Answer:
The ladder will reach 4.6 ft up the tree.
Step-by-step explanation:
When we draw out our triangle, we should see that we are given the horizontal leg and are trying to find the vertical leg. We use tan∅ to help solve:
tan53° = x/3.5
3.5tan53° = x
x = 4.64466
Heather has divided $6700 between two investments, one paying 8%, the other paying 5%. If the return on her investment is $428, how much does she have in each investment?
Answer:
First investment = $3100
Other investment = $3600
Step-by-step explanation:
Total investment made by Henry = $6700
Let one investment be x,
Then other investment = total investment - first investment = 6700 - x
A) For 8% interest, investment = x
dollar value of 8% investment = 8/100*x= 8x/100
A) For 5% interest, investment = 6700- x
dollar value of 8% investment = 5/100*(6700- x)= 5(6700- x)/100
Total return on both the investment = 8x/100 + 5(6700- x)/100
= (8x +33500 - 5x)/100 = (3x+33500)/100
Given that total return = 428
Therefore,
(3x+33500)/100 = 428
=> 3x+33500 = 428*100 = 42800
=> 3x = 42800- 33500 = 9300
=> x = 9300/3 = 3100
Thus, first investment = x = $3100
other investment = $(6700 - 3100) = $3600
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers 3 or odd are 1, 3, 5, and 7.
4 numbers out of 8.
4/8 = 1/2
P(3 or odd) = 1/2
Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce.
Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?
Answer:
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation s, the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{s}[/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.
In this question:
[tex]X = 17.79, \mu = 17, s = 0.08[/tex]
How many standard deviations is the sample mean from the mean of the distribution of sample?
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{17.79 - 17}{0.08}[/tex]
[tex]Z = 9.875[/tex]
The sample mean is 9.875 standard deviations from the mean of the distribution of sample
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the _______. a.remainder b.divisor c.dividend d.quotient
Answer:
The answer is not "REMAINDER" it's "Quotient"
Step-by-step explanation:
Cancelling identical factors in the numerator and the denominator will give the quotient.
When dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that when dividing polynomials using factorization, cancelling identical factors in the denominator and the numerator will give the remainder.
A quotient in mathematics is the amount created by dividing two numbers. The term "quotient" is used frequently in mathematics and is also known as the integer portion of a division, a fraction, or a ratio.
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The standard error of the estimate measures the scatter or dispersion of the observed values around a __________________________________________________________
Answer:
True mean/population mean
Step-by-step explanation:
The standard error in this case gives an estimate on how far the values observed during the course of the experiment ate likely to be from the true mean/population mean.
The perimeter of the rectangle shown below is 24 feet. What's the length of side x?
8 ft.
4 ft
811
A. 3 feet
B. 4 feet
C. 14 feet
D. 6 feet
Answer:
b)4feet
Step-by-step explanation:
In a rectangle two sides are equal.
Perimeter is the distance around the rectangle thus.
length=24-8-4-8
length=4
The number of people who voted in the most recent local election was up from the last local election by about 24%. Therefore the number of people who voted in this election was how many times the number who voted in the last election
Answer:
The number of people who voted in this election was 1.24 times the number who voted in the last election
Step-by-step explanation:
The multiplier for a increase of a% is 1 + a/100.
The multiplier for a decrease of b% is 1 - b/100.
In this question:
Up by about 24%, so we want the multiplier for a increase of 24%.
So
1 + (24/100) = 1 + 0.24 = 1.24
The number of people who voted in this election was 1.24 times the number who voted in the last election
Q.04: (11 points) Given the polar curve r = e θ , where 0 ≤ θ ≤ 2π. Find points on the curve in the form (r, θ) where there is a horizontal or vertical tangent line. g
I suppose the curve is [tex]r(\theta)=e^\theta[/tex].
Tangent lines to the curve have slope [tex]\frac{dy}{dx}[/tex]; use the chain rule to get this in polar coordinates.
[tex]\dfrac{dy}{dx}=\dfrac{dy}{d\theta}\dfrac{d\theta}{dx}=\dfrac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]
We have
[tex]y(\theta)=r(\theta)\sin\theta\implies\dfrac{dy}{d\theta}=\dfrac{dr}{d\theta}\sin\theta+r(\theta)\cos\theta[/tex]
[tex]x(\theta)=r(\theta)\cos\theta\implies\dfrac{dx}{d\theta}=\dfrac{dr}{d\theta}\cos\theta-r(\theta)\sin\theta[/tex]
[tex]r(\theta)=e^\theta\implies\dfrac{dr}{d\theta}=e^\theta[/tex]
[tex]\implies\dfrac{dy}{dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}[/tex]
The tangent line is horizontal when the slope is 0, which happens wherever the numerator vanishes:
[tex]\sin\theta+\cos\theta=0\implies\sin\theta=-\cos\theta\implies\tan\theta=-1[/tex]
[tex]\implies\theta=\boxed{-\dfrac\pi4+n\pi}[/tex]
(where [tex]n[/tex] is any integer)
The tangent line is vertical when the slope is infinite or undefined, which happens when the denominator is 0:
[tex]\cos\theta-\sin\theta=0\implies\sin\theta=\cos\theta\implies\tan\theta=1[/tex]
[tex]\implies\theta=\boxed{\dfrac\pi4+n\pi}[/tex]
. Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito. (a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points) (b) 20% of Chipotle burritos weigh more than what weig
Complete Question
Suppose the weight of Chipotle burritos follows a normal distribution with mean of 450 grams, and variance of 100 grams2 . Define a random variable to be the weight of a randomly chosen burrito.
(a) What is the probability that a Chipotle burrito weighs less than 445 grams? (3 points)
(b) 20% of Chipotle burritos weigh more than what weight
Answer:
a
[tex]P(X < 445 )= 0.3085[/tex]
b
[tex]k = 458.42[/tex]
Step-by-step explanation:
From question we are told that
The population mean is [tex]\mu = 450 \ g[/tex]
The variance is [tex]var = 100 \ g^2[/tex]
The consider weight is [tex]x = 445 \ g[/tex]
The standard deviation is mathematically represented as
[tex]\sigma = \sqrt{var}[/tex]
substituting values
[tex]\sigma = \sqrt{ 100}[/tex]
[tex]\sigma = 10[/tex]
Given that weight of Chipotle burritos follows a normal distribution the the probability that a Chipotle burrito weighs less than x grams is mathematically represented as
[tex]P(X < x ) = P ( \frac{X - \mu }{\sigma } < \frac{x - \mu }{\sigma } )[/tex]
Where [tex]\frac{X - \mu }{\sigma }[/tex] is equal to z (the standardized values of the random number X )
So
[tex]P(X < x ) = P (Z < \frac{x - \mu }{\sigma } )[/tex]
substituting values
[tex]P(X < 445 ) = P (Z < \frac{445 - 450 }{10} )[/tex]
[tex]P(X < 445 ) = P (Z <-0.5 )[/tex]
Now from the normal distribution table the value for [tex]P (Z <-0.5 )[/tex] is
[tex]P(X < 445 ) = P (Z <-0.5 ) = 0.3085[/tex]
=> [tex]P(X < 445 )= 0.3085[/tex]
Let the probability of the Chipotle burritos weighting more that k be 20% so
[tex]P(X > k ) = P ( \frac{X - \mu }{\sigma } > \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex]
=> [tex]P (Z> \frac{k - 450}{10 } ) = 0.2[/tex]
From the normal distribution table the value of z for [tex]P (Z> \frac{k - \mu }{\sigma } ) = 0.2[/tex] is
[tex]z = 0.8416[/tex]
=> [tex]\frac{k - 450}{10 } = 0.8416[/tex]
=> [tex]k = 458.42[/tex]
Find the midpoint of AC
Answer:
so the coordinates of mid-point of AC are (a/2,a/2)
Step-by-step explanation:
as the mid-point of AC is the same as the mid-point of BD
SO we will find the mid-point of BD
by using mid-point formula
[tex]M(x,y)=(\frac{x1+x2}{2} ,\frac{y1+y2}{2})\\M(x.y)=(\frac{0+a}{2},\frac{a+0}{2})\\ M(x,y)=(\frac{a}{2},\frac{a}{2})[/tex]
i hope this will help you :)
n a nature conservatory, the ratio of butterflies to total number of flying insects is 36 to 100. There are 450 total flying insects. (a) Create a table for how many butterflies there are for 1, 50, and 100 flying insects. Show your work. (b) How many butterflies are in the conservatory? Show your work.
Answer:
There are 172 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 172
Thus, there are 172 butterflies in the conservatory.
Answer:
There are 162 butterflies in the conservatory.
Step-by-step explanation:
Given
ratio of butterflies to total number of flying insects is 36 to 100
total number of butterflies / total number of flying insects = 36 / 100 = 9/25
Create a table for how many butterflies there are for 1, 50, and 100 flying insects.
