Tunde and Martha are married and share their income. Tunde earns $1,500 per year less than Martha. If their annual income is $47,500, how much does each earn?

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

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°.

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

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.

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.

Answer:

Option (B)

Step-by-step explanation:

If the probabilities of two events A and B are P(A) and P(B) then the conditional probability of an event that can be derived by the formula,

P(B | A) = [tex]\frac{P(A\cap B)}{P(A)}[/tex]

P(A ∩ B) = P(B|A) × P(A)

P(A ∩ B) = (0.8) × (0.4)

            = 0.32

Therefore, Option (B) will be the correct option.

Answer:

Option B is correct.

Step-by-step explanation:

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

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

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

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.

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]

Answer:

I tried the question and I got. a/4-b/2-5/2

Step-by-step explanation:

I hope this helps

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

Answer:

6 bags

Step-by-step explanation:

3/4 = .75

4.5/.75 = 6 =

6 BAGS

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.

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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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

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

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]

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.

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 :)

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

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

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]

Answer:

Step-by-step explanation: i really would day if 80 % was college students it would be more then enogh

P-value and interpret its meaning as a conditional probability is 206

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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°

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

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

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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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.

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

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%.

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.

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.

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