Answer:
700.4 cm
Step-by-step explanation:
This involves two similar triangles.
Both triangles are right triangles.
One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.
(1 cm)^2 + (30 cm)^2 = c^2
c^2 = 901 cm^2
c = sqrt(901) cm
The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [sqrt(901) cm]/x
3/70 = sqrt(901) cm/x
3x = 70 * sqrt(901) cm
x = 70 * sqrt(901) cm/3
x = 700.4 cm
Answer: 700.4 cm
The length of drainpipe is 700.4 cm.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
One has legs measuring 1 cm and 30 cm.
Using Pythagorean theorem.
(1 cm)² + (30 cm)² = c²
c² = 901
c =√901 cm
Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.
(30 cm)/(700 cm) = [√(901) cm]/x
3/70 = √(901) cm/x
3x = 70 x √(901) cm
x = 700.4 cm
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ7
A numerical measure of linear association between two variables is the
Answer:
Correlation Coefficient
Step-by-step explanation:
The correlation coefficient (r) is a numerical measure that measures the strength and direction of a linear relationship between two quantitative variables.
Pls show work ASAP
Multiplying polynomials
Answer:
Step-by-step explanation:
1. 6w*2v + 3*6w= 12vw + 18w
2. 7(-5v) - 7(8)= -35v - 56
3. 2x*(-2x) - 3(2x) = -4x^2 - 6x
4. -4*v - 4(1)= -4v - 4
5. 2n*6n + 2n + 2*6n + 2= 12n^2 + 14n + 2
6. 4n(2n) + 4n(6) + 2n + 6= 8n^2 + 26n + 6
7. x(6x) - 2x - 18x + 6 = 6x^2 - 20x + 6
8. 8p(6p) + 8p(2) - 2(6p) - 4 = 48p^2 + 16p - 12p - 4= 48p^2 + 4p - 4
9. 6p(5p) - 6p(8) + 8(5p) - 40= 30p^2 - 48p + 40p - 40= 30p^2 - 8p - 40
10. 3m(8m) + 3m(7) - 8m - 7 = 24m^2 + 21m - 8m - 7= 24m^2 + 13m - 7
11. 2a(8a) - 2a(5) - 8a + 5 = 16a^2 - 10a - 8a + 5 = 16a^2 - 18a + 5
12. 5n(5n) - 5n(5) + 6(5n) - 6(5)= 25n^2 - 25n + 30n - 30= 25n^2 + 5n - 30
13. 4p(4p) - 4p - 4p + 1 = 16p^2 - 8p +
14. 7x(5x) + 7x(6) -6(5x) - 6(6)= 35x^2 + 42x - 30x - 36= 35x^2 + 12x - 36
Solve the system of equations y= x squared + 3x-6 and y=2x-6
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Step-by-step explanation:
Step by step solution :
Step 1 : Equation of a Straight Line
Graph of a Straight Line
Calculate the Y-Intercept
Calculate the X-Intercept
Calculate the Slope
Answer for y=2x-6 is below
Answer:
Slope = 4.000/2.000 = 2.000
x-intercept = 6/2 = 3
y-intercept = -6/1 = -6.00000
Hope this helps.
A tree farming company is testing how many items customers purchase during their visits. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of pieces of information remembered (during a fixed time period). What is the missing probability P(X=6)? Note that the missing probability should be reported to the second decimal place.
Answer:
X probability = 0.02
Cumulative frequency at x ( 6 ) = 1
Step-by-step explanation:
X P ( X ) Cf ( X )
1 0.58 0.58
2 0.18 0.58 + 0.18 = 0.76
3 0.10 0.76 + 0.10 = 0.86
4 0.07 0.86 + 0.07 = 0.93
5 0.05 0.93 + 0.05 = 0.98
6 0.02 0.98 + 0.02 = 1
Which statement best describes the expression fraction 1 over 2 x (14 − 6) x 6 + 4?
Answer:
Find half the difference of 14 and 6, multiply by 6, then add 4.(B)
Step-by-step explanation:
The risk of a child developing cancer is approx 3 in 1500. If there are approx 11,721,722 children, how many have cancer?
Answer:
Approximately 23,433 children will have cancer.
