Answer:
an acute an angle
Step-by-step explanation:
the angel of 31 is smaller than 90 so that would make it an acute angle
A 31° angle is an acute angle because it measures less than 90 degrees.
What are Angles?An angle is formed when two straight lines or rays meet at a common endpoint.
We know that a right angle is always equal to 90 degrees.
Any angle less than 90 degrees is an acute angle
Any angle greater than 90 degrees is an obtuse angle.
A 31° angle is an acute angle because it measures less than 90 degrees. An acute angle is any angle that measures between 0 and 90 degrees.
Hence, A 31° angle is an acute angle because it measures less than 90 degrees.
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Show that the set of points that are twice as far from the origin as they are from (2, 2, 2) is a sphere. Find the center and radius of this sphere.
Answer:
This is a sphere with a center [tex](\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )[/tex] and radius [tex]\dfrac{4 \sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given that: (x,y,z)
where;
d₁ is the distance from the origin = [tex]\sqrt{x^2+y^2+z^2}[/tex]
d₂ is the distance from (2,2,2) = [tex]\sqrt{(x-2)^2+(y-2)^2+(z-2)^2}[/tex]
Also;
d₁ = 2d₂
[tex]\sqrt{x^2 + y^2 +z^2 } = 2 \sqrt{(x-2)^2 +(y-z)^2+(z-2)^2}[/tex]
By squaring both sides;
[tex]x^2 + y^2 +z^2 = 2^2((x-2)^2 +(y-z)^2+(z-2)^2)[/tex]
[tex]x^2 + y^2 +z^2 = 4(x-2)^2 +4(y-z)^2+4(z-2)^2[/tex]
[tex]x^2 + y^2 +z^2 =4(x^2 -2x -2x +4) + 4(y^2 -2y -2y +4) + 4(z^2 -2z-2z+4)[/tex]
[tex]x^2 + y^2 +z^2 =4x^2 -16x +16 + 4y^2 -16y +16 + 4z^2 -16z+16[/tex]
Collect the like terms:
[tex]0 = 4x^2 -x^2 -16x +16 + 4y^2 -y^2 -16y +16 +4z^2 -z^2 -16z +16[/tex]
[tex]0 = 3x^2 -16x +16 + 3y^2 -16y +16 +3z^2 -16z +16[/tex]
Divide both sides by 3
[tex]\dfrac{0}{3} = \dfrac{3x^2 -16x +16}{3} + \dfrac{3y^2 -16y +16 }{3} + \dfrac{ +3z^2 -16z +16}{3}[/tex]
[tex]0 = {x^2 - \dfrac{16x}{3} +\dfrac{16}{3} + {y^2 - \dfrac{16y}{3} +\dfrac{16}{3}+{z^2 - \dfrac{16z}{3} +\dfrac{16}{3}[/tex]
Using the completing the square method;
[tex]3(\dfrac{160}{9}) -16 = {x^2 - \dfrac{16x}{3} +\dfrac{160}{9} + {y^2 - \dfrac{16y}{3} +\dfrac{160}{9}+{z^2 - \dfrac{16z}{3} +\dfrac{160}{9}[/tex]
[tex]\dfrac{16}{3}= (x - \dfrac{8}{3})^2+ (y - \dfrac{8}{3})^2+ (z - \dfrac{8}{3})^2[/tex]
∴
This is a sphere with a center [tex](\dfrac{8}{3},\dfrac{8}{3},\dfrac{8}{3} )[/tex] and ;
radius; [tex]\sqrt{\dfrac{16}{3}}[/tex]
[tex]= \dfrac{4 \sqrt{3}}{3}[/tex]
What is 18/8 written in simplest form?
2 1/4
Answer:
Actually I think it would be 2 1/3
Step-by-step explanation:
18 goes into 8 twice right, so whole number 2 with 2 left over so that makes it 2 2/6 then 2/2 and 6/2 is 1 and 3 so 2 1/3.
Teacher made a table to show which months her students birthdays took place. There are four birthdays in August and in total they are 33 students. What is the ratio of students with August birthdays to the total number of students
Answer:
4:33 or 4/33
Step-by-step explanation:
With a coupon, you can get a pair of shoes that normally costs $84 for only $72. What percentage was the discount? Hint: First subtract to find the amount of discount$, then divide it by the original price.
