Answer:
2√3
Step-by-step explanation:
root 27
= √27
= 3√3
12 upon root 3
= 12 / √3
= ( 12 / √3 ) x ( √3 / √3 )
= ( 12 x √3 ) / ( √3 x √3 )
= 12√3 / 3
= 4√3
6 upon √3
= 6 / √3
= ( 6 / √3 ) x ( √3 / √3 )
= ( 6 x √3 ) / ( √3 x √3 )
= 6√3 / 3
= 2√3
root 3 = √3
root 3 + root 27 - 12 upon root 3 + 6 upon root 3
= √3 + 3√3 - 4√3 + 2√3
= 4√3 - 4√3 + 2√3
= 2√3
Answer:
2√3
Step-by-step explanation:
Our equation :
[tex]\sqrt{3} + \sqrt{27} - \frac{12}{\sqrt{3} } + \frac{6}{\sqrt{3} }[/tex]Simplifying
[tex]\sqrt{3} + \sqrt{9 *3} - \frac{12\sqrt{3} }{\sqrt{3}*\sqrt{3} } + \frac{6\sqrt{3} }{\sqrt{3}*\sqrt{3} }[/tex][tex]\sqrt{3}+3\sqrt{3} - \frac{12\sqrt{3} }{3}+\frac{6\sqrt{3} }{3}[/tex][tex]4\sqrt{3}-4\sqrt{3}+2\sqrt{3}[/tex]2√3the weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. a truck used to transport goats can only accommodate not more than 650 kg. if 10 goats are selected at random from the population, what is the probability that the total weight exceeds the maximum weight?
Using the normal distribution, it is found that there is a 0.0571 = 5.71% probability that the total weight exceeds the maximum weight.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, we have that the parameters are given as follows:
[tex]\mu = 60, \sigma = 10, n = 10, s = \frac{10}{\sqrt{10}} = 3.1623[/tex]
The probability that the total weight exceeds the maximum weight is the probability of a sample mean above 650/10 = 65 kg, which is one subtracted by the p-value of Z when X = 65.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{65 - 60}{3.1622}[/tex]
Z = 1.58.
Z = 1.58 has a p-value of 0.9429.
1 - 0.9429 = 0.0571.
0.0571 = 5.71% probability that the total weight exceeds the maximum weight.
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The area of a rectangle is x^2+2x-24 Which of the following could be one of the dimensions?
Answers:
(x-3)
(x-4)
(x-6)
(x+8)
WILL GIVE BRAINLIEST
Answer: (x-4)
Step-by-step explanation:
x^2 + 8x +15 is the area
x+5 is the length
x+3 is the width
(x+5)(x+3)=
x^2 + 3x +5x +15
x^2 +8x + 15
Answer:
(x-4)
Step-by-step explanation:
You want to put money into a bank. The first bank will take a 1st deposit of 500 dollars and pays 4.8% compounded
quarterly. The Second bank with take a 1st deposit of 3000 dollars but pays 2.7% compounded annual
Answer:
4
Step-by-step explanation:
the step equation because of the font
100 points if you can help me answer these 5 questions!! :)
Answer:
A. 30°, 70° and 80°
B. 10cm
Step-by-step explanation:
A. the two triangle have same angles so the angles of triangle 2 are 30°, 70° and 80°
B. the perimeter of triangle, is twice as long as the perimeter of triangle 2 so the perimeter of triangle 2 is 20÷2 = 10 cm
HELP! WILL GIVE BRAINLEST!The graph below shows an angle in standard position. What is the degree measure of the angle depicted?
Answer:
45 degree angle
Step-by-step explanation:
Let's say that the line crossing the middle of quadrant four was on the y-axis, that would be known as a 90 degree angle. Since it was cut in half, that would become a 45 degree angle.
!HELP! I feel asleep in class and I need help. 7h + 3
42
Step-by-step explanation:
7h+ 3 = 45
3 + 7h = 45
h=6
7×6 = 42
The cosine of one acute angle of a right triangle is 817.
What is the sine of the other acute angle?
The sine of the other acute angle is 15/17 if the cosine of one acute angle of a right triangle is 8/17.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have a cosine of one acute angle of a right triangle is 8/17.
Let's suppose the angle is α
[tex]\rm Cos\alpha = \frac{8}{17}[/tex]
As we know the cos is the ratio of adjacent to hypotenuse and Sin is the ratio of the opposite to hypotenuse.