Let the number of butter flies be x
when total no. of insects = 1
total number of butterflies / total number of flying insects =9/25=x/1
=> 9/25= x/1
=> x = 9/25
____________________________________
when total no. of insects = 50
total number of butterflies / total number of flying insects =9/25=x/50
=> 9/25= x/50
=> x = 9/25 * 50 = 18
_______________________________________
when total no. of insects = 100
total number of butterflies / total number of flying insects =9/25=x/100
=> 9/25= x/100
=> x = 9/25 * 100= 36
Thus, table is
butterfly total no of insects
9/25 1
50 18
100 36
______________________________________________
Given there There are 450 total flying insects in the conservatory
again using the same ratio and taking no. of butterflies as x
total number of butterflies / total number of flying insects =9/25=x/450
9/25=x/450
=>x = 9/25 * 450 = 9*18 = 162
Thus, there are 162 butterflies in the conservatory.
Look at picture please
Answer:
BCD
Step-by-step explanation:
Is that hegarty maths? Just curious. Anyway acute means a angle below 90
Answer:
∠C
Step-by-step explanation:
Angle A is incorrect because it is 90° and acute angles are LESS than 90°.
Angle B is incorrect because it is more than 90° which makes it obtuse.
Angle D is incorrect because it is more than 90° which makes it obtuse.
Angle C is correct because it is less than 90°.
After adding up all your expenses for the month you spent $465.36. your total budget for the month is$529.What percentage are under budget?(Round to the nearest whole percentage).Do not include symbol
Answer:
12%.
Step-by-step explanation:
It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.
Total budget = $529
Total expenditure = $465.36
Under budget = $529 - $465.36 = $63.64
We need to find the percentage of under budget.
[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]
[tex]\%=\dfrac{63.64}{529}\times 100[/tex]
[tex]\%=0.12030\times 100[/tex]
[tex]\%=12.030\%[/tex]
[tex]\%\approx 12\%[/tex]
Therefore, the required percentage is 12%.
In Vancouver, British Columbia, the probability of rain during a winter day is 0.42, for a spring day is 0.23, for a summer day is 0.16, and for a fall day is 0.51. Each of these seasons lasts one quarter of the year. If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
Answer:
31.82% probability that this day would be a winter day
Step-by-step explanation:
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: Rain
Event B: Winter day
Probability of rain:
0.42 of 0.25(winter), 0.23 of 0.25(spring), 0.16 of 0.25(summer) or 0.51 of 0.25(fall).
So
[tex]P(A) = 0.42*0.25 + 0.23*0.25 + 0.16*0.25 + 0.51*0.25 = 0.33[/tex]
Intersection:
Rain on a winter day, which is 0.42 of 0.25. So
[tex]P(A \cap B) = 0.42*0.25 = 0.105[/tex]
If you were told that on a particular day it was raining in Vancouver, what would be the probability that this day would be a winter day?
[tex]P(B|A) = \frac{0.105}{0.33} = 0.3182[/tex]
31.82% probability that this day would be a winter day
A negative value of Z indicates that
A. the number of standard deviations of an observation is to the right of the mean
B. the number of standard deviations of an observation is to the left of the mean
C. a mistake has been made in computations, since Z cannot be negative
D. the data has a negative mean
Answer:
We need to remember that the Z value comes froma normal standard distribution given by:
[tex] Z\sim N(\mu=0,\sigma=1)[/tex]
So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then value of Z indicates that :
B. the number of standard deviations of an observation is to the left of the mean
Step-by-step explanation:
We need to remember that the Z value comes froma normal standard distribution given by:
[tex] Z\sim N(\mu=0,\sigma=1)[/tex]
And the z score formula is given by:
[tex]z=\frac{X -\mu}{\sigma}[/tex]
So then the mean is 0 and all the values in the left are negative. So then if we want to analyze that if A is negative then value of Z indicates that :
B. the number of standard deviations of an observation is to the left of the mean
B. the number of standard deviations of an observation is to the left of the mean
A [tex]Z[/tex] score is a numerical measurement that describes a value's relationship to the mean of a group of values. The value of the [tex]Z[/tex] score tells you how many standard deviations you are away from the mean. A negative [tex]Z[/tex] score reveals the raw score is below the mean average. Also, a negative value of Z indicates that B. the number of standard deviations of an observation is to the left of the mean
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The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ = 26.50 mpg and a standard deviation of σ = 3.25 mpg.
Required:
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
Answer:
a) 0.65 mpg
b) Between 24.99 mpg and 28.01 mpg.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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, which is also called standard error, [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.
In this question, we have that:
[tex]\mu = 26.50, \sigma = 3.25, n = 25, s = \frac{3.25}{\sqrt{25}} = 0.65[/tex]
a. What is the standard error of X and the mean from a random sample of 25 fill-ups by one driver?
s = 0.65 mpg
b. Within what interval would you expect the sample mean to fall, with 98 percent probability?
From the: 50 - (98/2) = 1st percentile
To the: 50 + (98/2) = 99th percentile
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = -2.327*0.65[/tex]
[tex]X = 24.99[/tex]
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 26.50}{0.65}[/tex]
[tex]X - 26.50 = 2.327*0.65[/tex]
[tex]X = 28.01[/tex]
Between 24.99 mpg and 28.01 mpg.
Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability 0.23 of being funded. Since the grants are submitted to two different federal agencies, assume the outcomes for each grant are independent. Give your answer to four decimal places. a. What is the probability that both professors get their grants funded
Answer:
14.72% probability that both professors get their grants funded
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both happening is:
[tex]P(A \cap B) = P(A)*P(B)[/tex]
In this question:
Event A: Professor Jane is funded
Event B: Professor Joe is funded.
Professor Jane has a probability of 0.64 of being funded.
This means that [tex]P(A) = 0.64[/tex]
Professor Joe has probability 0.23 of being funded.
This means that [tex]P(B) = 0.23[/tex]
What is the probability that both professors get their grants funded
[tex]P(A \cap B) = P(A)*P(B) = 0.64*0.23 = 0.1472[/tex]
14.72% probability that both professors get their grants funded
Add the expressions four -2/3 B +1/4 a and 1/2 a+1/6b-7. What is the simplified some?
Answer:
I tried the question and I got. a/4-b/2-5/2
Step-by-step explanation:
I hope this helps
798/8×41 rounded to one significant figure
Answer:
2.5
Step-by-step explanation:
the other persons answer is wrong
The number after rounding to the one significant figure is 4000.
What is significant figure?
The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation
What is round off?Rounding off means a number is made simpler by keeping its value intact but closer to the next number
According to the given question we have an expression.
[tex]\frac{798}{8} (41)[/tex]
When we evaluate this expression we get
[tex]\frac{798}{8} (41)[/tex]
[tex]=99.75(41)[/tex]
[tex]= 4089.75[/tex]
Here, the first significant figure is 4 and the second one is 0 which is less than 5.
Hence, the number after rounding to the one significant figure is 4000.
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Select the action you would use to solve 4x = 16. Then select the property
that justifies that action.
A. Action: Divide both sides by 4.
B. Property: Multiplication property of equality.
C. Action: Multiply both sides by 4.
D. Property: Division property of equality.
E. Property: Addition property of equality.
O F. Action: Add 4 to both sides.
Answer:
A.
Step-by-step explanation:
Since you are trying to find x, you have to divide both sides by 4 to isolate x and get your answer.
Solve the system by the method of elimination.
Answer:
no solution
Step-by-step explanation:
x-y = 2
-4x +4y = 4
Multiply the first equation by 4
4(x-y) = 2*4
4x -4y = 8
Add this to the second equation
4x -4y = 8
-4x +4y = 4
------------------------
0x + 0y = 12
0 =12 is never true so there is no solution
Answer:
no solutions
Step-by-step explanation:
work is shown
Please answer this for me!!! 25 points to whoever answers this!!!!!!
Sean, Angelina, and Sharon went to an office supply store. Sean bought 7 pencils, 8 markers, and 7 erasers. His total was $22.00. Angelina spent $19.50 buying 4 pencils, 8 markers, and 6 erasers. Sharon bought 6 pencils, 4 markers, and 7 erasers for $17.75. What is the cost of each item?
Answer:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
Step-by-step explanation:
Let P denote pencils, M denote markers and E denote erasers. The quantities of each item and total amounts spent by each person can be modeled into the following linear system:
[tex]7P+8M+7E=22\\4P+8M+6E=19.5\\6P+4M+7E=17.75[/tex]
Solving the linear system:
[tex]7P-4P+8M-8M+7E-6E=22-19.5\\3P+E=2.5\\E=2.5-3P \\\\7P+8M+7E-2*(6P+4M+7E)=22-2*17.75\\-5P-7E=-13.5\\-5P*-7*(2.5-3P)=-13.5\\16P=-13.5+17.5\\P=0.25\\E=2.5-0.25*3\\E=1.75\\7P+8M+7E =22\\7*0.25+8M+7*1.75 =22\\8M=8\\M=1[/tex]
The price of each item is:
Pencil = $0.25
Marker = $1.00
Eraser = $1.75
The time it took for a man to walk from his house to the park and back was 2 hours. The distance from his house to the park is 7 miles. The rate at which he walked to the park was twice the rate at which he walked back. What is the man's rate (in mph) walking back to his house?
Answer:
5.25 mph
Step-by-step explanation:
Let r represent the rate at which the man walked back from the park. Then 2r is the rate at which he walked to the park. His total travel time is ...
time = distance/speed
total time = time to the park + time from the park
2 = 7/(2r) +7/r
2 = (7 +14)/(2r) . . . combine terms
r = 21/(2·2) = 5.25 . . . miles per hour
The man's rate walking back from the park is 5.25 miles per hour.
PLEASE HELP ME FOR BRAINLIEST Reduce to simplest form. 6/3+(-1/6)
Answer: 1 5/6, or 11/6, or 1.83333333
Step-by-step explanation:
[tex]\frac{6}{3} + -\frac{1}{6}[/tex]
6/3 is 2.
Thus, the answer is 2 - 1/6 or 1 5/6
Answer:
11/6
Step-by-step explanation:
First, we need to find a common denominator for the 2 fractions.
A common denominator for 3 and 6 is 6.
Let’s get the fraction 6/3 to a denominator of 6.
Multiply by 2/2
6/3 * 2/2
(6*2) / (3*2)
12/6
Now the fractions have common denominators and can be added.
12/6 + (-1/6)
When adding negative fractions, you can simply subtract.
12/6 - 1/6
Subtract across the numerator and leave the denominator as is
11/6
This fraction can be written as: 2 1/6, 11/6, or 1.83333
Help me please I dont understand
Answer:
42°
Step-by-step explanation:
This is right triangle and sum of 2 angles is 90°:
y+48°=90°
so y= 90°- 48°= 42°
Convert 100 kilometers to meters.
Answer:
100,000 meters
Step-by-step explanation:
There are 1000 meters in a kilometer so there are 100,000 meters in 100 kilometers.
Answer:
it is 100000 kilometers
Step-by-step explanation:
use the metric system and you get 10000 kilometers.
The area of a square is increasing at the constant rate of 16sq.ft./min. When the perimeter of the square is 36ft, how fast is the perimeter of the square increasing?
Answer:
The perimeter of square is increasing by 3.76ft/min and then by 3.4 ft/min.
Step-by-step explanation:
Given that area of square is increasing at a rate of 16 sq ft/min.
Given that final perimeter is 36ft
Perimeter of a square = 4 [tex]\times[/tex] side = 36
So, side, a' = 9 ft
We know that area of a square is given by the formula:
[tex]A = side^2 = a^2[/tex] (If we let side = a units)
Change in area =
[tex]a'^2 - a^2\\\Rightarrow 9^2 - a^2 = 16\\\Rightarrow 81 - 16 = a^2\\\Rightarrow a = 8.06\ ft[/tex]
So, side got changed from 8.06ft to 9 ft.
So, perimeter when side was 8.06 ft:
[tex]4 \times 8.06 = 32.24\ ft[/tex]
Hence, increase in the perimeter when perimeter is 36 ft is = 36 - 32.24 = 3.76 ft
For finding Next increase:
area gets changed from 81 sq ft to 81+16 = 97 sq ft
So, new side = [tex]\sqrt{97}[/tex] ft = 9.85 ft
Next increase in perimeter = 4 (New side - Old side)
= 4 (9.85 - 9)
= 3.4 ft/min
Find all solutions of the equation in the interval , 02π. =4cosx+−sin2x4 Write your answer in radians in terms of π. If there is more than one solution, separate them with commas.
Answer:
The answer is "2nπ".
Step-by-step explanation:
Given:
[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]
We know:
[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]
put the value of [tex]\sin^2 x[/tex] value in the above equation:
[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]
Let [tex]\cos x= A[/tex]
[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]
[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]
[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]
The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]
[tex]\boxed{\bold{x=2 n \pi}}[/tex]
The function graphed is reflected across the x-axis to create a new function. Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the same. The domain stays the same, but the range changes. The range stays the same, but the domain changes.
Answer:
Domain stays the same while the range changes
Step-by-step explanation:
While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.
=> x- coordinate = Domain
=> y-coordinate = Range
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
What is the domain and range of a function?Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.
When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.
The Domain represent as x-coordinate and the range as y-coordinate
The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.
Hence, option C is correct.
Learn more about appropriate domain here:
https://brainly.com/question/20073127
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In a basketball shooting competition there are ten balls from 1-10. The number of points earned is based on the number on the ball (I.e shoots a 7 gets 7 points), if a person misses 2 shots what number is not possible
52
44
41
38
35
The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part