Answer:
14[tex]\frac{2}{7}[/tex]%
Step-by-step explanation:
We can just follow the hint.
Amount of discount = $84 - $72
= $12
Percentage of discount = [tex]\frac{12}{84}[/tex] × 100%
= 14[tex]\frac{2}{7}[/tex]%
Answer:
14.3% discount.
Step-by-step explanation:
Heya! So by the hint that they gave us, I subtracted 72 from 84, and then divided the 12 by 84. The true answer is 0.143 (rounded to the hundredth), getting you close to the initial 12. I hope this helped at least a little bit!
A board 30 metres long is to be divided into 2pieces so that the larger piece is 3 metres longer than twice the shorter piece. How long will the pieces be?
Answer: 9 and 21
Step-by-step explanation:
board=30m
divide by 2 pieces
one piece, we call it a
b, the other piece is b= 2a+3
a+b=30
a+2a+3=30
3a=30-3
3a=27
a=9
b=21
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let ^ p denote the proportion in the sample who say they support the increase. Suppose that 13% of all adults in Ohio support the increase. The standard deviation of the sampling distribution is
Answer:
The standard deviation of the sampling distribution is [tex]\sigma =0.0087[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 1500
The population proportion is [tex]p = 0.013[/tex]
Generally the standard deviation of this sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{ \frac{p (1- p)}{ n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.13(1-0.13)}{1500} }[/tex]
=> [tex]\sigma =0.0087[/tex]
The standard deviation of the considered sampling distribution of the proportion supporting the increase is 0.0027 approx.
How to find the sample standard deviation for distribution of a sample proportion?Suppose the sample proportion be denoted by [tex]\hat{p}[/tex], then, its distribution is normally distributed with mean [tex]p[/tex] and the standard deviation of distribution of [tex]\hat{p}[/tex] is given by
[tex]\sigma = \sqrt{\dfrac{p(1-p)}{n}}[/tex]
where n is the sample size. It is true until [tex]np \geq 10[/tex] and [tex]n(1-p) \geq 10[/tex]
For the given case, we're given that:
Sample size= n = 10Proportion average value = p = 13% = 0.13 Standard deviation = [tex]\sigma = \sqrt{\dfrac{0.13(1-0.13)}{1500}} = \sqrt{\dfrac{0.13 \times 0.87}{1500}} \approx 0.0027[/tex]Thus, standard deviation of the sampling distribution is approximately 0.0027
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The area of a rectangle is greater than or equal to 154 square centimeters. The width of the rectangle is 12 centimeters and the length is x
centimeters. Select the possible value(s) of x.
Plz it’s a test LOLMDJSHS
Answer:
x ≤ 12.83
(Any number under or equal to 12.8333...)
Step-by-step explanation:
154 ≥ 12x
12.833.... ≥ x
x ≤ 12.83
The indefinite integral of ((6e^4x)(e^arctan(3e^4x)))/(1+9e^8x)
Answer:
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{e^\big{arctan(3e^{4x})}}{2} + C[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Integration
Integrals[Indefinite Integrals] Integration Constant CIntegration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
U-Substitution
U-SolveStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx[/tex]
Step 2: Integrate Pt. 1
[Integrand] Rewrite: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \int {\frac{6e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = 6\int {\frac{e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex]Step 3: integrate Pt. 2
Set variables for u-substitution.
Set u: [tex]\displaystyle u = 4x[/tex][u] Differentiate [Basic Power Rule, Multiplied Constant]: [tex]\displaystyle du = 4 \ dx[/tex]Step 4: Integrate Pt. 3
[Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{4e^\big{arctan(3e^{4x}) + 4x}}{1 + 9e^\big{8x}}} \, dx[/tex][Integral] U-Substitution: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3e^u) + u}}{1 + 9e^\big{2u}}} \, du[/tex]Step 5: Integrate Pt. 4
Set variables for u-substitution #2.