Let's suppose the length of the hypotenuse is x units
From the Pythagoras theorem:
[tex]\rm 17^2=x^2+8^2[/tex]
x = 15 units
Now the Sin ratio:
[tex]\rm Sin\alpha = \frac{15}{17}[/tex]
Thus, the sine of the other acute angle is 15/17 if the cosine of one acute angle of a right triangle is 8/17.
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John ate more calories than his body needs. What will happen if he doesn't burn them off?
A. The extra calories will be stored as fat.
B. Nothing. You can never eat too many calories.
C. He will get bigger muscles.
D. He will get the flu.
What is the product of (3a 2)(4a2 – 2a 9)? 12a3 − 2a 18 12a3 6a 9 12a3 − 6a2 23a 18 12a3 2a2 23a 18
The product of the two equation in which one is binomial equation another quadratic equation, is 12a³+2a²+23a+18.
How to multiply two equations?To multiply the two equation, each term of the first equation is multiples from the second term.
The first equation given in the problem is,
[tex]3a+ 2[/tex]
The second equation given in the problem is,
[tex]4a^2 -2a+ 9[/tex]
The product of these two equations are,
[tex]p=(3a+2)\times (4a^2 -2a+ 9)\\p=12a^3-6a^2+27a+8a^2-4a+18\\p=12a^3+2a^2+23a+18[/tex]
Hence, the product of the two equation in which one is binomial equation another quadratic equation, is 12a³+2a²+23a+18.
Learn more about the multiplication of two equation here;
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Answer: D: 12a^3 + 2a^2 + 23a + 18
Step-by-step explanation: got it right :)
pls help DUE TODAY (13points)
Answer:
42 ft²
Step-by-step explanation:
Rectangle Area: L * W
[tex]\bf A=(8ft)(6ft)[/tex]
[tex]\bf 48 \; ft^2[/tex]
[tex]\bf A= (3ft)(2ft)[/tex]
[tex]\bf 6\;ft^2[/tex]
[tex]\bf 48ft^2-6ft^2[/tex]
[tex]\boxed{\bf 42\; ft^2}[/tex]
Answer:
42
Step-by-step explanation:
6 x 6 is 36. 3 x 2 is 6. 36 + 6 is 42.
Sadie's monthly allowance is $75. She saves 60% of the allowance each month.
Select all expressions that demonstrate a correct method of calculating the amount of money she saves each
month.
0.60/100 • 75
60/100 • 75
60 • 75
0.60 • 75
60/100 * 75 & 0.60 * 75
60% can be rewritten as 0.60, and since 60/100=0.60, this expression is correct as well
The other two are incorrect because 0.60/100 would be 0.6%, and 60*75 would mean she is saving 6000%
Question
A former residential complex was found to be a Superfund site polluted with several hazardous materials. Tamela is an investigative journalist who would like to show whether the proportion of the residents of the complex who eventually died from cancer is greater than the regional average of 14%. She randomly selects 54 residents who lived in the complex and finds that 12 of those residents eventually died from cancer. Are all of the conditions for this hypothesis test met, and if so, what are the null and alternative hypotheses for this hypothesis test?
Considering the situation described, we have that:
The null hypotheses is [tex]H_0: p = 0.14[/tex].The alternative hypotheses is [tex]H_1: p > 0.14[/tex].What are the hypotheses tested?At the null hypotheses, it is tested if the proportion at the complex is the same as the rest of the population, that is, of 14%, hence:
[tex]H_0: p = 0.14[/tex].
At the alternative hypotheses, it is tested if it is greater, hence:
[tex]H_1: p > 0.14[/tex].
More can be learned about the test of an hypotheses at https://brainly.com/question/26454209
Write an explicit formula for the arithmetic sequence:
-2,7,16,25,...
Answer:
a_n = 9n - 11
Step-by-step explanation:
Explicit rule for an arithmetic sequence is a_n = a_1 + (n-1) d
a_1 is the first term of the sequence
d is the common difference. To find d you pick a number in the sequence and subtract it by the previous number. For example, 7 - (-2) = 9
16 - 7 = 9 so, d = 9
a_1 = -2 since it is the first term. Now substitute these numbers into the formula.
a_n = -2 + (n-1)(9)
And then we simplify.
9 • n = 9n
9 • -1 = -9
Then we’ll have a_n = -2 + 9n -9 and well simplify even further.
