Answer:
x = 3 or x = 4.
Step-by-step explanation:
We are given the following inequality:
[tex](x - 2)(x - 5) < 0[/tex]
It is a product, and a product is negative when one term is positive and the other is negative.
First case:
[tex]x - 2 > 0 \rightarrow x > 2[/tex]
And
[tex]x - 5 < 0 \rightarrow x < 5[/tex]
Thus, in the natural set: x = 3 and x = 4.
Second case:
[tex]x - 2 < 0 \rightarrow x < 2[/tex]
And
[tex]x - 5 > 0 \rightarrow x > 5[/tex]
Empty set.
Union of the cases:
Second case is the empty set, so we only count the first case. Thus x = 3 or x = 4.
Solve the system of equation y = -2+5
y = x^2 + 3x + 9
Answer:
9 is y
Step-by-step explanation:
One side of a triangle is 3 times longer than the shortest side and the third side is 4 centimeters longer than the shortest side. The perimeter of the triangle is 64.
How long is the shortest side of the triangle?
Answer:
First side is: 12cm
Second side is: 36cm
Third side is: 16cm
Step-by-step explanation:
Let x represent the shorter side
Then 3x represents the second side, and
x + 4 represents the third side.
Perimeter of three sides:
P = x + 3x + (x + 4)
Perimeter is 64, so
64 = x + 3x + (x + 4)
64 = 5x + 4
60 = 5x
12 = x
First side is x: 12cm
Second side is 3x: 3(12) = 36cm
Third side is x + 4: 12 + 4 = 16cm
Is my answer correct?
9514 1404 393
Answer:
yes
Step-by-step explanation:
By the "rule of 72", the amount will be doubled in 72/I years, where I is the annual interest rate in percent. That is, it can be estimated to take 72/4 = 18 years to double the $240 investment to $480. It would take another 18 years to double it again to $960. So, to achieve a balance of $1500 will be expected to take more than 36 years. The only reasonable answer choice is the one you have selected.
__
The exact solution is ...
log (1500/240)/log(1 +0.04) ≈ 46.72 years ≈ 47 years.
Standard Error from a Formula and a Bootstrap Distribution Sample A has a count of 30 successes with and Sample B has a count of 50 successes with . Use StatKey or other technology to generate a bootstrap distribution of sample differences in proportions and find the standard error for that distribution. Compare the result to the value obtained using the formula for the standard error of a difference in proportions from this section.
Answer:
Using a formula, the standard error is: 0.052
Using bootstrap, the standard error is: 0.050
Comparison:
The calculated standard error using the formula is greater than the standard error using bootstrap
Step-by-step explanation:
Given
Sample A Sample B
[tex]x_A = 30[/tex] [tex]x_B = 50[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
Solving (a): Standard error using formula
First, calculate the proportion of A
[tex]p_A = \frac{x_A}{n_A}[/tex]
[tex]p_A = \frac{30}{100}[/tex]
[tex]p_A = 0.30[/tex]
The proportion of B
[tex]p_B = \frac{x_B}{n_B}[/tex]
[tex]p_B = \frac{50}{250}[/tex]
[tex]p_B = 0.20[/tex]
The standard error is:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * (1 - 0.30)}{100} + \frac{0.20* (1 - 0.20)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.30 * 0.70}{100} + \frac{0.20* 0.80}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.21}{100} + \frac{0.16}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.0021+ 0.00064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.00274}[/tex]
[tex]SE_{p_A-p_B} = 0.052[/tex]
Solving (a): Standard error using bootstrapping.
Following the below steps.
Open StatkeyUnder Randomization Hypothesis Tests, select Test for Difference in ProportionsClick on Edit data, enter the appropriate data Click on ok to generate samplesClick on Generate 1000 samples ---- see attachment for the generated dataFrom the randomization sample, we have:
Sample A Sample B
[tex]x_A = 23[/tex] [tex]x_B = 57[/tex]
[tex]n_A = 100[/tex] [tex]n_B =250[/tex]
[tex]p_A = 0.230[/tex] [tex]p_A = 0.228[/tex]
So, we have:
[tex]SE_{p_A-p_B} = \sqrt{\frac{p_A * (1 - p_A)}{n_A} + \frac{p_A * (1 - p_B)}{n_B}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.23 * (1 - 0.23)}{100} + \frac{0.228* (1 - 0.228)}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{\frac{0.1771}{100} + \frac{0.176016}{250}}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.001771 + 0.000704064}[/tex]
[tex]SE_{p_A-p_B} = \sqrt{0.002475064}[/tex]
[tex]SE_{p_A-p_B} = 0.050[/tex]
Double Dice is a game in which two dice are rolled. A player wins the game if a certain sum is rolled. A player wins $7.00 if he rolls a sum of 5 or 6 and $20.00 if he rolls a sum of 2 or 3. He wins nothing if any other sum is rolled.
A. Define the random variable, X.
B. Write out the probability distribution function for the game.
C. What is the expected value of the game?
D. Assuming you have to pay $6.00 to play the game, explain what happens in the long run. (Is it a good idea to play the game?)
