Answer:
a) We are told smaller scores indicate a more feminine scent and larger scores a more masculine scent, also a score of 12 represents a gender-neutral scent.
Here the average from the sample for lavender is 10.28
To test for the evidence that lavender is not gender neutral on average, the null hypothesis H0 would take that lavender is gender-neutral, while the alternative hypothesis would take that the score of lavender is not gender neutral. We now have the null and alternative hypotheses as:
H0 : u = 12
H1 : u ≠ 12
Here, u represents the mean gender-orientation score for lavender. The alternative is two sided because we want to test if lavender is not gender neutral. Which means lavender might be more masculine of more feminine.
b) Given: p < 0.01 (2 tailed)
This means the p-value is less than level of significance 0.01.
Since the pvalue is less than the level of significance, we reject null hypothesis H0. This means there is sufficient evidence to conclude that the smell is not gender-neutral.
There is no reason to prefer a particular gender, that's why this is a two tailed hypothesis.
c) c.Assuming that the conditions for inference were met, which means the p-value is less than 0.01 so the null hypothesis H0 is rejected.
The conlusion would be that there is enough evidence to conclude that lavender is not gender-neutral
Pentagon ABCDE is rotated 90° counterclockwise about the origin to form pentagon A'B'C'D'E'. What is the y-coordinate of point C'?
please now
Answer:
The y-coordinate of point C' is 4
Step-by-step explanation:
In the picture attached, pentagon ABCDE is shown.
Rotation 90° counterclockwise about the origin transforms point (x,y) into (-y,x).
C is located at (4, 3), then C' is located at (-3, 4)
Answer:
4
Step-by-step explanation:
What is the value of x?
Answer:
x = 30
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the opposite interior angles
100 = 70+x
Subtract 70 from each side
100-70 = 70+x-70
30 =x
Answer:
[tex]x = 30 \: \: degrees[/tex]
Step-by-step explanation:
The sum of the of the exterior angle is equal to sum of the opposite interior angles in a triangle.
[tex]70 + x = 100 \\ x = 100 - 70 \\ x = 30 \: \: \: degrees[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Ellie goes out to dinner with her family. The total bill is $57. They decide to leave a 20% tip. How much money should they leave as their tip?
Answer:
78doalrse
Step-by-step explanation:
solos w
Answer:
$11.40
Step-by-step explanation:
This question asks us to find how much money the family should leave as their tip.
To find the tip, multiply the cost of the total bill by the tip rate.
cost of bill * tip rate
The total bill was $57, and they are leaving a 20% tip
$57 * 20%
Convert 20% to a decimal by dividing by 100 or moving the decimal place 2 spaces to the left.
20/100=0.20
20.0--> 2.0 --> 0.20
20%=0.20
$57 * 0.20
Multiply 57 and 0.20
11.4= $11.40
The family should leave a tip of $11.40
What is the solution of StartRoot x minus 4 EndRoot + 5 = 2? x = –17 x = 13 x = 53 no solution
The solution to the given function is determined as 13.
Solution of the function
The solution of the function is calculated as follows;
[tex]\sqrt{x - 4} \ +\ 5 = 2[/tex]
collect similar terms together
[tex]\sqrt{x - 4} \ = 2-5\\\\\sqrt{x - 4} \ = -3[/tex]
square both sides of the equation
[tex](\sqrt{x - 4} )^2 = (-3)^2\\\\x - 4 = 9\\\\x = 9 + 4\\\\x = 13[/tex]
Thus, the solution to the given function is determined as 13.
Learn more about solution of functions here: https://brainly.com/question/10439235
#SPJ9
Answer:
No solution
Step-by-step explanation:
Edge.
The highest and lowest scores on a test taken by 80 students are within 19 points of the average of the exam. The average for this exam was a 72. Set up an equation to solve for the highest and lowest scores. Show your original equation and the process used to find the highest and lowest exam score.
1. So start off by asking yourself, how will I get this answer? Absolute values!
2. So what the question is asking is for you to build and equation that shows us how to solve for the highest and lowest grades that are 19 points above and below the average of 72.
3. So your unknown is x, and for us to be able to plug in our highest and lowest scores it will always have to = 19 (that’s the rule we got from the question)
So now this is where your absolute value comes in.
4. Set it up
| x - 72 | = 19
5. Solve it
72-19=53 Minimum
72+19=91 Maximum
6. | 53 - 72 | = 19
| 91 - 72 | = 19
Change2800cm squared into litres
Answer:
You cannot do this because 2800 cm squared is area and liters is volume. however, if you mean 2800 cm cubed, then the answer is 2.8 liters.
Step-by-step explanation:
Color Blindness in Men and Women The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately of American men and of American women are red-green color-blind.1 Let and denote the events that a man or a woman is color-blind, respectively.
A) If an Americal male is selected at random, what is the probability that he is red-green color-blind?
B) If an American female is selected at random, what is the probability that she is not red-green color-blind?
C) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind?D) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?
Answer:
A. Probability the man is colorblind = 0.07
B. Probability the woman is not colorblind = 0.996
C. Probability neither the man or woman is colorblind = 0.926
D. Probability at least one of the woman or man is colorblind = 0.074
Note: The given question is missing some values. The question below is a sample question.
"The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosomes). Approximately 7% of American men and 0.4% of American women are red-green color-blind.
(a) If an American male is selected at random, what is the probability that he is red-green colorblind?
(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind?
(c) If one man and one woman are selected at random, what is the probability that neither are
red-green color-blind?
(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind?"
Step-by-Step Explanation:
Let cbM and cbW represent the events that a man or a woman is colorblind, respectively.
(a) 7% of men are colorblind, P(CBM) = 7/100 = 0.07.
(b) 0.4% of women are colorblind = 0.4/100 = 0.004
P(not cbW) = 1 - P(cbW)
P(not cbW) = 1 - 0.004 = 0.996.
(c) Probability the woman is not colorblind, P(not cbW) = 0.996,
Probability that the man is not color- blind, P(not cbM) = 1 - 0.07 = 0.93.
The two events are independent of each other, therefore, their probabilities are multiplied together:
P(neither is colorblind) = P(not cbM) × P(not cbW)
= 0.93 × 0.996 = 0.926.
(d) Probability that at least one is colorblind is the complement of the set P (neither is colorblind).
Therefore, P(at least one is colorblind) = 1 - P (Neither is Colorblind)
= 1 - 0.926 = 0.074
2 1 /4 meters by 1 7 /8
[tex](\frac{9}{4} )(\frac{15}{8} )[/tex]
[tex]\frac{135}{32}[/tex]
[tex]=4\frac{7}{32}[/tex]
Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 2 units right and 3 units down
B. shifted 3 units right and 2 units down
C. shifted 2 units right and 4 units down
D. shifted 4 units right and 3 units down
Answer:
Option (A)
Step-by-step explanation:
In the figure attached,
Quadrilateral ABCD has been translated to get an image quadrilateral A'B'C'D'.
To get the rule by which the pre-image ABCD has been translated, we will choose a point A(1, 1) from the given pre-image.
Coordinates of point A' are (3, -2).
So the change is,
A(1, 1) → A'(3, -2)
A(1, 1) → A'[(1 + 2), (1 - 3)]
A(x, y) → A'[(x + 2), (y - 3)]
Therefore, point A has been shifted 2 units right and 3 units down.
Option (A) will be the answer.
Consider the curve given by the equation (2y+1)^3 − 24x = −3.
(a) Show that dy/dx = 4/(2y+1)^2.
(b) Write an equation for the line tangent to the curve at the point (−1,−2).
(c) Evaluate d2y/dx2 at the point (−1,−2).
(d) The point (16,0) is on the curve. Find the value of (y−1)′(0).
Answer:
(a) dy/dx = 4/(2y+1)^2.
(b) y = 4/9 x - 14/9
(c) d2y/dx2 = -64/243
Step-by-step explanation:
You have the following equation
[tex](2y+1)^3-24x=-3[/tex] (1)
(a) You first derivative implicitly the equation (1) respect to x:
[tex]\frac{d}{dx}[(2y+1)^3-24x]=\frac{d}{dx}[-3]\\\\3(2y+1)^2(2\frac{dy}{dx})-24=0[/tex]
next, you solve the last result for dy/dx:
[tex]6(2y+1)^2\frac{dy}{dx}=24\\\\\frac{dy}{dx}=\frac{4}{(2y+1)^2}[/tex](2)
(b) The equation for the tangent line is given by:
[tex]y-y_o=m(x-x_o)[/tex] (3)
with yo = -2 and xo = -1
To find the slope m you use the result of the equation (2), because dy/dx evaluated in (-1,-2) is the slope at such point:
m = [tex]\frac{dy}{dx}=\frac{4}{(2(-2)+1)^2}=\frac{4}{9}[/tex]
Hence, by replacing in the equation (3) you obtain:
[tex]y-(-2)=\frac{4}{9}(x-(-1))\\\\y+2=\frac{4}{9}x+\frac{4}{9}\\\\y=\frac{4}{9}x-\frac{14}{9}[/tex]
hence, the equation for the tangent line is y = 4/9 x - 14/9
(c) To find d2y/dx2 you derivative the result obtain in the equation (2):
[tex]\frac{d^2y}{dx^2}=\frac{d}{dx}[4(2y+1)^{-2}]\\\\\frac{d^2y}{dx^2}=-8(2y+1)^{-3}(2\frac{dy}{dx})\\\\\frac{d^2y}{dx^2}=-16(2y+1)^{-3}\frac{dy}{dx}[/tex] (4)
the second derivative for the point (-1,-2) is obtained by replacing y=-2 and dy/dx=m=4/9 in the equation (4):
[tex]\frac{d^2y}{dx^2}=-16(2(-2)+1)^{-3}(\frac{4}{9})=-\frac{64}{243}[/tex]
hence, d2y/dx2 evaluated in (-1,-2) is -64/243
Answer:
(A) The value of [tex]dy/dx=\frac{4}{(2y+1)^2}[/tex].
(B) The equation of the tangent is : [tex]y=(4/9)x-(14/9)[/tex]
(C) The value of [tex]\frac{d^2y}{dx^2}=-64/243[/tex]
(D) The point (16,0) is not on curve so it can not be determined by the given equation.
Step-by-step explanation:
Given information:
The equation [tex](2y+1)^3-24x=-3[/tex]
(A) For the first derivative of the given equation:
[tex]\frac{d}{dx}[(2y+1)^3-24x ]= \frac{d}{dx}(-3)[/tex]
[tex]3(2y+1)^2(dy/dx)-24=0[/tex]
[tex](dy/dx)=\frac{4}{(2y+1)^2}[/tex]
Hence , from the above equation it is shown that the value of
[tex]dy/dx=\frac{4}{(2y+1)^2}[/tex]
(B) The equation of the tangent to the curve is given by:
[tex]y-y_o=m(x-x_0)\\[/tex]
On putting the given values in the above equation
We get:
[tex]m=\frac{4}{(2(-2))+1)^2}[/tex]
[tex]m=4/9[/tex]
Hence, the equation of the tangent can be written as :
[tex]y-(-2)=(4/9)(x-(-1))\\y+2=\frac{4}{9}x+\frac{4}{9}[/tex]
So, the equation of the tangent is :
[tex]y=(4/9)x-(14/9)[/tex]
(C) Now ,
To find [tex]d^2y/dx^2[/tex] for the equation
We have to find double derivative of the equation;
[tex]\frac{d^2y}{dx^2} =\frac{d}{dx}[4(2y+1)^{-2}]\\\frac{d^2y}{dx^2} = -16(2y+1)^{-3}\frac{dy}{dx}[/tex]
On putting the values from the given information in the above equation;
[tex]\frac{d^2y}{dx^2} =-16(2(-2)+1)^{-3}(4/9)[/tex]
[tex]\frac{d^2y}{dx^2}=-64/243[/tex]
(D) For the equation [tex](2y+1)^3-24x=-3[/tex]
First check for the given points (16,0) if it satisfies the given equation or not.
Now on checking for the same the point is not satisfying the given equation hence, we can not find the value of [tex](y-1)'(0)[/tex].
For more information visit:
https://brainly.com/question/5797309?referrer=searchResults
Someone let me know this answer
Solve using the quadratic formula. Leave Irrational answers in radical form.
x2 + x - 20 = 0
The solutions are
and
Answer:
x1 = 4
x2 = -5
Step-by-step explanation:
There is a formula to solve the quadratic equations, which is:
[-b +- √ (b² - 4 ac) ] / (2a)
Quadractic equations have this look:
ax² + bx + c = 0
You need to stablish the numbers:
where a, is the number with x², b the x and c, the independent term.
x² + x - 20 = 0 For this case:
a = 1 ; b = 1 ; c = -20. We replace in the formula
[-1 +- √ (1² - 4 1 (-20)) ] / (2 .1)
(-1 + √81) / 2 = 4
(-1 - √81) / 2 = -5
Answer:
x1= 4 , x2= -5
Step-by-step explanation:
put in calculator MOD 5 3
a= 1 b= 1 c= -20
Luke collected 1,034 baseball cards, 1,289 football cards, and 1,566 hockey cards. Use mental math to find the number of cards in Luke’s collection. Solve this problem any way you choose.
Answer:
3889
Step-by-step explanation:
you add all the numbers to get the answer
Answer:3889
Step-by-step explanation:So what u want to do is add them
1034
1289
1566
3889
Are these correct? If not please help me write the correct answer.
Answer:
Mostly correct
For Q3, you are doing great, you remembered that negative numbers can happen if the exponent is an odd number.
For Q4, I think you were confused with the fractions,
4(i)
[tex](\frac{2}{3} )^{4} = (\frac{2^{4}}{3^{4}}) = (\frac{16}{81}) =0.198[/tex]
4(ii) is also wrong but I'll let you try to fix it yourself following what I given you for 4(i). You should get 1/64
Hope this helps!
Answer:
i = correct
ii = correct
iii = correct
iv = correct
4
i = 16/81 => 0.1975308642
ii= 1/64
Graph a line with a slope of -5 that contains the
point (-3,-4).
y
6
.
.
2
-6
-4
2
4
-6
Answer:
Step-by-step explanation: idk
In a random sample of A women, 65% favored stricter gun control laws. In a random sample of B men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of C
Answer:
We conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.
Step-by-step explanation:
The complete question is : In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws. Test the claim that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control. Use a significance level of 0.05.
Now, we are given that in a random sample of 360 women, 65% favored stricter gun control laws.
And in a random sample of 220 men, 60% favored stricter gun control laws.
Let [tex]p_1[/tex] = proportion of women favoring stricter gun control laws.
[tex]p_2[/tex] = proportion of men favoring stricter gun control laws.
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1> p_2[/tex] {means that the proportion of women favoring stricter gun control is higher than the proportion of men favoring stricter gun control}
The test statistics that would be used here Two-sample z-test for proportions;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of women favoring stricter gun control laws = 65%
[tex]\hat p_2[/tex] = sample proportion of men favoring stricter gun control laws = 60%
[tex]n_1[/tex] = sample of women = 360
[tex]n_2[/tex] = sample of men = 220
So, the test statistics = [tex]\frac{(0.65 -0.60)-(0)}{\sqrt{\frac{0.65(1-0.65)}{360}+\frac{0.60(1-0.60)}{220} } }[/tex]
= 1.205
The value of z test statistics is 1.205.
Now, at 5% significance level, the z table gives critical value of 1.645 for right-tailed test.
Since, our test statistics is less than the critical value of z as 1.205 < 1.645, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the proportion of women favoring stricter gun control is smaller than or equal to the proportion of men favoring stricter gun control.
Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin? Rejection of the claim about______is more serious because the wrong______V dosage could cause more serious adverse reactions than a wrong______dosage. It would be wise to use a_______significance level for testing the claim about the aspirin.
Answer:
Rejection of the claim about aspirin is more serious because the wrong aspirin dosage could cause more serious adverse reactions than a wrong vitamin C dosage. It would be wise to use a greater significance level for testing the claim about the aspirin.
Step-by-step explanation:
The wrong dosage of aspirin will cause more damage than a wrong dosage of vitamin C. Then, if we perform an hypothesis test for each mean, the rejection of the claim about the aspirin content is more serious than the vitamin C content.
In the case of the aspirin, we want to minimize the Type II error (accepting a false null hypothesis). This can be achieved increasing the sample size or/and increasing the significance level. Then, a significative difference between the claimed content and the sample content will be easily detected.
WILL MARK BRAINLIEST
Sherlene bought 3 pounds of coffee and 2 pounds of chocolate for a total of $24. Which equation, written in standard form, correctly represents this scenario and correctly indicates what the
variables represent?
A) The correct equation is 3x + 2y = 24, where x is the price per pound of coffee and y is
the price per pound of chocolate.
B) The correct equation is 5x + y = 24, where x is the combined price per pound of
coffee and chocolate, and y is the total number of pounds purchased.
C) The correct equation is 3x + 2x + y = 24, where x is the combined price per pound of
coffee and chocolate, and y is the total number of pounds purchased.
D) The correct equation is 3x + 2y = 24, where x is the price per pound of chocolate and
y is the price per pound of coffee.
Answer:
AAAAAAAAAAAA answer is A
Step-by-step explanation:
Suppose a large shipment of stereos contained 18% defectives. If a sample of size 306 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 6%
Answer:
99.36% probability that the sample proportion will differ from the population proportion by less than 6%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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 sample proportion p in a sample of size n, we have that the sampling distribution of the sample proportions has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex].
In this question:
[tex]n = 306, p = 0.18, \mu = 0.18, s = \sqrt{\frac{0.18*0.82}{306}} = 0.0220[/tex].
What is the probability that the sample proportion will differ from the population proportion by less than 6%
This is the pvalue of Z when X = 0.18 + 0.06 = 0.24 subtracted by the pvalue of Z when X = 0.18 - 0.06 = 0.12. So
X = 0.24
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.24 - 0.18}{0.022}[/tex]
[tex]Z = 2.73[/tex]
[tex]Z = 2.73[/tex] has a pvalue of 0.9968
X = 0.12
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.12 - 0.18}{0.022}[/tex]
[tex]Z = -2.73[/tex]
[tex]Z = -2.73[/tex] has a pvalue of 0.0032
0.9968 - 0.0032 = 0.9936
99.36% probability that the sample proportion will differ from the population proportion by less than 6%
Point A(3,-2) and point B (-1,6) are endpoints of AB Point C is the midpoint of AB What is the equation of a line perpendicular to that passes through
point c ?
Answer:
y = 0.5x + 1.5
Step-by-step explanation:
I just graphed the points with GeoGebra. Hope this Helps!
What type of probability is used in this scenario a bag has 10 red marbles 7 blue marbles and 12 yellow marbles the probability of drawing a yellow at random is 12/29
Find the value of the trig function indicated
Answer:
Step-by-step explanation:
base x height divided by 2
4x3=12
12 divided by 2 = 6
6x5= 30
16. Terry has a monthly mortgage payment of $979. Her annual property taxes are
$1200, her PMI is $62/month, and her homeowner's insurance is $800 per year. How
much is deposited into Terry's escrow account each month?
Answer:
$228.67
Step-by-step explanation:
Given that:
Terry has a monthly mortgage payment of $979.
Terry's annual taxes are $1200 per year. That implies that his escrow each month require to posses 1/12 of that amount.
i.e 1/12 × 1200 = $100 per month.
For his homeowner's insurance which is $800 per year,
His escrow account each month is = 1/12 × 800 = $66.67
PMI = $62 per month.
Thus: The amount that is deposited into Terry's escrow account each month is the sum total of $100 + $ 66.67 + $62 = $228.67
f f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?
Answer:
We study if the composition of both functions equals the identity ("x"), that is if
[tex]f(g(x))=x[/tex]
Step-by-step explanation:
The composition of the two functions should render 'x" if one is the inverse of the other. That is, we need to find what [tex]f(g(x))[/tex] renders. Notice as well that the same verification could be done with examining [tex]g(f(x))[/tex].
Let's work with [tex]f(g(x))[/tex] :
[tex]f(g(x))=f(\frac{1}{5} x+5)=5\,(\frac{1}{5} x+5)-25= x+25-25=x[/tex]
So we see that the composition of both functions indeed render "x", and that way we have verified that one is the the inverse of the other.
Answer:
B. One-fifth (5 x minus 25) + 5
Step-by-step explanation:
Just got it right on the test.
What’s the correct answer for this question? Select the ones That apply
Answer:
A and C
Step-by-step explanation:
CD and AB
Answer:
CD & AB
Hope this helps!
What is the area of a circle with a radius of 42 in use 3.14 for pi
The right answer is 5538.96 units^2
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer: 5538.96
Step-by-step explanation: 3.14× 42×42
42×42=1764
∴ 3.14×1764= 5538.96
POSSIBLE POINTS: 1
In the US, the average citizen receives an annual dose of 360 mrem of radiation. If eating a banana creates a 0.01 mrem dose, how many bananas
are equivalent to the annual dose of an average citizen?
720 bananas
36.000 bananas
25,000 bananas
180,000 bananas
Answer:
36,000
Step-by-step explanation:
So all we have to do is divide 360 by 0.01. that equals 36,000
Solving for Unknown Angles
Lines x and y are parallel.
Parallel lines x and y are intersected by lines s and t. At the intersection of lines x, t, and s, clockwise from top left, the angles are blank, blank, (6 x + 8) degrees, blank, (7x minus 2) degrees, blank. At the intersection of lines x and y, the angles are 106 degrees, 1, blank, blank. At the intersection of lines y and t, the angles are 2, blank, blank, blank.
Use the diagram to determine the measure of the unknown angle.
m∠1 = (6x + 8)°
m∠1 = 74°
What is the value of x?
What is the measure of ∠2?
(7x - 2)° + m∠2 = 106°
m∠2 =
°
Answer:
x=11
Step-by-step explanation:
x=11 because, 6x+8= 74, so you do 74-8=66 and 66/6= 11. so x=11,
the measure of 2 is 7(11)-2+m=106.
so you add 2 on both sides to cancel it out, and you end up with 7(11)+m=108
now you do 7(11)= 77, and you subtract from both sides and get 31.
therefore, m=31.
hope this helps!
Answer:
x=11
Step-by-step explanation:
From a group of 8 people 5 will each win $1000.How many different winning groups are possible?
Answer:
6720 ways different
Step-by-step explanation:
In this case, we must calculate the different ways using the permutation formula:
nPr = n! / (n - r)!
where n is the total number of people and r would come being the group of person that you want to put together the groups, therefore n = 8 and r = 5
replacing:
8P5 = 8! / (8 - 5)!
8P5 = 6720
That is to say that there are 6720 ways different winning groups are possible
Solve the equation sin sq x = 3cos sq x.
The value of x that satisfies the equation if x lies in the second quadrant is °.
The value of x that satisfies the equation if x lies in the third quadrant is
Answer:
Second quadrant = 120°.
Third quadrant = 210°
Step-by-step explanation:
We are given that:
[tex]sin^2(x) = 3cos^2(x)[/tex]
The following property is known:
[tex]sin^2(x) +cos^2(x)=1\\[/tex]
Combining both expressions:
[tex]sin^2(x) =1-cos^2(x)\\sin^2(x) = 3cos^2(x)\\\\1-cos^2(x) = 3cos^2(x)\\cos^2(x)=\frac{1}{4}\\cos(x)=\pm \frac{1}{2}[/tex]
If x lies in the second quadrant, then cos(x) = -1/2:
[tex]x=cos^{-1}(1/2)\\x=120^o[/tex]
The value of x that satisfies the equation if x lies in the second quadrant is 120°.
If x lies in the third quadrant, then cos(x) = -1/2:
[tex]x=120+90=210^o[/tex]
The value of x that satisfies the equation if x lies in the third quadrant is 210°
Answer:
The value of x that satisfies the equation if x lies in the second quadrant is 120
The value of x that satisfies the equation if x lies in the third quadrant is
240
Step-by-step explanation:
This is correct for Plato/Edmentum users :) Hope I could help !