Answer: 8
Step-by-step explanation: Think of the 32 in this problem as 32/1.
So rewriting, we have 1/4 × 32/1.
Now, the 4 and 32 cross-cancel to 1 and 8.
So we have 8/1 or just 8.
Two sides of a triangle have the same length. The third side measures m less than twice the common length. The perimeter of the triangle is m. What are the lengths of the three sides?
Answer:
The length of the first side of a triangle = 6 m
The length of the second side of a triangle = 6 m
The length of the third side of a triangle = 9 m
Step-by-step explanation:
The complete question is: Two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m. What are the lengths of the three sides?
We are given that two sides of a triangle have the same length. The third side measures 3 m less than twice the common length. The perimeter of the triangle is 21 m.
Let the common length of the two sides of a triangle be 'x m'.
So, the length of the first side of a triangle = x m
the length of the second side of a triangle = x m
the length of the third side of a triangle = (2x - 3) m
As we know that the perimeter of a triangle is given by;
The Perimeter of a triangle = Sum of all sides of a triangle
21 m = x + x + (2x - 3)
21 m = 2x + 2x - 3
21 m = 4x - 3
4x = 21 + 3
4x = 24 m
x = [tex]\frac{24}{4}[/tex] = 6 m
Hence, the length of the first side of a triangle = x = 6 m
the length of the second side of a triangle = x = 6 m
the length of the third side of a triangle = (2x - 3) = 12 - 3 = 9 m
Okay, last question! thank you for helping btw! B is the midpoint of AC if AB =3x-2 and BC= 6x-5 Find AC.
Answer:
9x-7
Step-by-step explanation:
AB =3x-2
BC= 6x-5
AC=AB+AC
AC=(3X-2)+(6X-5)
AC=3X-2+6X-5
AC=3X+6X-2-5
AC=9X-7
A precalculus course has 32 class meetings that last 1.75 hours each. How many minutes does the course meet in a semester. Express your answer in scientific notation.
Answer:
3.36 * 10³ minutesStep-by-step explanation:
If one pre calculus class lasts 1.75hours
32 class meetings will last 32*1.75 = 56 hours
Hence the number of hours that the precalculus meets in the semester is 56 hours. In order to know the number of minutes the same class meet, we will convert 56 hours to minutes.
Since 1 hour = 60 minutes
56hours = (56*60) minutes
56hours = 3360 minutes
Expressing 3360 in scientific notation means expressing it in exponential form.
3360 = 3.36 * 10³ minutes
Hence the precalculus class meets for 3.36 * 10³ minutes in a semester.
Find the absolute value. -|-1|
-|-1|=
Answer:
-1
Step-by-step explanation:
|-1 |= 1
-|-1| = 1
Answer:
-1
Step-by-step explanation:
The question should not be "find the absolute value". Finding the absolute value is part of this problem, but it is not the entire problem.
Think of absolute value of a number as the distance from that number to zero on the number line. A distance is not negative. It is only positive or zero. For example, the number 4 is 4 units from zero on the number line. Then the absolute value of 4 is 4. |4| = 4. Similarly, the number -4 is also 4 units from zero on the number line, so the absolute value of -4 is also 4. |-4| = 4. The absolute value of zero is zero since zero is at a distance of zero units from zero. An absolute value can only be zero or positive. It is never negative.
In your problem, you need to deal with the absolute value of -1 first. -1 is 1 unit from zero on the number line, so the absolute value of -1 is 1.
|-1| = 1
Your problem has one extra step which is the negative outside the absolute value.
-|-1| = -1
What are 2 Equivalent ratios for 3 and 8
Answer:
3 to 8 = 6 to 16 = 30 to 80
Step-by-step explanation:
Each time you multiply both numbers of a ratio by the same number, you get an equivalent ratio.
3 to 8
Multiply both 3 and 8 by 2:
6 to 16
Multiply both 3 and 8 by 10:
30 to 80
3 to 8 = 6 to 16 = 30 to 80
What is the order greatest to least, a b or c?
Somebody please help me
Answer:
find the area of two triangles and subtract them.
