Answer: 45° and speed of light in prism 2×10⁸m/s
Step-by-step explanation:
The minimum deviation of the equilateral glass prism will form 60° angle.
So angle of incidence = 3/4×60
= 3 ×15
= 45°
Minimum deviation = δmin
= 30
After finding the value of μ using prism law
μ = 1.41
Speed of light will be 2×10⁸m/s
Must click thanks and mark brainliest
Solve for x
Answer choices:
4
5
8
3
2
opposite angles are equal
[tex]\\ \sf\longmapsto 13x+19=84[/tex]
[tex]\\ \sf\longmapsto 13x=84-19[/tex]
[tex]\\ \sf\longmapsto 13x=65[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{65}{13}[/tex]
[tex]\\ \sf\longmapsto x=5[/tex]
Answer:
[tex]\boxed {\boxed {\sf x=5}}[/tex]
Step-by-step explanation:
We are asked to solve for x.
We are given a pair of intersecting lines and 2 angles measuring (13x+19)° and 84°. The angles are opposite each other, so they are vertical angles. This means they are congruent or have the same angle measure.
Since the 2 angles are congruent, we can set them equal to each other.
[tex](13x+19)=84[/tex]
Solve for x by isolating the variable. This is done by performing inverse operations.
19 is being added to 13x. The inverse operation of addition is subtraction. Subtract 19 from both sides of the equation.
[tex]13x+19-19= 84 -19[/tex]
[tex]13x= 84 -19[/tex]
[tex]13x=65[/tex]
x is being multiplied by 13. The inverse operation of multiplication is division. Divide both sides by 13.
[tex]\frac {13x}{13}= \frac{65}{13}[/tex]
[tex]x= \frac{65}{13}[/tex]
[tex]x= 5[/tex]
For this pair of vertical angles, x is equal to 5.
For what numbers is f(0) = sec 0 not defined?
Answer:
stundeez
Step-by-step explanation:
Nicki Minaj hdhsbskdhsnsk
In an experiment, you choose to have two randomly assigned groups. In one, you take measurements both pretest and posttest; with the second, a posttest-only measure. This describes which task of conducting an experiment
Answer:
The answer is "Specific treatment levels".
Step-by-step explanation:
When we experimenting with 'level' which is related to the quantity or magnitude of treatment. For this part of an experiment or study, a group or individual is exposed to a specified set of circumstances. For example: If four categories are exposed to different doses of a given drug, then each dose reflects a level of a treatment factor in the model.
14. What, if any, is a real solution to 5x +1 +9 - 3?
1
C
D. There is no real solution.
I believe the question is:
What is the solution to 5x + 1 +9 - 3
In this case, we solve for X.
5x + 1 + 9 - 3
5x + 10 - 3
5x + 7
5x = -7
x = -7/5
Unfortunately, It is not one of the answer choices it looks like.
Maybe you should reword your question but hopefully this is correct.
If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5
The value of x in a given expression is -7/5.
We have given that,
5x + 1 + 9 - 3
We have to determine the value of x.
What is the variable?A variable is any factor, trait, or condition that can exist in differing amounts or types. Scientists try to figure out how the natural world works
In this case, we solve for X.
5x + 1 + 9 - 3
5x + 10 - 3
5x + 7
5x = -7
x = -7/5
If you meant to say 5x+1 + 9 < 3 --> 5x + 10 < 3 --> 5x < -7 --> x < -7/5.
Therefore we get the value of x is -7/5.
To learn more about the value of the variable visit:
https://brainly.com/question/5030068
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Algebra 2, please help! thank you
The function y = 2 cos 3(x + 2π∕3) +1 has a phase shift (or horizontal shift) of
A) –2π∕3
B) 3
C) 1
D) 2
Answer:
-2pi/3
Step-by-step explanation:
y = 2 cos 3(x + 2π∕3) +1
y = A sin(B(x + C)) + D
amplitude is A
period is 2π/B
phase shift is C (positive is to the left)
vertical shift is D
We have a shift to the left of 2 pi /3
Answer:
A
Step-by-step explanation:
The standard cosine function has the form:
[tex]\displaystyle y = a\cos (b(x-c)) + d[/tex]
Where |a| is the amplitude, 2π / b is the period, c is the phase shift, and d is the vertical shift.
We have the function:
[tex]\displaystyle y = 2 \cos 3\left(x + \frac{2\pi}{3}\right) + 1[/tex]
We can rewrite this as:
[tex]\displaystyle y = \left(2\right)\cos 3\left(x - \left(-\frac{2\pi}{3}\right)\right) + 1[/tex]
Therefore, a = 2, b = 3, c = -2π/3, and d = 1.
Our phase shift is represented by c. Thus, the phase shift is -2π/3.
Our answer is A.