Set v: [tex]\displaystyle v = 9e^{2u} + 1[/tex] [v] Differentiate [Exponential Differentiation, Chain Rule]: [tex]\displaystyle dv = 18e^{2u} \ du[/tex][v] U-Solve: [tex]\displaystyle u = ln \Big( \frac{\sqrt{v - 1}}{3} \Big)[/tex][dv] U-Solve: [tex]\displaystyle du = \frac{e^{-2u}}{18} \ dv[/tex][U-Solve] Rewrite u: [tex]\displaystyle e^u = \frac{\sqrt{v - 1}}{3}[/tex]Step 6: Integrate Pt. 5
[Integral] U-Solve: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(3(\frac{\sqrt{v - 1}}{3})) + ln(\frac{\sqrt{v - 1}}{3})}}{1 + 9(\frac{\sqrt{v - 1}}{3})^2} \frac{1}{18e^{2u}}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3[1 + v - 1]} \frac{1}{18(\frac{\sqrt{v - 1}}{3})^2}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{\sqrt{v - 1}e^\big{arctan(\sqrt{v - 1})}}{3v} \frac{1}{2(v - 1)}\, dv[/tex][Integral] Simplify: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{3}{2}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{6v\sqrt{v - 1}} \, dv[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int {\bigg( 6e^\big{4x} \cdot \frac{e^\big{arctan(3e^{4x})}}{1 + 9e^\big{8x}} \bigg)} \, dx = \frac{1}{4}\int {\frac{e^\big{arctan(\sqrt{v - 1})}}{v\sqrt{v - 1}} \, dv[/tex]Step 7: Integrate Pt. 6
Set variables for u-substitution #3.
Set z: [tex]\displaystyle z = arctan(\sqrt{v - 1})[/tex][z] Differentiate [Arctrig Differentiation, Chain Rule]: [tex]\displaystyle dz = \frac{1}{2v\sqrt{v - 1}} \ dv[/tex]See attachment for rest of work (would not fit entire answer in answering box).
There are 6 'blobs' in your bed. Each day the number of
blobs doubles. Create a table (with 4 rows) to represent
the number of blobs in your bed as a function of the
number of days that passed. Write an equation to
represent the scenario.
*How many blobs will be in your bed after 3 days?
Answer:
why the hell you got blobs in your bed?
Step-by-step explanation:
What is the answer to Y=30x+25
Answer:
x=1/30y + -5/6
Step-by-step explanation:
The $40 million lottery payment that you have just won actually pays $2
Answer:
wait what is the question?
Step-by-step explanation:
??
Explain if the following is a proportional relationship: Sam used 6 gallons of gas to drive 50 miles and 4 gallons of gas to drive 100
miles.
Answer:
it's not a proportional relationship. ..............
Write a number sentence that illustrates the following. A number with two decimal places multiplied by a number with one decimal place. The product has only two nonzero digits. Choose the correct answer below.
A. 0.08 x 0.6 = 0.48
B. 0.08 x 0.6 = 0.0048
C. 0.8 x 0.6 = 0.48
D. 0.08 x 0.6 = 0.048
Answer:
D
Step-by-step explanation:
Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Store X: 4 cans for $2.48 Store Y: 5 cans for $3.00 *
Answer:
Y=300
X= 4
M= 49x9=4
3x4=3
Step-by-step explanation:
3x = y and x - 2y = 10
Answer: Rewrite equations:
3x=y;x−2y=10
Step: Solve3x=yfor y:
3x=y
3x+−y=y+−y(Add -y to both sides)
3x−y=0
3x−y+−3x=0+−3x(Add -3x to both sides)
−y=−3x
−y
−1
=
−3x
−1
(Divide both sides by -1)
y=3x
Step: Substitute3xforyinx−2y=10:
x−2y=10
x−23x=10
−5x=10(Simplify both sides of the equation)
−5x
−5
=
10
−5
(Divide both sides by -5)
x=−2
Step: Substitute−2forxiny=3x:
y=3x
y=(3)(−2)
y=−6(Simplify both sides of the equation)
Step-by-step explanation:
Suppose that the local sales tax rate is 5 %
and you purchase a car for $ 27,400
.
a. How much tax is paid?
b. What is the car's total cost?