Triangle 1 = 1/2 x 20 x 20 = 200
Triangle 2 = 1/2 x 15 x 10 = 75
Area of shaded region: 200 - 75 = 125
The answer is F. 125
can someone help pls
Answer:
-8
Step-by-step explanation:
slope is change in y divided by change in x
slope = (12-36)/(11-8)
slope = -24/3
slope = -8
can earn 5 coins
Andrew is starting his own snow plowing business. Andrew has calculated that he needs to earn
$500 per week to support his family. If he knows he will only be able to work 50 hours per week,
what is the minimum amount of dollars per hour will he need to charge his customers?
Answer:Ten dollars per hour
Step-by-step explanation:
50 hour =500 dollars
1 hour = ?
Using the criss cross method we multiply one hour by five hundred dollars and divide by fifty dollars.
?=(1 hour×500 dollars)/50 hour
?= 500 dollars/50
?=10 dollars per hour
Your friend isn’t sure what size waist he is. He measures himself with a tape measure. What waist size is he in inches?
Answer:
32 1/2 inches
Step-by-step explanation:
Why this is true is the line is in the middle of 32 and 33 witch means it is 32 1/2
XY=4x, YZ=x, and XY=25
x=
YZ=
Answer:
both answer is 31°
Hope it is helpful for you
6.2megagrams/hectoliter to kilograms/deciliter
Answer:
6.2 kilograms/ deciliters
Step-by-step explanation:
megagrams to kilograms
1 megagram = 1000 kilograms
hectoliter to deciliter
1 hectoliter = 1000 deciliter
Using conversion factors
6.2megagrams 1000 kilgrams 1 hectoliter
---------------------- * ----------------------- * -------------------------
hectoliter 1 megagram 1000 deciliters
Canceling like terms
6.2 kilograms/ deciliters
Answer:
[tex]\Large \boxed{\mathrm{6.2 \ kilograms/deciliter}}[/tex]
Step-by-step explanation:
1 megagram = 1000 kilograms
6.2 megagrams = x (kilograms)
Cross multiplying.
x = 1000 × 6.2
x = 6200
6.2 megagrams = 6200 kilograms
1 hectoliter = 1000 deciliters
[tex]\displaystyle \sf \frac{6200 \ kilograms}{1 000\ deciliters }[/tex]
[tex]\displaystyle \frac{6200}{1000} =6.2[/tex]
6.2 megagrams/hectoliter = 6.2 kilograms/deciliter
Which of the following is the solution to 13/(x+2) = 8/(x-1)?
[tex] \frac{13}{(x + 2)} = \frac{8}{(x - 1)} [/tex]
By cross - multiplication
[tex] \implies13 \times (x - 1) = 8 \times (x + 2)[/tex]
[tex] \implies13x - 13 = 8x + 16[/tex]
[tex] \implies13x - 8x = 16 + 13[/tex]
[tex] \implies5x = 29[/tex]
[tex] \implies \: x = \frac{29}{5} [/tex]
[tex] \implies \: x = 5.8[/tex]
Solve for X
X/5 = 15
Answer:
75
Step-by-step explanation:
X/5=15
X=15*5
X=75
Ans.75
2-7, please help BRAINLEST
Answer:
n=11 is the answer.
Step-by-step explanation:
19+n=30
In order to find the value of n subtracting 19 on both sides
19-19+n=30-19
n=11 is your answer
Hope it will help you :)
Select the correct solution to the equation 4(3m−1)=2(m+3)
Answer:
m=1
Step-by-step explanation:
just expand the brackets using the distributive law and proceed to isolate x
Recently a sample of 36 pieces of thread showed a mean breaking strength of 8.93 oz. Can one conclude at a significance level of (a) 0.05, (b) 0.01 that the thread has become inferior?
Complete Question
It has been found from experience that the mean breaking strength of a particular brand of thread is 9.72 oz with a standard deviation of 1.4 oz. Recently a sample of 36 pieces of thread showed a mean breaking strength of 8.93 oz. Can one conclude at a significance level of (a) 0.05, (b) 0.01 that the thread has become inferior?