ABC are points; (2,3), (4,7), (7,3) respectively. Find the equation of the line through the point (3,-5) which is parallel to the line with the equation 3x+2y-5=0
Answer:
y = -3x/2 - 1/2
Step-by-step explanation:
slope m = -3/2
-5 = (-3/2)×3+b
or, b = -1/2
putting it into y = mx + b
y = -3x/2 - 1/2
Answered by GAUTHMATH
Assume a researcher wants to compare the mean Alanine Aminotransferase (ALT) levels in two populations, individuals who drink alcohol and individuals who do not drink alcohol. The mean ALT levels for the individuals who do not drink alcohol is 32 with a standard deviation of 14, and 37 individuals were in the sample. The mean ALT levels for individuals who drink alcohol is 69 with a standard deviation of 19, and 38 individuals were in the sample. Construct and interpret a 95% confidence interval demonstrating the difference in means for those individuals who drink alcohol when compared to those who do not drink alcohol.
a. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.22 and 39.78.
b. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.33 and 39.67
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
d. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.41 and 39.59.
Answer:
c. The researchers are 95% confident that the true mean difference in ALT values between the population of drinkers and population of non-drinkers is between 24.32 and 39.68.
Step-by-step explanation:
Given :
Groups:
x1 = 69 ; s1 = 19 ; n1 = 38
x2 = 32 ; s2 = 14 ; n2 = 37
1 - α = 1 - 0.95 = 0.05
Using a confidence interval calculator to save computation time, kindly plug the values into the calculator :
The confidence interval obtained is :
(24.32 ; 39.68) ; This means that we are 95% confident that the true mean difference in ALT values between the two population lies between
(24.32 ; 39.68) .
what is the prime product of 120
Answer:
[tex]2^{3} * 3 * 5[/tex]
Step-by-step explanation:
This table gives a few (x,y) pairs of a line in the coordinate plane.
Answer:
The x-intercept of the line will be (10, 0)
Step-by-step explanation:
start from -12
get to -2...
-12 + (10) = -2
-2 + (10) = 8
therefore, the x-intercept is (10, 0)
On the first day of a two-day meeting, 10 coffees and 10 doughnuts were purchased for a total of $20.00. Since nobody drank the coffee and all the doughnuts were eaten, the next day only 2 coffees and 14 doughnuts were purchased for a total of $13.00. How much did each coffee and each doughnut cost?
Answer:
1.25 dollars- the value of each coffee
0.75 dollars- the value of each doughnut
Step-by-step explanation:
Suppose that value of one coffee is x dollars, when one doughnut costs y dollars. The value o 10 coffee is 10x, when 10 doughnuts cost 10y. The sum is 10x+10y and it is 20.
10x+10y= 20 (we can divide each part by 10)
x+y=2
2coffee cost 2x, 14 doughnuts cost 14y
2x+14y=13 (it can be divided by two)
x+7y=6.5
We have the system of equations x+y=2, x+7y=6.5
Subtract the first equation from the second one (the left side of the first equation from the left side
x+7y - (x+y)= 6.5-2
6y=4.5
y=4.5/6= 3/4 = 0.75 dollars- the value of each doughnut
x=2-0.75=1.25 dollars- the value of each coffee
Write a rule to describe the transformation.
A. reflection across y=x
B. rotation 90º clockwise about the origin
C. rotation 180º about the origin
D. rotation 90º counterclockwise about the origin
Answer:
C. rotation 180º about the origin
Step-by-step explanation:
Given
Quadrilaterals GWVY and G'W'V'Y'
Required
Describe the transformation rule
Pick points Y and Y'
[tex]Y = (5,-4)[/tex]
[tex]Y' = (-5,4)[/tex]
The above obeys the following rule:
[tex](x,y) \to (-x,-y)[/tex]
When a point is rotated by 180 degrees, the rule is:
[tex](x,y) \to (-x,-y)[/tex]
Hence, (c) is correct
what is the absolute value of |9|?
Answer:
9
Step-by-step explanation:
it's as simple as that 9 is 9 away from 0
I need help on this math problem
Answer:
for the first one, simply add g(x) and h(x) :
x+3 + 4x+1 = 5x + 4
the second one, you would multiply them :
(x+3)(4x+1) = 4x^2 + 13x + 3
the last one, you would subtract :
(x+3)-(4x+1) = -3x + 2
and then substitute 2 for 'x' :
-3*2 + 2 = -6 + 2 = -4
Answer:
1. 5x+4
2. [tex]4x^2+13x+3[/tex]
3. -4
Step-by-step explanation:
1. (x+3)+(4x+1)
Take off the parentheses and Add.
5x+4
2. (x+3)(4x+1)
Use the FOIL method to multiply.