Step-by-step explanation:
3/1500 can be simplified to 1/500, which can also be written as 0.002. To find the number of children who have cancer, we do 11,721,722 * 0.002, which gives us 23,433.444 which we can round to 23,433.
Can you guys help me out with this one too? Plzzzzz helppp
Answer:
I think that it would be A
Step-by-step explanation:
If it were not a sailor, I would say B, but a sailor can face a hurricane at sea.
The population of coyotes in the northwestern portion of Alabama is given by the formula p (t )equals (t squared plus 100 )ln (t plus 2 ), where t represents the time in years since 2000 (the year 2000 corresponds to t equals 0 ). Find the rate of change of the coyote population in 2002 (tequals2).
Answer:
The rate of change of the Coyote population in 2002 is 32
Step-by-step explanation:
Given the formula for the population of a Coyotes in the Northwestern portion of Alabama, we are to calculate rate of change of the Coyote population in the year 2002 where t = 2
The formula is given as;
P(t) = (t^2 + 100) ln (t + 2)
The rate of change refers to the first integral of the formula;
Thus we need to calculate this by the use of product formula;
The first differential of t^2 + 100 is 2t
while that of ln(t + 2) is 1/(t + 2)
P’(t) = 2t(ln (t+2)) + (t^2 + 100) (1/t+2)
Now, we substitute 2 for the value of t here.
P’(2) = 2(2)( ln (2 + 2) + (2^2 + 100)(1/(2+2))
P’(2) = 4 ln 4 + 104(1/4)
P’(2) = 4ln 4 + 26
P’(2) = 5.55 + 26 = 31.55 which is approximately 32
A television weighs 8.50 pounds. How many grams is this? (Hint: You need to
use two unit conversion fractions. 1 pound equals about 0.454 kg.)
Answer:
Hello
The answer is 3855'5
Step-by-step explanation:
At first change lbs to kg.
Then you'll change the kg to grkg×1000=gr
السؤال الرابع
اب ج مثلث قائم الزاوية في ب ، فيه أب = 6 سم ،
ب ج= 8 سم . فجد قيمة جتاأ ؟
Answer:
10 cm
Step-by-step explanation:
نستخدم فيثاغورس
ٲب²+ب ج²=ج ٲ²
ج ٲ²= 6²+8²
ج ٲ²= 100
ج ٲ= 10 سم
A sample of 60 items from population 1 has a sample variance of 8 while a sample of 40 items from population 2 has a sample variance of 10. If we want to test whether the variances of the two populations are equal, the test statistic will have a value of
Answer:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Step-by-step explanation:
Information given
[tex]n_1 = 60 [/tex] represent the sample size 1
[tex]n_2 =40[/tex] represent the sample size 2
[tex]s^2_1 = 8[/tex] represent the sample variance 1
[tex]s^2_2 = 10[/tex] represent the sample variance 2
The statistic to check the hypothesis is given by:
[tex]F=\frac{s^2_2}{s^2_1}[/tex]
Hypothesis to test
We want to test if the two variances are equal, so the system of hypothesis are:
H0: [tex] \sigma^2_1 = \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 \neq \sigma^2_2[/tex]
The statistic would be given by:
[tex]F=\frac{s^2_2}{s^2_1}=\frac{10}{8}=1.25[/tex]
Can someone please give me the answer to this?
Answer:
About 36.87
Step-by-step explanation:
The sine of an angle in a right triangle is the length of the opposite side divided by the length of a hypotenuse, which in this case is 3/5. Therefore, the measure of the angle is the arcsin of 3/5 or about 36.87 degrees. Hope this helps!
Can anyone help me with this?
Answer:
Option (2)
Step-by-step explanation:
Option (1).
Time taken by Tina to walk = 56 minutes
Time taken by her sister to walk the same distance = x minutes
If both the sisters take the same time to walk, then
x = 56 minutes
Option (2).
Let the height of Tina = x inches
and the height of her brother = 56 inches
if Tina is shorter than her brother then,
x < 56 inches
Option (3).
Tina's dog weighed two months ago = 56 pounds
If the dog gained the weight in two months then weight before 2 months will be less than the present weight.