Answer:
At both [tex]\alpha = 0.05[/tex] and [tex]\alpha = 0.01[/tex] the conclusion is that the thread has become inferior
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 9.72 \ oz[/tex]
The standard deviation is [tex]\sigma = 1.40\ oz[/tex]
The sample size is n = 36
The sample mean is [tex]\= x = 8.93 \ oz[/tex]
The null hypothesis is [tex]H_o : \mu = 9.72 \ oz[/tex]
The alternative hypothesis is [tex]H_a : \mu < 9.72 \ oz[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{ 8.93 -9.72}{ \frac{ 1.4 }{ \sqrt{36} } }[/tex]
=> [tex]t = -3.33[/tex]
So
The p-value obtained from the z- table is
[tex]p-value = P( Z < -3.39) = 0.00034946[/tex]
So at [tex]\alpha = 0.0 5[/tex]
[tex]p-value < \alpha[/tex]
So we reject the null hypothesis,hence we conclude that the thread has become inferior
So at [tex]\alpha = 0.0 1[/tex]
[tex]p-value < \alpha[/tex]
So we reject the null hypothesis,hence we conclude that the thread has become inferior
Let a and b 2 positive real number such that a
Answer:
Proved
Step-by-step explanation:
Given
Integers: a and b
Where [tex]a < b[/tex]
Required
Show that [tex]a^n < b^n[/tex]
We start by writing out the given expression
[tex]a < b[/tex]
Then, take nth root of both sides
[tex]a^n < b^n[/tex]
For instance:
Let a = 2, b = 2 and n = 4
First
Since [tex]2 < 3[/tex]
Then
[tex]2^4 < 3^4[/tex]
[tex]16 < 81[/tex]
Proved
This is so for all positive values of a,b and n where a < b
Which are characteristics of table salt (NaCl)?
is insoluble in water
is held together by hydrogen bonds
is often supplemented with iodine
is held together by ionic bonds
is a compound
Answer:
The correct option (c) "is held together by ionic bonds".
Step-by-step explanation:
Table salt is NaCl. It is a combination of Sodium and Chlorine.
There is 1 valance electron in sodium. Its electronic configuration is 2,8,1
The electronic configuration of Chlorine is 2,8,7. It means that it needs 1 electron so that its octet gets completed.
Na transfers one electron to Cl. It becomes Na⁺. Cl gains one electron From Na. It becomes Cl⁻.
As a resuslt, Na⁺ and Cl⁻ forms. Both Na and Cl are ions. They held together by ionic bonds.
Help me please thank y’all
Answer:
30°
Step-by-step explanation:
60+60+2x=180
120+2x=180
2x=180-120
2x=60
x=30°
In ΔDEF, the measure of ∠F=90°, DE = 82 feet, and EF = 55 feet. Find the measure of ∠E to the nearest tenth of a degree.
Answer:
< E = 42.1° is the answer
Set up and evaluate a double integral to find the volume of the solid bounded by the graphs of the equations. z = xy, z = 0, y = x, x =1, first octant.
Answer:
1/8
Step-by-step explanation:
Given:
z = xy
z = 0
y = x
x =1
To find:
volume of the solid bounded by the graphs of the equations
Solution:
Compute integral of volume in the first octant:
[tex]Volume = V = \int\limits^1_0\int\limits^x_0 {z} \, dydx[/tex]
[tex]\int\limits^1_0\int\limits^x_0 {z} \, dydx = \int\limits^1_0\int\limits^x_0 {xy} \, dydx[/tex]
[tex]= \int\limits^1_0x\int\limits^x_0 {y} \, dydx[/tex]
= [tex]\int\limits^1_0[/tex] x y²/2 |ˣ₀ dx
= 1/2 [tex]\int\limits^1_0[/tex] x y² |ˣ₀ dx
= 1/2 [tex]\int\limits^1_0[/tex] x (x²-0²) dx
= 1/2 [tex]\int\limits^1_0[/tex] x³dx
= [tex]\frac{1}{2} \frac{x^{3+1} }{3+1}[/tex] |¹₀
= (1/2) (x⁴/4) |¹₀
= 1/8 x⁴ |¹₀
= 1/8 (1⁴ - 0⁴)
= 1/8 (1)
V = 1/8
The water inside a right cylinder tank is 6 inches above the bottom part of the tank of radius 1 feet and length 2 feet. Find the volume of the water.
