Answer:
rationalising factor wud be
2 - root3
as on multiying both and applying identity we end up
2^2 - (root3)^2
4 - 3 = 1
we got a rational number so rationalisng factor is
2 - root3
Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.
Answer:
total = m/n * c
m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid
-5 + 3 and also what is 1/4 of 24
What is the answer i am struggling
Answer:
-5+3=-2
1/4 of 24 = 6
Step-by-step explanation:
a farmer needs 5 men to clear his farm in 10 days. How many men will he need if he must finish clearing the farm in two days if they work at the same rate?
Answer:
25 workers
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
,
What is the value of x?
Answer:
x=30°
hopefully this answer can help you to answer the next question
Part E
1e. Subtract the binomial 12y2 – 4y3 from the trinomial 7y - 2y3 + 5y2
Answer:
2y^3-7y^2+7y
Step-by-step explanation:
7y - 2y^3 + 5y^2 - ( 12y^2 – 4y^3)
Distribute the minus sign
7y - 2y^3 + 5y^2 - 12y^2 + 4y^3
Combine like terms
2y^3-7y^2+7y
1->dương vô cùng 1/x*(9+lnx^2)dx
It looks like you are trying to compute the improper integral,
[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]
or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then
[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]
The distance between Ali's house and 1 point
college is exactly 135 miles. If she
drove 2/3 of the distance in 135
minutes. What was her average speed
in miles per hour?
Ali's average speed was 40 miles per hour.
What is an average speed?
The total distance traveled is to be divided by the total time consumed brings us the average speed.
How to calculate the average speed of Ali?
The total distance between the college from Ali's house is 135 miles.
She drove 2/3rd of the total distance in 135 minutes.
She drove =135*2/3miles
=90miles.
Ali can drive 90miles in 135 mins.
Therefore, her average speed is: 90*60/135 miles per hour.
=40 miles per hour.
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5 less than three times a number is 37 what is the number
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x - 5 = 37
Step 2: Solve for x
[Addition Property of Equality] Add 5 on both sides: 3x = 42[Division Property of Equality] Divide 3 on both sides: x = 14Add :-
a+2b-3c, -3a+b+2cand 2a -3b+c
Answer:
[tex]a + 2b -3 c + - 3a + b + 2c + 2a - 3b + c \\ = a - 3a + 2a + 2b + b - 3b - 3c + 2c + c \\ 0a + 0b + 0c \\ thank \: you[/tex]
a+2b-3c+(-3a+b+2c) +(2a-3b+c)
=a+2b-3c-3a+b+2c+2a-3b+c
=a-3a+2b+2b+b-3b-3c++2b+c
=0a+0b+0c
=0
Therefore, the addition of the expressions, a+2b-3c+(-3a+b+2c) +(2a-3b+c) is zero or 0.
To know more about algebraic expressions
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A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
3.06 as. a fraction PLEASE HELP
Answer:
153/50
Step-by-step explanation:
3.06
Rewriting as
There are two numbers after the decimal so we put the number over 100
306/100
Divide top and bottom by 2
153/50
To write 3.06 as a fraction you have to write 3.06 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
3.06 = 3.06/1 = 30.6/10 = 306/100
And finally we have:
3.06 as a fraction equals 306/100
If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144= c^2
169 = c^2
Take the square root of each side
sqrt(169) = sqrt(c^2)
13= c
Answer:
The length of the hypotenuse is 13.
Step-by-step explanation:
[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]
[tex]a^2 = 12^2 + 5^2[/tex]
[tex]a^2 = 144 + 25[/tex]
[tex]a^2 = 169[/tex]
a=[tex]\sqrt{169}[/tex]
a= 13
Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.
HOPE THIS HELPED
Can you please help me
9514 1404 393
Answer:
1/63
Step-by-step explanation:
There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:
4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63
The larger fraction is 1/63 unit larger than the smaller fraction.
How is the series 6+13+20+...+111 represented in summation notation?
Notice that
6 + 7 = 13
13 + 7 = 20
so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is
a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1
The last term in the series is 111, which means the series consists of 16 terms, since
7k - 1 = 111 ==> 7k = 112 ==> k = 16
Then in summation notation, we have
[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]
Drag each factor to the correct location on the image.
If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0,
P(x).
Answer:
(x-7) and (x+12) are the factors and the rest are non factors...
Naomi invested $3,425 in an account that
pays 3% simple interest. what was the total
balance of the account after 15 years?
Answer:
$4,966.25
Step-by-step explanation:
3 x 15 = 45
After 15 years, Naomi would have earned a total of 45% interest rate.
