f(16) = 136 seats.
Step-by-step explanation:
This situation can be expressed as an explicit function where 'n' is the row number.
The question also states that the number of seats increases by 8. Use this in the equation:
f(n) = 16 + 8(n-1)
Solve for the number of seats in the 16th row by plugging in 16 for n:
f(16) = 16 + 8(16-1)
f(16) = 16 + 8(15)
f(16) = 16 + 120
f(16) = 136 seats.
According to a recent study, some experts believe that 15% of all freshwater fish in a particular country have such high levels of mercury that they are dangerous to eat. Suppose a fish market has 150 fish we consider randomly sampled from the population of edible freshwater fish. Use the Central Limit Theorem (and the Empirical Rule) to find the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15. You can use the Central Limit Theorem because the fish were randomly sampled; the population is more than 10 times 150; and n times p is 22.5, and n times (1 minus p) is 127.5, and both are more than 10.
Answer:
The approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=0.15[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
As the sample size is large, i.e. n = 150 > 30, the central limit theorem can be used to approximate the sampling distribution of sample proportion by the normal distribution.
Compute the mean and standard deviation as follows:
[tex]\mu_{\hat p}=0.15\\\\\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.15(1-0.15)}{150}}=0.0292[/tex]
So, [tex]\hat p\sim N(0.15, 0.0292^{2})[/tex]
In statistics, the 68–95–99.7 rule, also recognized as the empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the Normal distribution lie within one, two and three standard deviations of the mean, respectively.
Then,
P (µ-σ < X < µ+σ) ≈ 0.68
P (µ-2σ <X < µ+2σ) ≈ 0.95
P (µ-3σ <X < µ+3σ) ≈ 0.997
Then the approximate probability that the market will have a proportion of fish with dangerously high levels of mercury that is more than two standard errors above 0.15 is 0.95.
That is:
[tex]P(\mu_{\hat p}-2\sigma_{\hat p}<\hat p<\mu_{\hat p}+2\sigma_{\hat p})=0.95\\\\P(0.15-2\cdot0.0292<\hat p<0.15+2\cdot0.0292)=0.95\\\\P(0.092<\hat p<0.208)=0.95[/tex]
which term is the rate at which work is done
Answer:
The answer is power.Hope this helps you
1)
Check all the expressions that are equal to this one:
5. (4+1)
A. (5 • 4) + 1
B. 5.4 + 5 - 1
C. (4+1) • 5
D. 5. (1 + 4)
Evaluate the expression ........
Answer:
13
Step-by-step explanation:
p^2 -6p +6
Let p=-1
(-1)^2 -6(-1) +6
1 +6+6
13
Denise is planning to put a deck in her back yard. The deck will be a 10-by-7-foot rectangle with a semicircle of diameter 4 feet, as shown below. Find the area of the deck (in square feet).(round your answer to two decimal places)
Answer:
[tex]approx. = 85.28 {ft}^{2} [/tex]
Step-by-step explanation:
You can think of this as adding the area of the rectangular portion of the deck (length x width) and the semicircular portion (πr^2)/2.
(l×w)+(πr^2)/2
(10×7)+((π2^2)/2
79+2π
[tex]approx. = 85.28 {ft}^{2} [/tex]