[tex]4x^2+x+12x+3[/tex]
[tex]4x^2+13x+3[/tex]
3. First, set up the equation as (g-h)(x)
(x+3)-(4x+1)
x+3-4x-1
Solve.
-3x+2
Substitute in 2 for x.
-3(2)+2
-6+2
-4
If 2x - 5y – 7 = 0 is perpendicular to the line ax - y - 3 = 0 what is the value of a ?
A) a =2/3
B) a =5/2
C) a = -2/3
D) a = -5/2
Answer:
D) a = - 5/2
Step-by-step explanation:
2x -5y - 7 = 0
5y = 2x - 7
y = 2/5 x - 7
the slope of this line is therefore 2/5 (factor of x).
the perpendicular slope is then (exchange y and x and flip the sign) -5/2, which is then a and the factor of x.
Complete the table y+1=7/8x
Answer:
y = 7/8x - 1
Step-by-step explanation:
graph shown
People were asked if they owned an artificial Christmas tree. Of 78 people who lived in an apartment, 38 own an artificial Christmas tree. Also it was learned that of 84 people who own their home, 46 own an artificial Christmas tree. Is there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees
Answer:
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
Step-by-step explanation:
Before testing the hypothesis, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Apartment:
38 out of 78, so:
[tex]p_A = \frac{38}{78} = 0.4872[/tex]
[tex]s_A = \sqrt{\frac{0.4872*0.5128}{78}} = 0.0566[/tex]
Home:
46 out of 84, so:
[tex]p_H = \frac{46}{84} = 0.5476[/tex]
[tex]s_H = \sqrt{\frac{0.5476*0.4524}{84}} = 0.0543[/tex]
Test if the there a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees:
At the null hypothesis, we test if there is no difference, that is, the subtraction of the proportions is equal to 0, so:
[tex]H_0: p_A - p_H = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the subtraction of the proportions is different of 0, so:
[tex]H_1: p_A - p_H \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_A - p_H = 0.4872 - 0.5476 = -0.0604[/tex]
[tex]s = \sqrt{s_A^2 + s_H^2} = \sqrt{0.0566^2 + 0.0543^2} = 0.0784[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0604 - 0}{0.0784}[/tex]
[tex]z = -0.77[/tex]
P-value of the test and decision:
The p-value of the test is the probability of the difference being of at least 0.0604, to either side, plus or minus, which is P(|z| > 0.77), given by 2 multiplied by the p-value of z = -0.77.
Looking at the z-table, z = -0.77 has a p-value of 0.2207.
2*0.2207 = 0.4414
The p-value of the test is 0.4414, higher than the standard significance level of 0.05, which means that there is not a a significant difference in the proportion of apartment dwellers and home owners who own artificial Christmas trees.
The data show the traveler spend- ing in billions of dollars for a recent year for a sample of the states. Find the range, variance, and standard deviation for the data.
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
Solution :
Given data :
20.1 33.5 21.7 58.4 23.2 110.8 30.9
24.0 74.8 60.0
n = 10
Range : Arranging from lowest to highest.
20.1, 21.7, 23.2, 24.0, 30.9, 33.5, 58.4, 60.0, 74.8, 110.8
Range = low highest value - lowest value
= 110.8 - 20.1
= 90.7
Mean = [tex]$\frac{\sum x}{n}$[/tex]
[tex]$=\frac{20.1+21.7+23.2+24.0+30.9+33.5+58.4+60.0+74.8+110.8}{10}$[/tex]
[tex]$=\frac{457.4}{10}$[/tex]
[tex]$=45.74$[/tex]
Sample standard deviation :
[tex]$S=\sqrt{\frac{1}{n-1}\sum(x-\mu)^2}$[/tex]
[tex]$S=\sqrt{\frac{1}{10-1}(20.1-45.74)^2+(21.7-45.74)^2+(23.2-45.74)^2+(24.0-45.74)^2+(30.9-45)^2}$[/tex]
[tex]\sqrt{(33.5-45.74)^2+(58.4-45.74)^2+(60.0-45.74)^2+(74.8-45.74)^2+(110.8-45.74)^2}[/tex]
[tex]$S=\sqrt{\frac{1}{9}(657.4+577.9+508.0+472.6+220.2+149.8+160.2+203.3+844.4+4232.8)}$[/tex][tex]$S=\sqrt{\frac{1}{9}(8026.96)}$[/tex]
[tex]$S=\sqrt{891.88}$[/tex]
S = 29.8644
Variance = [tex]S^2[/tex]
[tex]=(29.8644)^2[/tex]
= 891.8823
you start at (5,3) you move down 4 units and up 6 units. where do you end?
You end up at the point (5, 5).
CAN SOMEONE HELP ME PLEASE CAN YOU FIGURE OUT WHERE I PUT 4 PI ON THE NUMBER LINE
Answer:
see below
Step-by-step explanation:
Pi is approximately 3.14
4*3.14 =12.56
So about halfway between 12 and 13
Im new, and i hope someone tells me the right answers!