3,425 x 1.45 = 4,966.25
Don't use .45 as the multiplier
3,425 x .45 = 1,541.25 <- incorrect
3 write the factor of the following (1) 48 (2) 36 (3) 28 (4) 100 (5) 125
Answer:
FACTORING THE NUMBERS :-
well u didnt say to prime factors so i am writing all factors
1) 48 => 1, 2, 3, 4, 6, 8, 12, 16, 24 and 48 ( all are plus and minus )
2) 36 => 1, 2, 3, 4, 6, 9, 12, 18 and 36 ( all are plus and minus )
3) 28 => 1, 2, 4, 7, 14 and 28 ( all are plus and minus )
4) 100 => 1, 2, 4, 5, 10, 20, 25, 50, and 100 ( all are plus and minus )
5) 125 => 1, 5, 25, 125 ( all are plus and minus )
is it worth brainliest...
yes ofc
I need help Plz help
The PTA sells 100 tickets for a raffle and puts them in a bowl. They will randomly pull out a ticket for the first prize and then another ticket for the second prize. You have 10 tickets and your friend has 10 tickets. What is the probability that your friend wins the first prize and you win the second prize?
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
PLS HELP QUICK IM BEGGINGGGG!!!!! PLEASE HELP ME!!
The following box plot represents the heights of the students in Mr. Taylor's fourth grade math class.
In a complete sentence, answer the following question:
One of the values in this data set is 138. In this box plot, what does this value mean?
Answer:
The value 138 means that this height (138cm) is less than the average height of a 4th grader.
Answer: No credit wanted
Step-by-step explanation:
The other guy is completely right.
[tex]\sqrt{25}[/tex]
Answer:
5
Step-by-step explanation:
Calculate the square root of 25 and get 5.
190 of 7
6 7 8 9 10
-3
4
5
6
The slope of the line shown in the graph is
and the intercept of the line is
Answer:slope 2/3
Y-int 6
Step-by-step explanation:
pls help me asap !!!
Answer:
11
Step-by-step explanation:
Hopefully you can see that this is an isosceles triangle and remembering the inequality theorem of a triangle (4,4,11 triangle cannot exist). Iso triangle has two side the same length - as well as two angles the same.
Police sometimes measure shoe prints at crime scenes so that they can learn something about criminals. Listed below are shoe print lengths, foot lengths, and heights of males. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Based on these results, does it appear that police can use a shoe print length to estimate the height of a male? Use a significance level of α=0.01
It does not appear that police can use a shoe print length to estimate the height of a male.
The given parameters are:
[tex]\begin{array}{cccccc}{Shoe\ Print} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ Height (cm) & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
Rewrite as:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} \ \\ y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} \ \end{array}[/tex]
See attachment for scatter plot
To determine the correlation coefficient, we extend the table as follows:
[tex]\begin{array}{cccccc}{x} & {28.6} & {29.4} & {32.2} & {32.4} & {27.3} & y & {172.5} & {176.7} & {188.4} & {170.1} & {179.2} & x^2 & {817.96} & {864.36} & {1036.84} & {1049.76} & {745.29} & y^2 & {29756.25} & {31222.89} & {35494.56} & {28934.01} & {32112.64} & x \times y & {4933.5} & {5194.98} & {6066.48} & {5511.24} & {4892.16} \ \end{array}[/tex]
The correlation coefficient (r) is:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
We have:
[tex]n =5[/tex]
[tex]\sum xy =4933.5+5194.98+6066.48+5511.24+4892.16 =26598.36[/tex]
[tex]\sum x =28.6+29.4+32.2+32.4+27.3=149.9[/tex]
[tex]\sum y =172.5+176.7+188.4+170.1+179.2=886.9[/tex]
[tex]\sum x^2 =817.96+864.36+1036.84+1049.76+745.29=4514.21[/tex]
[tex]\sum y^2 =29756.25+31222.89+35494.56+28934.01+32112.64=157520.35[/tex]
Calculate mean of x and y
[tex]\bar x = \frac{\sum x}{n} = \frac{149.9}{5} = 29.98[/tex]
[tex]\bar y = \frac{\sum y}{n} = \frac{886.9}{5} = 177.38[/tex]
Calculate SSx and SSy
[tex]SS_x = \sum (x - \bar x)^2 =(28.6-29.98)^2 + (29.4-29.98)^2 + (32.2-29.98)^2 + (32.4-29.98)^2 + (27.3-29.98)^2 =20.208[/tex]
[tex]SS_y = \sum (y - \bar x)^2 =(172.5-177.38)^2 + (176.7-177.38)^2 + (188.4-177.38)^2 + (170.1-177.38)^2 + (179.2-177.38)^2 =202.028[/tex]
Calculate [tex]\sum(x - \bar x)(y - \bar y)[/tex]
[tex]\sum(x - \bar x)(y - \bar y) = (28.6-29.98)*(172.5-177.38) + (29.4-29.98)*(176.7-177.38) + (32.2-29.98)*(188.4-177.38) + (32.4-29.98)*(170.1-177.38) + (27.3-29.98) *(179.2-177.38) =9.098[/tex]
So:
[tex]r = \frac{\sum(x - \bar x)(y - \bar y)}{\sqrt{SS_x * SS_y}}[/tex]
[tex]r = \frac{9.098}{\sqrt{20.208 * 202.028}}[/tex]
[tex]r = \frac{9.098}{\sqrt{4082.581824}}[/tex]
[tex]r = \frac{9.098}{63.90}[/tex]
[tex]r = 0.142[/tex]
Calculate test statistic:
[tex]t = \frac{r}{\sqrt{\frac{1 - r^2}{n-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{1 - 0.142^2}{5-2}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{\frac{0.979836}{3}}}[/tex]
[tex]t = \frac{0.142}{\sqrt{0.326612}}[/tex]
[tex]t = \frac{0.142}{0.5715}[/tex]
[tex]t = 0.248[/tex]
Calculate the degrees of freedom
[tex]df = n - 2 = 5 - 2 = 3[/tex]
The [tex]t_{\alpha/2}[/tex] value at:
[tex]df =3[/tex]
[tex]t = 0.248[/tex]
[tex]\alpha = 0.01[/tex]
The value is:
[tex]t_{0.01/2} = \±5.841[/tex]
This means that we reject the null hypothesis if the t value is not between -5.841 and 5.841
We calculate the t value as:
[tex]t = 0.248[/tex]
[tex]-5.841 < 0.248 < 5.841[/tex]
Hence, we do not reject the null hypothesis because they do not appear to have any correlation.
Read more about regression at:
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I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
A toddler is allowed to dress himself on Mondays, Wednesdays, and Fridays. For each of his shirt, pants, and shoes, he is equally likely to put it on correctly as incorrectly. Getting these articles of clothing on correctly are independent of each other. On the other days, the mother dresses the toddler with 100% accuracy. Given that the toddler is correctly dressed, what is the probability that today is Monday
Answer:
0.0286 = 2.86% probability that today is Monday.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Dressed correctly
Event B: Monday
Probability of being dressed correctly:
100% = 1 out of 4/7(mom dresses).
(0.5)^3 = 0.125 out of 3/7(toddler dresses himself). So
[tex]P(A) = 0.125\frac{3}{7} + \frac{4}{7} = \frac{0.125*3 + 4}{7} = \frac{4.375}{7} = 0.625[/tex]
Probability of being dressed correctly and being Monday:
The toddler dresses himself on Monday, so (0.5)^3 = 0.125 probability of him being dressed correctly, 1/7 probability of being Monday, so:
[tex]P(A \cap B) = 0.125\frac{1}{7} = 0.0179[/tex]
What is the probability that today is Monday?
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.0179}{0.625} = 0.0286[/tex]
0.0286 = 2.86% probability that today is Monday.
There are two machines available for cutting corks intended for use in wine bottles. The first produces corks with diameters that are normally distributed with mean 3 cm and standard deviation 0.10 cm. The second machine produces corks with diameters that have a normal distribution with mean 3.04 cm and standard deviation 0.04 cm. Acceptable corks have diameters between 2.9 cm and 3.1 cm. What is the probability that the first machine produces an acceptable cork
Answer:
0.6827
Step-by-step explanation:
Given that :
Mean, μ = 3
Standard deviation, σ = 0.1
To produce an acceptable cork. :
P(2.9 < X < 3.1)
Recall :
Z = (x - μ) / σ
P(2.9 < X < 3.1) = P[((2.9 - 3) / 0.1) < Z < ((3.1 - 3) / 0.1)]
P(2.9 < X < 3.1) = P(-1 < Z < 1)
Using a normal distribution calculator, we obtain the probability to the right of the distribution :
P(2.9 < X < 3.1) = P(1 < Z < - 1) = 0.8413 - 0.1587 = 0.6827
Hence, the probability that the first machine produces an acceptable cork is 0.6827
PLEASEE HELP ME ASAPPP (geometry)
Answer:AE=EC và BF=FC => EF là đường trung bình của tam giác ABC
=> EF // và bằng 1/2 AB
=> AB = 16
Step-by-step explanation:
Answer:
AB=16
Step-by-step explanation:
Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long.
The mid-segment of a triangle, which joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and half the length of that third side of the triangle.
AD=DB
AD+DB=AB=2EF
AB=2×8=16