-2 -9 = -11
So we get
a_n= 9n -11
hope that helped! God bless you!!
What type of graph would you use for a set of categorical data with 25 people surveyed?
bar graph
line graph
pictograph
stem-and-leaf plot
Answer:
line graph
oihhoihjkii
A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades. how many 7-card hands are possible with 2 hearts, 2 diamonds, 2 clubs, and 1 spade? assume that the order of the cards does not matter, and use the formula for combinations to find your answer.
The number of ways of selecting 7-cards with 2 hearts, 2 diamonds, 2 clubs, and 1 spade is 1,169,176.
What are permutation and combination?A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
A standard deck of 52 cards contains 13 cards with hearts, 13 with diamonds, 13 with clubs, and 13 with spades.
The number of ways of selecting 7-cards with 2 hearts, 2 diamonds, 2 clubs, and 1 spade will be
[tex]\rm Number \ of \ ways = \ ^{13}C_2 \times ^{13}C_2 \times ^{13}C_2 \times ^{13}C_1 \\\\Number \ of \ ways = 78 \times 78 \times 78 \times 13 \\\\Number \ of \ ways = 6,169,176[/tex]
The number of ways is 6,169,176.
More about the permutation and the combination link is given below.
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A rectangle is _____ a trapezoid.
a. always
b.never
c.sometimes
Answer:
never.
Step-by-step explanation:
C. Explain why triangle PQR is isosceles.
Check the picture below.
Which equation correctly describes the relationship between the
measure of the inscribed angle and the measure of the
intercepted arc in the figure?
m JKL= mJL
1/2m JKL = mJL
2(m JKL) =mJL
m JKL = 360° – mJL
The relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)
What is the Inscribed Angle Theorem?The inscribed angle theorem states in a circle, the measure of the angle that is inscribed is always half of the arc that is intercepted. Which means that the intercepted arc is twice the measure of the inscribed angle.
In the image given:
m∠JKL is the inscribed angle.m(JL) is the intercepted arcTherefore, the relationship that describes the measure of the inscribed angle and the measure of the intercepted arc is: 2(m∠JKL) = m(JL)
Learn more about the inscribed angle theorem on:
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Answer:
2(m∠JKL)=mJL
Step-by-step explanation:
I took the test :)
48% as a common fraction
Answer:
12/25
Step-by-step explanation:
48% is the same as 48/100 = 12/25
What is the answer?
Do I add?
Answer:
yess add your anwser is 32.235
if 3 = 75 how many 3s will it take to get to 1659
Answer:
≈22
Divide 1,659 by 75(3)75 × 2 = 150 important
Write 2 at the top of your division problem, subtract 150 by 165 short form of 1,659150 - 165 = 15(9) the 9 comes from dropping the ones place in 1,659
Reconsider how many times 75 goes into 1,659(22) and since we do not have any other numbers, we write 150 and 159, because again, 1,659 has to help us solve the problem by dropping the ones place.150 - 159 = 9
_______________________________________________________
With that information, the problem is solved! We got our exact estimate, and a remainder of 9 to make up for the missing 9 in 1,650! 22 × 75 = 1,650 so add 9, the remainder.
_______________________________________________________
What did we learn today?We learned how to do long division using remainders.
Still have questions? Ask me in the comments box, and I may be able to assist.
Help please. I do not understand the assignment my teacher has given me.
Step-by-step explanation:
Match in the given pattern
1-->F
2-->A
3-->E
4-->C
5-->B
6-->D
I hope it helps you
The diagram shows the height (4.5) of a cone that holds ice cream. The cone has a volume of
1.5π cubic inches.
I need explanations please, I will mark you brainliest if I get a good explanation on how and what the sum is about.
The radius of the cone that holds ice cream which has height of 4.5 inches and 1.5π cubic inches, is 1 inches.
What is of volume of cone?Volume of cone is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
The volume of the cone can be given as,
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Here, (r) is the radius of the base of the cone and (h) is the height of the cone.
The diagram of the cone is shown, in which,
The height of a cone that holds ice cream is 4.5 inches (h=4.5). The cone has a volume of 1.5π cubic inches (V=1.5π).Let suppose the radius of the cone is r inches long. Thus, put the values in the above formula,
[tex]V=\dfrac{1}{3}\pi r^2h\\1.5\pi=\dfrac{1}{3}\pi r^2(4.5)\\1.5\pi\times3=\pi r^2(4.5)\\\dfrac{1.5\pi\times3}{\pi \times 4.5}= r^2\\1= r^2\\r=\sqrt{1}\\r=1\rm\; inches[/tex]
Thus, the radius of the cone that holds ice cream which has height of 4.5 inches and 1.5π cubic inches, is 1 inches.