Answer:
3.417
Kindly check explanation
Step-by-step explanation:
X : $7 ; $20 ; $0
Sample space for the sum of two die rolls :
Probability of obtaining a sum of 5 or 6 ;
P(sum of 5 or 6) = 9/36 = 1/4
Probability of obtaining a sum of 2 or 3 ;
P(Sum of 2 or 3) = 3/36 = 1/12
Probability of obtaining a sum of other Tha 2,3, 5 or 6 ; = 24/ 36 = 2/3
The probability distribution :
X _____ 0 _______ 7 _____ 20
P(x) ___ 2/3 _____ 1/4 ____ 1/12
Expected value of the game ; E(X) ;
E(X) = Σx*p(x)
E(X) = (0*2/3) + (7*1/4) + (20*1/12)
E(X) = 0 + 1.75 + 1.6667
E(X) = 3.417
This means that if the game is paid for a long time, the mean or expected winning will be ; $3.417
If game has to be played with $6 ; then to determine if it is a good idea to play the game on a long run, we calculate the payoff ;
The payoff is :
Expected value - playing cost
$3.417 - $6 = - $2.583
Since payoff is negative, we can conclude that it is not a good idea to play the game in the long run : as the expected value is lesser than the playing fee.
Graph the line.
y=3x
Answer:
desmos(dot)com/calculator/gv8jsoui4w
Step-by-step explanation:
Create a table of appropriate x values e.g. x = 2 and substitute into y=3x which will be y=3*2 meaning y=6 at the point x=2. Repeat with different x values until you have enough points to draw a straight line.
please answer this. i’m so confused
Answer:
1
Step-by-step explanation:
All sides have to be congruent making option 1 correct
~ LadyBrain
A summer music program admits a total of 30 students. Every year the program is filled. Some years there are only girls, and some years there are only boys. A function, f, is written that gives the number of girls, y, enrolled in the program based on the number of boys, x. If this function is graphed over the appropriate domain, which statement must be true? Select all the statements
that apply.
Answer:
c d
Step-by-step explanation:
trust me
Evaluate: (ƒ − g)(−2)
From the graph,
f(-2) = 0
and, g(-2) = 0
(ƒ − g)(−2)= f(-2)-g(-2) = 0
OPTION B is the correct answer
2 1/3 - (-5) =
what does it equal
Answer:
7 1/3
Step-by-step explanation:
See image below:)
Find the equation of the line below.
10
(4,8)
х
t(1,2)
- 10
10
- 10
O A. y = 2x
O B. y = 1x
O C. y = x
O D. ya
Answer:
y=2x
Step-by-step explanation:
The line passes through the origin, so the y-intercept = 0
the slope m can be found with
m = (y2-y1)/(x2-x1) = (8-2)/(2-1) = 2
Therefore the equation of the line is
y = 2x + 0 = 2x
Answer:
A) y = 2x
Step-by-step explanation:
We are given the points (4,8) and (1,2).
[tex]\frac{2-8}{1-4}=\frac{-6}{-3}=\frac{6}{3}=\boxed{2}[/tex]
The line passes through the origin.
Option A should be correct.
Hope this helps.
The
Slope
a line that goes
through the points (r, 6 ) and (4,2
is 4 find r
7. Solve for b.
b
26°
Answer:
64°
Step-by-step explanation:
We know that a right angle is 90°
so we do 90° - 26° = 64°
(Will mark brainlest ) help me to find the value of x or theta (step by step)
Answer:
X = 6
Step-by-step explanation:
sin○ = opposite side/hypotenuse
sin 45 = 3 root2/x
1/root2 = 3 root2/x
x = 3 × 2
x = 6
Answer:
x=6 cm
Step-by-step explanation:
take 45 degree as reference angle
using sin rule
sin 45 =opposite/hypotenuse
[tex]\frac{1}{\sqrt{2} } =\frac{3\sqrt{2} }{x}[/tex]
do cross multiplication
[tex]x=\sqrt{2} * 3\sqrt{2}[/tex]
x=6
Can any one help?
Solve the following equations:
Answer:
2- x=16/3 or 5.3
4- x=8
Step-by-step explanation:
yeah
Researchers at a medical school conducted a study to test the effectiveness of a new drug for lowering cholesterol. The 52 subjects who volunteered for the study were each given a randomly generated number. Subjects with an odd number were given the new drug, while those with an even number were given a placebo. Cholesterol levels before and after the treatment were measured for each subject, and the differences were computed.
This study is an example of ______________ study. The difference in cholesterol level is _____________ the variable. The treatment with drug or placebo is the ____________ variable.
Answer:
1. An Experimental
2. Dependent
3. Independent
Step-by-step explanation:
Considering the description of how the research was carried out, it can be concluded that This study is an example of AN EXPERIMENTAL study. This because the researcher is trying to study the effectiveness of a new drug for lowering cholesterol
The difference in cholesterol level is the DEPENDENT variable. This is because the difference in cholesterol level is what the researcher wants to determine.
The treatment with a drug or placebo is the INDEPENDENT variable. This is because this is what the researcher manipulates to determine the difference in cholesterol level which is the dependent variable in this experimental study.
PLEASE HELP ASAP!!! WILL MARK BRAINLIEST !!
Answer:
CA = LJ
Step-by-step explanation:
The third side
CA = LJ
Answer:
CA=LG is correct answer
Which is the decimal expansion of the following 1/5
Answer:
Decimal expansion of 1/5 = 0.2
Sum of all edges of all shape
Answer:
Infinient amount buddy. They are infinent amounts of polygons, as a polygon is a shape with more then 3 sides and closed. This means as long as a number is bigger then 3, there will be a shape for it, so infinent sides
Step-by-step explanation:
An object dropped from a height of 500 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=500−16t^2. Express t as a function of height h, and find the time to reach a height of 100 feet
Step-by-step explanation:
the answer is in the above image
Select the correct answer. How does the risk of needing insurance impact the cost of premlums? А. In some cases, higher risk results in lower costs. B. Higher risk always results in lower costs.
C. Higher risk always results in higher costs.
D In some cases, higher risk results in higher costs.
Answer:
A
Step-by-step explanation:
Which expression is equivalent to
^3 sqrt 1/1000 c^9 d^12
Answer:
[tex] \sqrt[3]{ \frac{1}{1000} {c}^{9} {d}^{12} } \\ = \frac{1}{10} {c}^{3} {d}^{4} [/tex]
Jenny made $35,000 in taxable income last year suppose the income tax rate is 10% for the first 9000+16% for the amount over 9000 how much money is jenny pay in income tax for last year
Answer:
for the first 9000 $ tax rate is 10%
so tax = 10% of 9000 = 900
rest of the amount = 35000-9000 =26000
tax rate is 16%
tax on 26000 = 16% of 26000 = 3900
total tax Debra has to pay for last year = 900 + 3900 = $4800
Step-by-step explanation:
Answer:
900+3900=$4800
#CarryOnLearning
Which measure of central tendency best describes the data set below?
{0, 80, 85, 88, 90, 95}
A. the mean, 73
B. the mode, none
C. the range, 95
D. the median, 86.5
Answer:
The correct answer would be D, the median 86.5. In this set of data most of the values are in the 80's or 90's.
Step-by-step explanation:
d point is the answer
Answer:
D) The median, 86.5
Step-by-step explanation:
Most of the data is clustered in the 80s. Therefore, D is correct.
What is the image point of (1,-7) after the transformation T-3,-1 degrees R180 degrees?
Answer:
first hust rotate 180 and next reflect it over x axis.
the given point (-7,3) id in second quadrant but after rotation it will be in fourth quadrant.
afterwards you have to refect that point over x-axis which gives you the image of the points on first quadrant ie. (7,1).
Can someone please help me?
Answer:
A
Step-by-step explanation:
to find the inverse, there are two steps
1-interchange x and y
2-solve for y
so y=x+1/x
interchange to get x=y+1/y
and solving for y we multiply both sides by y to get xy=y+1
subtract both sides by y yielding xy-y=1
factor out y to get y(x-1)=1
then divide to get y=1/x-1
Three relatives will share an inheritance of 196,800 in the ratio of 3 to 7 to 2. How many dollars of the inheritance will each of the relatives receive?
Answer:
49200
114800
32800
Step-by-step explanation:
196800/12=ans
ans * 3
ans * 7
ans * 2
In a triangle, the measure of the first angle is twice the measure of the second angle. The measure of the third angle is 80° more than the measure of the second angle. Use the fact that the sum of the measures of the three angles of a triangle is 180° to find the measure of each angle. what is the measure of the first angle?
Answer:
The measure of the first angle is 50°.
Step-by-step explanation:
Let the three angles be a, b, and c.
The measure of the first angle is twice the measure of the second angle. In other words:
[tex]a=2b[/tex]
The measure of the third angle is 80° more than the measure of the second angle. In other words:
[tex]c=b+80[/tex]
And since the interior angles of a triangle must equal 180°:
[tex]a+b+c=180[/tex]
Substitute a and c:
[tex](2b)+b+(b+80)=180[/tex]
Combine like terms:
[tex]4b+80=180[/tex]
Subtract 80 from both sides:
[tex]4b=100[/tex]
And divide both sides by four:
[tex]b=25^\circ[/tex]
So, the measure of the second angle is 25°.
Since the measure of the first is twice the second, the measure of the first angle is 50°.
(And since the measure of the third is 80° than the second, the measure of the third angle is 105°.)
WILL GIVE BRAINLIEST FOR ANSWER
Answer:
the answe is 187 cm square
You have 3 five dollar bills and 4 ten dollar bills in your pocket. If you pull out 2 bills, what is the probability they are both tens?
Answer: I think its 4%
Step-by-step explanation: 3+4=7 7/2=3.5
Answer:
1/14
Step-by-step explanation:
