Answer:
(B)[tex]9 \pi $ units squared[/tex]
Step-by-step explanation:
In circle B, AB is one of the radii; and
AB=6
Central Angle of ABC [tex]=\dfrac{\pi}{2}$ radians[/tex]
Now, Area of a Sector
[tex]\text{Area of a Sector}=\dfrac{\theta}{2\pi} \times \pi r^2 \\=\dfrac{\frac{\pi}{2}}{2\pi} \times \pi \times 6^2\\=\dfrac{\pi}{4\pi} \times \pi \times 6^2\\=\dfrac{36}{4} \times \pi \\= 9 \pi $ units squared[/tex]
Answer:
b
Step-by-step explanation:
Solve.
3^x+1 = 9^ 5x
a. x=3
b. x = 1/3
c. x=9
d. x= 1/9
Answer:
x = 1/9
Step-by-step explanation:
3^ (x+1) = 9 ^ (5x)
Replace 9 with 3^2
3^ (x+1) = 3^2 ^ (5x)
We know that a^b^c = a ^(b*c)
3^ (x+1) = 3^(2 * (5x))
3^ (x+1) = 3^(10x)
The bases are the same so the exponents are the same
x+1 = 10x
Subtract x from each side
x+1-x = 10x-x
1 = 9x
Divide each side by 9
1/9 = 9x/9
1/9 =x
what equation results from completing the square and then factoring? x^2+24x=33
a.) (x+24)^2=57
b.) (x+12)^2=57
c.) (x+12)^2=177
d.) (x+24)^=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
The given equation is x²+24x=33.
We need to factorise the equation using completing the square method.
What is completing the square method?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Now, x²+24x-33=0
Add and subtract (b/2)²=144 to the equation.
x²+24x-33+144-144=0
⇒x²+24x+144-33-144=0
⇒(x+12)²-177=0
⇒(x+12)²=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
To learn more about completing the square method visit:
https://brainly.com/question/26107616.
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What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Since two diameters are intersecting eachother, the angles inside them would be vertical angles so they'll be congruent.
So
m<LYM = m<JYM
Also their arcs would be equal to their angles measures so,
Arc JK = 52°
A hotel rents 220 rooms at a rate of $ 40 per day. For each $ 1 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .
Answer:
The rooms should be rented at $75 per day for a maximum income of $11250 per day.
Step-by-step explanation:
If the daily rental is increased by $ x
then
Rental: R (x )=( 40 + x ) dollars per room-day
Number of rooms rented: N ( x ) = ( 220 − 2 x ) and
Income: I ( x ) = ( 40 + x ) ( 220 − 2 x ) =8800+140x-2x² dollars/day
The maximum will be achieved when the derivative of I ( x ) is zero.
[tex]\frac{dI(x)}{dx} =140-4x=0[/tex]
x=35
so, ($40+$35)=75$per day
I ( x35) =8800+140(35)-2(35)²= 11250
John conducted a taste test on a new brand of French fries. He gave each participant 5 of the new brand of fries and 5 of the old brand of fries and asked them to rate which brand they preferred. The participants rated both brands of fries as equally preferable. Based on this, he recommended to the manufacturer to move ahead with producing this new brand. However, the brand did not sell well. People reported feeling nauseous after they had consumed a whole portion.
Which validity is weak in this example?
a. internal validity
b. external validity
c. statistical validity
d. construct validity
Answer:
b. external validity
Step-by-step explanation:
External Validity is the applicability of the results of an experiment to the real world. Most times, there are threats to the validity of an experiment which could result in little or no effect on the general population. For example, if the method of selection reflects a measure of bias, then this could affect the result. Also if the participants are taking different aspects of the same test, it could also affect its validity as they may not be able to make a correct conclusion. If the sample size is not reflective of the entire population, it could also pose a threat to the validity of the experiment.
John's experiment is weak in its external validity because it cannot be generalized to the entire population of customers. He has to identify the threats to the validity of his experiment and correct them. For example, the sample selection may be biased.
2/5 plus 1/4 plus 7/10
The answer is 1 7/20
2/5 x 4/4 + 7/10 x 2/2 + 1/4 x 5/5
= 8/20 + 14/20 + 5/20
= 27/20
= 1 7/20
Answer:
27/20 or 1 and 7/20
Step-by-step explanation:
All you do is find common factors.
In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.
a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
b. Roughly what proportion of vehicle speeds exceeded 57 mph?
Answer:
(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) Roughly 16% of vehicle speeds exceeded 57 mph.
Step-by-step explanation:
We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.
For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.
Let X = vehicle speed at impact
SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])
Here, [tex]\mu[/tex] = population average speed = 42 mph
[tex]\sigma[/tex] = standard deviation = 15 mph
Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;
68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;
[ [tex]\mu-\sigma , \mu+\sigma[/tex] ] = [42 + 15 , 42 - 15]
= [57 , 27]
So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.
It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.
This means that roughly 16% of vehicle speeds exceeded 57 mph.
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
Please help. I’ll mark you as brainliest if correct!
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
To determine the density of grains, a student uses a 50ml beaker graded by 5ml increments and a scale with 1g absolute uncertainty. The measurement of the volume results in 3 full beakers and 1 beaker filled up to 30ml. Measured mass of a plastic container with all the grains is 185 grams; measured mass of the same container without grains is 65 grams. What is the mass of the grains
Answer:
The mass of the grains = 120 ± 1 g
Step-by-step explanation:
we are given the following:
Total mass of container + grains = 185 grams
Mass of container = 65 grams
Therefore, mass of grains is calculated as follows:
Mass of grains = ( Mass of container + grains) - mass of container
= 185 - 65 = 120 grams.
since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g
Find the value of x from this adjoining figure
Answer:
[tex]x=15^\circ[/tex]
Step-by-step explanation:
Please refer to the attached figure for labeling of given diagram:
We are given the following angles:
[tex]\angle AOC = 3x^\circ\\\angle BOD = 2x^\circ\\\angle EOF = 7x^\circ[/tex]
Angles opposite to each other when they are formed by crossing of two lines are known as vertically opposite angles. And vertically opposite angles are always equal to each other.
Using property of vertically opposite angles:
[tex]\angle EOF = \angle AOB = 7x^\circ[/tex]
Line CD is a straight line, so [tex]\angle COD = 180^\circ[/tex]
Also,
[tex]\angle COD = \angle COA+\angle AOB+\angle BOD = 180^\circ\\\Rightarrow 3x + 7x + 2x=180^\circ\\\Rightarrow 12x =180^\circ\\\Rightarrow x = \dfrac{180}{12}\\\Rightarrow x = 15^\circ[/tex]
Hence, answer is [tex]x = 15^\circ[/tex].
Assume that random guesses are made for seven multiple choice questions on an SAT test, so that there are n=7 trials, each with probability of success (correct) given by p= 0.2. Find the indicated probability for the number of correct answers.
Find the probability that the number x of correct answers is fewer than 4.
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of guesses made for the sat questions.
Since the probability of getting the correct answer to a question is fixed for any number of trials and the outcome is either getting it correctly or not, then it is a binomial distribution. The probability of success, p = 0.2
Probability of failure, q = 1 - p = 1 - 0.2 = 0.8
the probability that the number x of correct answers is fewer than 4 is expressed as
P(x < 4)
From the binomial distribution calculator,
P(x < 4) = 0.97
A consumer affairs investigator records the repair cost for 4 randomly selected TVs. A sample mean of $91.78 and standard deviation of $23.13 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the TVs. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
Critical value at 90% confidence = 1.645
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = $91.78
Standard deviation r = $23.13
Number of samples n = 4
Confidence interval = 90%
Using the z table;
z(α=0.05) = 1.645
Critical value at 90% confidence = 1.645
Substituting the values we have;
$91.78+/-1.645($23.13/√4)
$91.78+/-1.645($11.565)
$91.78+/-$19.024425
$91.78+/-$19.024
= ( $72.756, $110.804)
Therefore, the 90% confidence interval (a,b) = ( $72.756, $110.804)
A company makes candles in the shape of a right cone. The lateral surface of each candle is covered with paper for shipping and each candle also has a plastic circular base. Find the amount of paper needed to cover the lateral surface of each candle. Then find the total amount of paper and plastic needed for the candle. Round to the nearest tenth. Use 3.14 for π.
Answer:
If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.
Step-by-step explanation:
The question is incomplete: no numerical values for the dimensions of the cone are given.
A right cone is defined by the radius r of the base and the height h.
The base area is the area of a circle with radius r:
[tex]A_b=\pi r^2[/tex]
The lateral area is calculated as:
[tex]A_l=\pi \cdot r\cdot l[/tex]
As the values for r and h are not given, we will use an example with r=2 and h=3.
Then, the amount of paper needed is:
[tex]A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2[/tex]
The amount of plastic needed is:
[tex]A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2[/tex]
If theta=3pi/4
Sin theta=?
Cos theta=?
Answer:
For ease of writing, θ [tex]=x[/tex]
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Our angle is [tex]x=\frac{3\pi }{4}[/tex]
To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).
Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.
And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.
For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]
This means that
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
The square of a number is 12 less than 7 times the number.what is the number?
Answer:
n = 3 or n = 4
Step-by-step explanation:
Let the unknown number be n.
Then:
n² = 7n - 12
In standard quadratic form, we have:
n² - 7n + 12 = 0
In factored form, we have:
(n - 3)(n - 4) = 0, and so
n = 3 and n = 4
Can someone help me?
Answer:
Step-by-step explanation:
a)4a-6a d)2x+4y-10x
=-2a. =-8-+4y
b)14-1-10
=3
c)2+8
=10
e)answer is 6 x raised to the power 3
f)7x raised to the power 2-5x-y
Fiad the sample variance and standard deviation.
21, 10, 3, 7, 11
Answer:
SD = 5.987, Var(X) = 35.85
Step-by-step explanation:
Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.
Hope this helps!
Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
sum what is the sum of 199+ -24=
?
Answer:
175
Step-by-step explanation:
+ × - = -
thus 199+(-24)
199-24
175
Answer: 199 + -24 = 175
Step-by-step explanation: 199 is a positive number and -24 is a negative number. If the positive number is bigger than the negative number you subtract. So forget that the - sign is there and subtract it.
Please answer this correctly
Answer:
1.5 meters
Step-by-step explanation:
The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:
3.75=h*(1.7+3.3)/2
3.75=h*2.5
h=3.75/2.5=1.5
Hope this helps!
Answer:
Step-by-step explanation:
use the formula and rearrange for h.
1/2 x h x (a + b) = A
1/2 x (1.7 + 3.3) x h = 3.75
2.5 x h = 3.75
h = 1.5
hope this helps! :)
Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
find the equation ( in form of y = mx+c) of line which has a gradient of -3 and a y intercept of -2
Answer:
The answer is y = -3x - 2.
Step-by-step explanation:
Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :
[tex]y = mx + c[/tex]
[tex]let \: m = - 3 \\ let \: c = - 2[/tex]
[tex]y = - 3x - 2[/tex]
for each sequence find the first 4 terms and the 10th term n+5 , , , , ...,
Answer:
10,15.20.25
Step-by-step explanation:
+5 in each number
Im stuck who can help me
Answer:
Option D
Step-by-step explanation:
This question is based on the " Partition Postulate. " You might be familiar with it, it states that a whole is composed of several parts. In this case you could say that this " whole " is ∠ ABC, and the " parts " are ∠1 and ∠2. By this Theorem you could also state the following;
[tex]m< ABC = m< 1 + m< 2,\\\\Substitute,\\110 = 4x + ( 5x + 10 ),\\110 = 4x + 5x + 10,\\4x + 5x + 10 = 110 - Option D\\\\Solution - Option D[/tex]
Hope that helps!
What is the solution? X/12+3< or = 7
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
Donte simplified the expression below. 4(1+3i) - (8-5i)
4 + 3i - 8 + 5i
-4 + 8i
What mistake did donte make?
Answer:
Donde didn't multiply 4(1+3i)
Answer: it’s A he did not apply distributive property yo
Step-by-step explanation:
Write the product in standard form.
(2 - 3i)(2 + i)
Answer:
Brainelist?
Step-by-step explanation:
7-4i
just use a online calculator
Answer:
7-4i
Step-by-step explanation:
(2 - 3i)(2 + i)
FOIL
first 2*2 = 4
Outer: 2i
Inner: -3i*2 = -6i
Last: -3i*i = -3i^2 = -3(-1) = 3
Add them together
4+2i-6i+3
7-4i
Express the following in usual form
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300