Answer:
A: Tax paid us $1370
B: Total cost= car cost + taxes
$27,400+ $1370
=$28,770
Step-by-step explanation:
Cecilia bought 5 games of
bowling for $25 and Frankie
bought 7 games for $42.
Which is the better buy?
please help me asap
What is the answer to this equation 12-1/4=
Answer:
11 3/4
Step-by-step explanation:
12-1/4=11 3/4
Answer:
11.75
Step-by-step explanation:
1/4=.25
12-0.25=11.75
Don’t worry about number 4 just tell me the answer to number two
Answer:
B
Step-by-step explanation:
First, you must combine like terms.
5a - a - a would be 3a.
-6 + 4 would be -2.
3a-2
Answer:
The answer would be B. -a+4+5a-a-6.
You would need to put like terms together. 4 and -6 is -2. -a, 5a, and -a is 3a.
I need a legit answer with just a little explanation please it would mean alot to me
Answer: C.
Step-by-step explanation: Plug in x in the formula. Solve for each y by plugging in each x in the formula and seeing if it works. This took me like 3 min to solve
Divide the fractions:
5/8 divided by 1/24 =
Answer:
The answer to this question is 15.
Step-by-step explanation:
We know that dividing a fraction by another fraction is the same as multiplying a fraction by the other fractions reciprocal, where the numerator and denominator are switched.
5/8 ÷ 1/24 =
5/8 x 24/1 =
120/8
120 ÷ 8 = 15.
Hence, the answer to this question is 15.
Hope this helps! :D
Final Answer:
15
Step-by-step explanation:
5/8 ÷ 1/24
5/8 ÷ 24/1
5/8 × 24/1 = 120/8
120/8 ⇒ 15/1 ⇒ 15
Christian earns $12 per hour working at the coffee shop. if he works for 8 hours on Saturday, how much money will he earn
Answer:
$96
Step-by-step explanation:
$12 per hour / 8 hours
$12 x 8 $96
3х + 4 = 14
х = 2y - 12
Answer:
(-2, 5)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Solving systems of equations using substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
3x + 4y = 14
x = 2y - 12
Step 2: Solve for y
Substitution
Substitute in x: 3(2y - 12) + 4y = 14Distribute 3: 6y - 36 + 4y = 14Combine like terms: 10y - 36 = 14Isolate y term: 10y = 50Isolate y: y = 5Step 3: Solve for x
Define equation: x = 2y - 12Substitute in y: x = 2(5) - 12Multiply: x = 10 - 12Subtract: x = -2Solve and graph the inequality
6X + 32 > -4
Answer:
Simplifying
6x + 32 = 180
Reorder the terms:
32 + 6x = 180
Solving
32 + 6x = 180
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-32' to each side of the equation.
32 + -32 + 6x = 180 + -32
Combine like terms: 32 + -32 = 0
0 + 6x = 180 + -32
6x = 180 + -32
Combine like terms: 180 + -32 = 148
6x = 148
Divide each side by '6'.
x = 24.66666667
Simplifying
x = 24.66666667
6x + 32> -4
6x > -4 - 32
6x > -36
x > -6
Isabella is making a bracelet for her friend. She has to decide which type of band to use, either leather or Siver. She also plans on picking two charms for the
bracelet. One of the charms will be of an animal, either a cat or a dog. The other charm will be of a sport, either basketbal, baseball, or soccer. How many
different bracelet combinations does Isabella have to choose from?
O 3
07
O 8
O 12
Answer:
There are 12 combinations.
Step-by-step explanation:
Options:
1. Silver or Leather
2. Cat or Dog
3. Basketball, baseball, or soccer
Now we need to multiply the options together, so 2 × 2 × 3 = 12.
Which equation matches the function shown below?
Answer:
Step-by-step explanation:
Pick the two easiest points to deal with.
(0,4) and (2,0)
Find m
m = (y2 - y1)/(x2 - x1)
y2 = 4
y1 = 0
x2 =0
x1 = -2
m = (4 - 0)/(0 - - 2)
m = 4/2 = 2
Now use one of the points to find b
y = mx + b Use (0,4)
4 = 2*0 + b
b = 4
The equation you want is y = 2x + 4
ayee someone help pleasee
Answer:
Both are solutions of x.
Step-by-step explanation:
[tex]x^{2} =49[/tex]
For [tex]x^{2} =f(a)[/tex] the solutions are [tex]x=\sqrt{f(a)} ,-\sqrt{f(a)}[/tex]
[tex]x=\sqrt{49} ,x=-\sqrt{49}[/tex]
[tex]\sqrt{49}[/tex]
Factor the number: [tex]49=7^{2}[/tex]
Apply radical rule: [tex]\sqrt[n]{x^n} =a[/tex]
[tex]\sqrt{7^2} =7[/tex]
=7
[tex]-\sqrt{49}[/tex]
Factor the number: [tex]49=-7^2[/tex]
Apply radical rule: [tex]\sqrt[n]{x^n} =a[/tex]
[tex]-\sqrt{7^2}=7[/tex]
[tex]=-7[/tex]
Which of the following is equal to the absolute value of 7?
o the distance between 7 and zero on a number line
o the distance between -3 and -4 on a number line
o the distance between -7 and 7 on a number line
the distance between 1 and 7 on a number line
(PLS I NEED IT TODAY)
A cash register contains coins. • 10 pennies • 11 nickels • 13 dimes • 6 quarters A cashier will randomly choose two coins one at a time without replacement. What is the probability that the cashier will choose a penny first, followed by a dime?
F 13/160
G 1/12
H 13/245
J 7/12
♡ Answer ♡
G) 1/12
♡ Step-by-step explanation ♡
In order to figure out this problem, we have to take a few relatively simple steps.
First, we must count the total number of coins in the cash register. Do not change the value of these coins. Simply take the numbers listed in the problem and add them up. Your process for completing this step should look something like this: 10+11+13+6 equals 40. With this being said, there are 40 coins in the cash register.
Next, we must remember the values of the two coins the question is asking for: pennies and dimes. Keep in mind that, out of all 40 coins, 10 of them are pennies and 13 of them are dimes.
Then, we write the fractions used to find the answer to this problem. In the question, the cashier (hypothetically) draws a penny first, and then a dime. This means a penny is drawn before a dime is drawn. (Although it seems like a miniscule detail, this knowledge is actually something extremely important to remember. This small piece of information can actually change the entire answer if not used properly.)
In this problem, the cashier would choose a single penny out of the 10 in contrast to the total 40 coins. Since there are 10 pennies overall, and 40 coins overall, the probability of choosing a penny first is 10/40.
After we complete the probability of choosing a penny before all else, we must find the probability of choosing a dime after choosing a penny. Since the dime will be chosen after the penny is chosen, one coin will be gone: the chosen penny. So, the total amount of coins within the cash register changes (or more specifically decreases (by 1)) from 40 to 39. However, the amount of dimes, 13, stays the same. With this information in mind, we can write a fraction of 13/39 for the probability of choosing a dime after choosing a penny.
Finally, now that we have both probability fractions, we can figure out the answer to the question. In order to do this, we multiply and simplify both fractions. 10/40*13/39 is 130/1560. 130 ÷ 130 is 1. 1560 ÷ 130 is 12. 1 ÷ 12 can also be written as 1/12. Therefore, the answer to this problem is G) 1/12.
(The paragraph and author's note below are technically optional thought processes and information, but read them if you wish. Although I would recommend reading further, considering another way to solve the question is mentioned, it is entirely you (the reader's) choice.)
You can also check this answer through the other/alternate way of solving this problem: by simplifying both probability fractions before you multiply them. 10/40 can be simplified to 1/4. 13/39 can be simplified to 1/3. After doing this, we multiply both simplified probability fractions in order to find, or in this case check, the answer. 1/4*1/3 is 1/12. 1/12 is the same fraction as the one present in choice G. This is the same answer as the one we previously got. This enforces the idea that G) 1/12 is indeed the answer to this question.
A/N (Author's Note): Although it took quite a while to jot down, this was truly a blast to write and explain! I hope this helped those that needed/wanted it. Have a wonderful week reader(s)!