Let the weight of her dog is x pounds now,
x > 56 pounds
Option (4).
Amount with Tina = $x
Cost of the camera = $56
If the money with Tina has enough money to buy the camera, then the amount of money with her will be higher than the cost of the camera.
x > $56
Option (2) will be the answer.
MIDDLE SCHOOL MATH BRAINLEIST AND 5 STARS AS SOON AS YOU ANSWER!!!!!!!! PLEASE HELP AND THANKS SO MUCH IM SUPER GRATEFUL!!!!!!!!!!!
Answer:
Bottom prism: 126*11=1386
Top Prism: 2*45=90
Total volume: 1386+90= 1746 cubic cm
How many percent is the change in the price, if:The price was $160 and now it is $40?
Answer:
75% reduction
Step-by-step explanation:
The price dropped by $120. As a percentage of the original price, that is ...
-$120/$160 × 100% = -75%
The price changed by -75%.
Answer:
75% decrease.
Step-by-step explanation:
The original price is $160 and we went to $40.
That means the price got reduced by $120 in the process.
$120/$160 = 0.75 = 75%.
So in other words, we lost 75% of the price ($120) and got left with 25% of the price ($40).
I hope this helps!
Rema spent 6 days reading her book, completing the same fraction of the book each day. If she read a total of StartFraction 8 Over 9 EndFraction of her book after 6 days, what fraction of the book did she read each day? StartFraction 5 Over 54 EndFraction of the book StartFraction 3 Over 27 EndFraction of the book StartFraction 7 Over 54 EndFraction of the book StartFraction 4 Over 27 EndFraction of the book PLZ HELP!!!!!!!!!!!!!!! 30 PTS!!!!!!!!!!!!!!!!!!!!!!
Answer:
4over27
Step-by-step explanation:
8over9 divided by 6 equals 8over54 which simplifies to 4over27
Answer:
4 over 27
Step-by-step explanation:
she spent 6 day reading, there 7 day in a week so we have to change it to 7 and four pages.
What’s the correct answer for this? Select all the ones that apply ?
Answer:
A and D
Step-by-step explanation:
Either rotate the dilated circle 180° about point C or Translate the dilated circle so that it's centre is at point B so that we come to know that the circles are similar
The difference of a rational number and an irrational number is ____ an irrational number. Which word correctly fills in the blank to create a true statement?
A) sometimes
B) always
C) never
Answer:
a
Step-by-step explanation:
The difference between a rational number and an irrational number is always an irrational number. The correct option is B.
What is a rational and irrational number?A Rational Number is a number of the form p/q, p & q are integers, and q ≠ 0. An irrational number is all real numbers except rational numbers i.e. it is a non-repeating and non-terminating decimal number or it can not be expressed in a ratio of two integers.
Further, natural numbers can be rational numbers. Also, all repeating and terminating decimals are rational.
The difference between a rational number and an irrational number is always an irrational number. For example:
2 - √3 is always an irrational number where 2 is rational and √3 is an irrational number.
Hence addition and subtraction of rational and irrational numbers is always an irrational number.
To know more about an irrational number follow
https://brainly.com/question/511377
#SPJ5
*I am greater than 80
*I am less than 90
*I am an even number
*My digits (of the mystery number) add up to 12
What’s my number
Answer:
Step-by-step explanation:
84?
8+4 is 12, and 84 is greater than 80, and less than 90
Answer:
84
Step-by-step explanation:
What value of x satisfies the system of equations {2x+5y=35x=−10−15y? Enter your answer as the correct value for x, like this: 42
Answer:
x = 23
Step-by-step explanation:
2x + 5y = 35 * (-3) ------> -6x -15y = -105 (A)
x = -10 - 15y -----> x + 15y = -10 (B)
(A) + (B)
-5x = -115
x = 23
What is
7 1/4 - 3 3/4 =?