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a spherical tank holds 8,000 ft^3 of water. What is the diameter of the tank?
Answer:
24.8 ft
Step-by-step explanation:
Formula to find the volume of a sphere is :
Volume = [tex]\frac{4}{3}[/tex] π r³
Here,
r ⇒ radius
Given that,
Volume ⇒ 8000 ft³
Let us find the radius of the tank now.
Volume = [tex]\frac{4}{3}[/tex] π r³
8000 = [tex]\frac{4}{3}[/tex] π r³
8000 = [tex]\frac{4}{3}[/tex] × 3.14 × r³
8000 × 3 = 4 × 3.14 × r³
24000 = 12.56r³
Divide both sides by 12.56.
1910.822 = r³
∛1910.822 = r
12.40 ft = radius
And now let us find the diameter of the sphere.
d = 2r
d = 2 × 12.40
d = 24.8 ft
The diameter of the tank is 24.80 ft
Step-by-step explanation:
Given-
A spherical tank holds 8,000 ft^3 of wateri.e. The volume of spherical tank = 8,000 ft^3
Now, the formula for finding volume of any spherical figure is-
[tex] \boxed{\mathfrak{ \purple{volume \:of \: sphere = \frac{4}{3} \pi {r}^{3} }}}[/tex]Therefore, substituting value, we get
[tex]⇢8000 = \frac{4}{3} \pi {r}^{3} [/tex]
[tex]⇢8000 \times \frac{3}{4 } = \frac{22}{7} \pi {r}^{3} [/tex]
Transposing 4/3 to left hand side ,it will become 3/4 . And Here, 8000 will get cancelled by 4 leaving 2000
[tex]⇢2000 \times 3 \times \frac{7}{22} = {r}^{3} [/tex]
Similarly , On performing further calculations, we get. ..
[tex]⇢ \frac{21000}{11} = {r}^{3} [/tex]
[tex]⇢1910.822 = {r}^{3} [/tex]
[tex]⇢ \sqrt[3]{1910.822} = r[/tex]
[tex]⇢ \underline{12.40 = r}[/tex]
Thus, the radius of the tank is 12.40 ft
Now,
The diameter of the tank = 2 × radius
[tex] \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 12.40[/tex]
[tex] \: \: \: \: \: \: \: \: \: \: \: \: = 24.80[/tex]
•°• The diameter of the tank comes out 24.80 ft
identify wether or not the solution is liner quadratic or exponential
Answer:
...
Step-by-step explanation:
there is no photo for the solution(2) (1) Evan joined an online game. His team of 7 players was up against another team of 10. Each player can lose 6 "lives" before they are out of the game. How many lives do all the players have combined?
Select all expressions that are equivalent to -4(x + 2) - 2x + 4.
A. -6x - 4
B. -4x + 2 - 2x + 4
C. -10x
D. -4x + -8 - 2x + 4
E. -4x - 2x - 8 + 4
Answer:
=>A. -6x - 4
Step-by-step explanation:
=>-4(x + 2) - 2x + 4
=> -4x-8-2x+4
=> -6x-4
what is the area of the parallelogram?
35cm!
4 + 4 = 8
7 + 7 = 14
13 + 8 = 21 (13 + (8 - 1 ) = 20 + 1 = 21)
21 + 14 = 35 (4 + 1 = 5, 20 + 10 = 30, 30 + 5 = 35)
Might be kind of hard to explain but just try to explain as much as u can.
The rule for a rotation by 270 ° about the origin is (x,y) ⇒ (y,-x)
Rotating the triangle PQR to create an image of the triangle involves moving the triangle PQR in a circular direction.
The coordinates of the given triangle are:
P = (-10,15)Q = (-20,5)R = (-10,5)Using the rule, the coordinates now are:
P' = (15,10)Q' = (5,20)R '= (5,10)In the attatchment, the answer is in pictoral form.
If f(x) = 3x2 1 and g(x) = 1 – x, what is the value of (f – g)(2)? 12 14 36 38
Answer:
that's the answer man ur welcome btw