A factor is a natural number that can be multiplied by another natural number to get a value. The greatest common factor refers to when one compares the factors of two numbers, the largest natural number that both numbers have in common is the number's greatest common factor.
In the case of ([tex]m^2[/tex]) and ([tex]m^4[/tex]), the greatest common factor is ([tex]m^2[/tex]) because there are no factors of ([tex]m^2[/tex]) that are larger than it. No number can have a factor larger than itself. Since ([tex]m^2[/tex]) is also a factor of ([tex]m^4[/tex]) it is the greatest common factor of the two numbers.
Please help me! Thank you!
Find the length of BC
A. 27.22
B. 11.62
C. 22.02
D. 19.78
Answer:
B
Step-by-step explanation:
Since we know the measure of ∠B and the side opposite to ∠B and we want to find BC, which is adjacent to ∠B, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
The angle is 54°, the opposite side measures 16 units, and the adjacent side is BC. Substitute:
[tex]\displaystyle \tan 54^\circ = \frac{16}{BC}[/tex]
Solve for BC. We can take the reciprocal of both sides:
[tex]\displaystyle \frac{1}{\tan 54^\circ} = \frac{BC}{16}[/tex]
Multiply:
[tex]\displaystyle BC = \frac{16}{\tan 54^\circ}[/tex]
Use a calculator. Hence:
[tex]\displaystyle BC \approx 11 .62\text{ units}[/tex]
BC measures approximately 11.62 units.
Our answer is B.
Find the area If you get this correct i WILL GIVE YOU 100 POINTS
Answer:
Area of yellow portion =54 in
Pls help I literally am crying I don’t understand ):
Answer: Passes out in slow
Step-by-step explanation:
Step 1 be Einstein
1/10 + 3/5
ANSWER QUICK PLS FIRST ANSWER GETS BRAINLIEST
Ayuda por fa con estos ejercicios por fa urgente
Step-by-step explanation:
A ball is thrown straight up from a rooftop 320 feet high. The formula below describes the ball's height above the ground, h, in feet, t seconds after it was thrown. The ball misses the rooftop on its way down and eventually strikes the ground. How long will it take for the ball to hit the ground? Use this information to provide tick marks with appropriate numbers along the horizontal axis in the figure shown.
h=-16t^2+16t+32
A circular fence is being placed to surround a tree. The diameter of the
fence is 4 feet. How much fencing is used? *
Answer:
12.6 ft
Step-by-step explanation:
a store sign reads "Take 75% of the original price when you take an additional 15% off the sale price, which is 60% off the original price." Is the stores sign accurate?
Answer:
The new price is 66% off the original not 75% off
Step-by-step explanation:
Let x be the original price
First take 60 percent off
x - x*60% = new price
x- .60x = .40x
The new price is .40x
Then take 15 % off
(.40x) - (.40x)*15%
.40x - .40x*.15
.40x - .06x
.34x
100 -.34 =.66
The new price is 66% off the original not 75% off
If x+y=
= 12 and x = 2y, then x =
O
2
06
08
10
Answer:
2y + y = 12
3y = 12
y = 4
now , x = 2y
x = 2 ( 4 )
x = 8
hope that helps ✌
What is 3.142857 rounded three decimal places
Answer:
3.143
Step-by-step explanation:
Since you're rounded it to the third decimal, you look at the fourth one. And since the fourth one is 8, ur going round 2, which is the third decimal to 3.
Answer:
The answer is below
Step-by-step explanation:
In this question, to round three decimal place, we need to count three numbers after the dot.
Here..
the three numbers are 142
so after that we round it, so first of all we ignore 1 and, and focus on the number 2 and 4.
and if the number is below 5, it is rounded to the last number, but if the number is 5 or more than it, then we round it to the next number.
For example
142 - here we have 2, which is below 5, so we round it to '140'
where as if we have..
147 - here we have 7, which is above 7, so we round it to '150'
____________________________________________________________
So in this problem we round 142, so the number 2 is below 5 so it is round to 140
therefore the answer is - 3.14
T
On Melissa's 6th birthday, she gets a $2000 CD that earns 5% interest, compounded semiannually. If the
CD matures on her 16th birthday, how much money will be available?
TE
$
(S
9514 1404 393
Answer:
$3277.23
Step-by-step explanation:
The future value of the CD with interest at rate r compounded semiannually for t years will be given by ...
A = P(1 +r/2)^(2t)
where P is the principal value.
For the given rate and time, this is ...
A = $2000(1 +0.05/2)^(2·10) = $2000(1.025^20) ≈ $3277.23
The value of the CD at maturity will be $3277.23.