Answer:
3 1/2
Step-by-step explanation:
7 1/4 - 3 3/4
Borrow 1 from the 7 in the form of 4/4
6 + 4/4 + 1/4 - 3 3/4
6 5/4 - 3 3/4
3 2/4
Simplify the fraction
3 1/2
Answer:
[tex]3 \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]7 \frac{1}{4} - 3 \frac{3}{4} \\ \frac{29}{4} - \frac{15}{4} \\ = \frac{14}{4} \\ = \frac{7}{2} \\ = 3.5 = 3 \frac{1}{2} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Use the Divergence Theorem to compute the net outward flux of the field F=<-2x,y,-2z> across the surface S, where S is the boundary of the tetrahedron in the first octant formed by the planex+y+z=2.
The net outward flux across the boundary of the tetrahedron is:___________.
The net outward flux across the boundary of the tetrahedron is: -4
What is the gradient of a function in a vector field?
The gradient of a function is related to a vector field and it is derived by using the vector operator ∇ to the scalar function f(x, y, z).
Given vector field:
F = ( -2x, y, - 2 z )
[tex]\mathbf{\nabla \cdot F = ( i \dfrac{\partial }{\partial x }+ j \dfrac{\partial}{\partial y} + k \dfrac{\partial}{\partial z}) \langle -2x, y, -2z \rangle}[/tex]
[tex]\mathbf{ \nabla \cdot F = ( \dfrac{\partial }{\partial x }(-2x)+ \dfrac{\partial}{\partial y}(y) + \dfrac{\partial}{\partial z}(-2z))}[/tex]
= -2 + 1 -2
= -3
According to divergence theorem;
Flux [tex]\mathbf{=\iiint _v \nabla \cdot (F) \ dv}[/tex]
x+y+z = 2; [tex]1^{st}[/tex] Octant
x from 0 to 2y from 0 to 2 -xz from 0 to 2-x-y[tex]= \int\limits^2_0 \int\limits^{2-x}_0 \int\limits^{2-x-y}_0 -3dzdydx[/tex]
[tex]=-3 \int\limits^2_0 \int\limits^{2-x}_0 (2-x-y)dy dx[/tex]
[tex]= -3 \int\limits^2_0[(2-x)y - \dfrac{y^2}{2}]^{2-x}__0 \ \ dx[/tex]
[tex]= -3 \int\limits^2_0(2-x)^2 - \dfrac{(2-x)^2}{2} dx[/tex]
[tex]= -3 \int\limits^2_0\dfrac{(2-x)^2}{2} dx = - \dfrac{3}{2} \int\limits^2_0(4-4x+x^2) dx[/tex]
[tex]=- \dfrac{3}{2}(4x-x^2 + \dfrac{x^3}{3})^2_0[/tex]
[tex]=- \dfrac{3}{2}(8-8+\dfrac{8}{3})[/tex]
[tex]=- \dfrac{3}{2}(\dfrac{8}{3})[/tex]
= -4
Therefore, we can conclude that the net outward flux across the boundary of the tetrahedron is: -4
Learn more about the gradient of a function here:
https://brainly.com/question/6158243
A research company desires to know the mean consumption of meat per week among people over age 29. A sample of 2092 people over age 29 was drawn and the mean meet consumption was 2.9 pounds. Assume that the standard deviation is known to be 1.4 pounds. Construct a 95% confidence interval for the mean consumption of meat among people over age 29. Round your answer to one decimal place.
Answer:
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1.4}{\sqrt{2092}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 2.9 - 0.1 = 2.8 pounds
The upper end of the interval is the sample mean added to M. So it is 2.9 + 0.1 = 3 pounds.
The 95% confidence interval for the mean consumption of meat among people over age 29 is between 2.8 pounds and 3 pounds.
Answer:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=2.9[/tex] represent the sample mean
[tex]\mu[/tex] population mean
[tex]\sigma =1.4[/tex] represent the population standard deviation
n=2092 represent the sample size
Confidence interval
The confidence interval is given by:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
Since the Confidence interval is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]z_{\alpha/2}=1.96[/tex]
Replacing the info we got:
[tex]2.9-1.96\frac{1.4}{\sqrt{2092}}=2.84[/tex]
[tex]2.9+1.96\frac{1.4}{\sqrt{2092}}=2.96[/tex]
The confidence interval is given by [tex]2.84 \leq \mu \leq 2.96[/tex]
A machine in the student lounge dispenses coffee. The average cup of coffee is supposed to contain 7.0 ounces. A random sample of seven cups of coffee from this machine show the average content to be 7.4 ounces with a standard deviation of 0.70 ounce. Do you think that the machine has slipped out of adjustment and that the average amount of coffee per cup is different from 7 ounces
Answer:
[tex]t=\frac{7.4-7}{\frac{0.7}{\sqrt{7}}}=1.512[/tex]
The degrees of freedom are
[tex]df=n-1=7-1=6[/tex]
And the p value for this case is:
[tex]p_v =2*P(t_{(6)}>1.512)=0.181[/tex]
The p value is a higher value and using a significance levels of 5% or 10% we see that the p value is higher than the significance level and then we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is different from 7 ounces.