Answer:
864π in³Step-by-step explanation:
Volume of the water is equivalent to the volume of a cylinder = πr²h where;
r is the radius of the cylindrical tank
h is the height of the water
Given parameters
radius of the cylindrical tank r = 1feet = 12 inches
height of the water inside the tank = 6inches
Volume of the water = πr²h
Volume of the water = π(12)²*6
Volume of the water = π*144*6
Volume of the water = 864π in³
Hence the volume of the water is 864π in³
Answer:
[tex]\huge \boxed{\mathrm{2714.34 \ in^3 }}[/tex]
Step-by-step explanation:
The volume formula for a right cylinder is given as :
[tex]V=\pi r^2 h[/tex]
[tex]V \Rightarrow \sf volume[/tex]
[tex]h \Rightarrow \sf height[/tex]
[tex]r \Rightarrow \sf radius[/tex]
The radius 1 feet ⇒ 12 inches
The height of the water in the cylinder is 6 inches
[tex]V=\pi (12)^2 (6)[/tex]
[tex]V= 2714.336053...[/tex]
The volume of the water is 2714.34 cubic inches.
Matthew goes hiking every 12 days and swimming every nine days he did both kinds of exercise today how many days from now will you go both hiking and swimming again
Answer:
3 days
Step-by-step explanation:
hiking = every 12 days = 1 day
swimming = every 9 days = 1 day
today = he did both exercise = 1 day
find:
how many days from now will you go both hiking and swimming again?
= 3 days
g European roulette. The game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green. A ball is spun onto the wheel and will eventually land in a slot, where each slot has an equal chance of capturing the ball. Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money. (a) Suppose you play roulette and bet $3 on a single round. What is the expected value and standard deviation of your total winnings
Answer:
The expected value and standard deviation of your total winnings are -$0.081 and $3 respectively.
Step-by-step explanation:
We are given that the game of European roulette involves spinning a wheel with 37 slots: 18 red, 18 black, and 1 green.
Gamblers can place bets on red or black. If the ball lands on their color, they double their money. If it lands on another color, they lose their money.
Let the probability of the ball landing on red slot = [tex]\frac{18}{37}[/tex]
The probability of the ball landing on black slot = [tex]\frac{18}{37}[/tex]
The probability of the ball landing on green slot = [tex]\frac{1}{37}[/tex]
Now, it is stated that Gambler can place bets only on the red or black slot, so;
The probability of winning the bet will be = [tex]\frac{18}{37}[/tex]
and the probability of losing the bet will be = [tex]\frac{18}{37}+\frac{1}{37}[/tex]
= [tex]\frac{19}{37}[/tex]
If the gambler wins he gets $3 and if he loses he will get -$3.
So, the expected value of gambler's total winnings is given by;
E(X) = [tex]\sum X \times P(X)[/tex]
= [tex]\$3 \times \frac{18}{37} + (-\$3 \times \frac{19}{37})[/tex]
= [tex]\$3 \times (-\frac{1}{37})[/tex] = -$0.081
Now, the standard deviation of gambler's total winnings is given by;
S.D.(X) = [tex]\sqrt{(\sum X^{2} \times P(X))-(\sum X \times P(X))^{2} }[/tex]
So, [tex]E(X^{2})=\sum X^{2} \times P(X)[/tex]
= [tex]\$3^{2} \times \frac{18}{37} + (-\$3^{2} \times \frac{19}{37})[/tex]
= [tex]\$9 \times (\frac{18}{37}+\frac{19}{37})[/tex] = $9
Now, S.D.(X) = [tex]\sqrt{\$9-(-\$0.081)^{2} }[/tex]
= [tex]\sqrt{8.993}[/tex] = $2.99 ≈ $3
Hence, the expected value and standard deviation of your total winnings are -$0.081 and $3 respectively.
Draw and label. Two points, J and K.
Answer:
see attached
Step-by-step explanation:
It usually works to follow instructions. Here are your two points.
In 2009, the world population was 6.8 billion. The exponential growth rate was 1.13% per year. So the following could be used as a model for the growth of the world's population: P=6.8e ,where P is world population in billions, t represents the number of years past 2009. (2009 would be represented by t = 0.)
a. Estimate the population of the world in 2018 using this model.
b. Using the internet, find an approximation for the world population in 2018. What is the difference between the estimate from the internet and the answer in part (a)?
c. Using algebraic methods and the model given, estimate the year when the world population will be 9 billion.
Answer: 9 million
Step-by-step explanation:
The population of the world in 2018 using this model is 7.5 billion.
What is population growth and population decrease formula?If a constant rate of growth be R% per annum, then population after n years = P(1+R/100)ⁿ.
Given that, P= 6.8 billion and rate of growth =1.13%.
Now, 6.8(1+1.13/100)ⁿ
= 6.8(1+0.0113)ⁿ
= 6.8(1.0113)ⁿ
a. The population of the world in 2018 using this model.
So, time period is n=9
Now, 6.8(1.0113)⁹
= 7.5 billion
b. World population is 2018 was 7.6 billion
The difference between the estimate from the internet and the answer in part (a) is 7.6-7.5
= 0.1 billion
c. Estimate the year when the world population will be 9 billion
9=6.8(1.0113)ⁿ
(1.0113)ⁿ=1.32
n=24.7 years
Therefore, the population of the world in 2018 using this model is 7.5 billion.
To learn more about the population increase and decrease visit:
https://brainly.com/question/27779235.
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Find the general solution of the differential equation. (Use C for the constant of integration.) dy dx = 36 − 12x2 x3 − 9x + 3
Answer:
[tex]y = -4ln(x^3 - 9x + 3) + C\\[/tex]
Step-by-step explanation:
Given the differential equation [tex]\frac{dy}{dx} = \frac{36-12x^2}{x^3-9x+3}\\ \\[/tex], we will use the variable separable method to solve the differential equation as shown;
[tex]\frac{dy}{dx} = \frac{36-12x^2}{x^3-9x+3}\\ \\dy = \frac{36-12x^2}{x^3-9x+3}dx\\ \\\\\\integrate \ both \ sides\\\\\int\limits dy = \int\limits\frac{36-12x^2}{x^3-9x+3}dx\\ \\\\using\ substitution\ method \ to \ solve \ RHS\\\\\int\limits\frac{36-12x^2}{x^3-9x+3}dx\\\\let \ u = x^3-9x+3; du/dx = 3x^2-9\\\\dx = du/3x^2-9\\\\\int\limits\frac{36-12x^2}{x^3-9x+3}dx\\\\ = \int\limits\frac{36-12x^2}{u}*\frac{du}{3x^2-9} \\\\= \int\limits\frac{12(3-x^2)}{u}*\frac{du}{3(x^2-3)}\\\\[/tex]
[tex]= \int\limits\frac{-12(x^2-3)}{u}*\frac{du}{3(x^2-3)}\\\\= -4\int\limits \frac{du}{u}\\ = -4lnu + C\\= -4ln(x^3 - 9x + 3)[/tex]
The differential solution becomes:
[tex]y = -4ln(x^3 - 9x + 3)[/tex][tex]+C[/tex]
Find the distance.
-3,5 and 7,-1
Answer:
≈ 11.66 units
Step-by-step explanation:
Given points:
(-3,5) and (7,-1)To find:
The distance between the given pointsThe distance between two points is calculated by formula:
d= √((x2-x1)² + (y2-y1)²)d= √(((7-(-3))² + (-1-5)²) = √(10²+(-6)²)= √136 ≈ 11.66 unitsAnswer is ≈ 11.66 units
Based on your knowledge of the hypothetical method, which of the following accurately describe the relationship between evidence and hypotheses?
a. A hypothesis does not direct the search for evidence.
b. A hypothesis can be proven true as long as one of its implications is shown to be true.
c. A hypothesis can be proven false if one of its implications is shown to be false.
d. A hypothesis is derived from the evidence at hand: the evidence produces the hypothesis.
Answer:
d. A hypothesis is derived from the evidence at hand; the evidence produces the hypothesis.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The evidence suggests that a certain hypothesis is tested for its reliability. The hypothesis is accepted or rejected on the basis of its underlying evidences.