Step-by-step explanation:
Information provided
[tex]\bar X=7.4[/tex] represent the sample mean
[tex]s=0.7[/tex] represent the sample standard deviation
[tex]n=7[/tex] sample size
[tex]\mu_o 7[/tex] represent the value to verify
t would represent the statistic
[tex]p_v[/tex] represent the p value
System of hypothesis
We want to verify if the average amount of coffee per cup is different from 7 ounces, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 7[/tex]
Alternative hypothesis:[tex]\mu \neq 7[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{7.4-7}{\frac{0.7}{\sqrt{7}}}=1.512[/tex]
The degrees of freedom are
[tex]df=n-1=7-1=6[/tex]
And the p value for this case is:
[tex]p_v =2*P(t_{(6)}>1.512)=0.181[/tex]
The p value is a higher value and using a significance levels of 5% or 10% we see that the p value is higher than the significance level and then we FAIL to reject the null hypothesis and we don't have enough evidence to conclude that the true mean is different from 7 ounces.
One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to fill the pool if the drain is left open?
Answer: 12 hours
Step-by-step explanation:
Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open
1/6 = portion of pool filled per hour by the inlet pipe
1/12 = portion of pool emptied per hour by the drain
1/x = portion of pool filled per hour if the inlet pipe and drain are both open
Then, 1/6 - 1/12 = 1/x
Multiply by the LCD, 12x, to obtain
2x - x = 12
x = 12 hours
pls pls help! ik it’s super simple but i’m slow
Which equation represents this number sentence?
Two less than one-fourth of a number is 10.
Answer:
[tex]\frac{1}{4} x-2=10[/tex]
Step-by-step explanation:
Let x be that number.
[tex]\frac{1}{4} x-2=10[/tex]
If you want to find the number..
[tex]\frac{1}{4} x=10+2[/tex]
[tex]0.25x=12[/tex]
[tex]x=12/0.25[/tex]
[tex]x=48[/tex]
Rajeev walked 7/8 mile in 1/4 hour. what was his speed in miles per hour?
Answer:
V(speed)=3.5 mile per hour
Step-by-step explanation:
[tex]V=mile per hour[/tex]
[tex]V=\frac{7}{8}/ \frac{1}{4}[/tex]
[tex]V=\frac{7}{8}*\frac{4}{1}[/tex]
[tex]V=\frac{7}{8}*4[/tex]
[tex]V=3.5[/tex]
PLEASE HELP!! I WILL GIVE YOU EVERYTHING
Answer:
Step-by-step explanation:
7.9
Answer:
y - 4 = (-3/2)(x - 4)
Step-by-step explanation:
Here's how we obtain the blue graph:
1) translate the red graph 5 units to the right, and
2) translate the resulting graph 5 units upward.
The equation of the blue graph is y - 4 = (-3/2)(x - 4)
Which table represents a nonlinear function?
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 19, negative 11, negative 3, 5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries 15, 12, 9, 6.
Answer:
A two column table with five rows. The first column, x, has the entries, 0, 1, 2, 3. The second column, y, has the entries, negative 1.5, 1.5, 3, 4.5.
Step-by-step explanation:
When the x-values are evenly spaced, a linear function will have evenly-space y-values.
In the first table, the y-differences are all +8.
In the second table, the y-differences are 0, 1.5, 1.5, so are not all the same.
In the third table, the y-differences are all -3.
The second table represents a non-linear function.
__
In the graph, you can see that the points from the second table (purple) are not on a straight line.
Answer:
B
Step-by-step explanation:
