Jeff bicycles 126 miles at the rate of r mph. The same trip would have taken 2 hours longer if he had decreased his speed by 4 mph. Find r. His original speed was r = _____________ mph.

Answer:

[tex]\boxed{x = 4}[/tex]

Step-by-step explanation:

If ΔABC ~ ΔDEF

Then their sides must be proportional such that:

=> [tex]\frac{x}{3} = \frac{8}{6}[/tex]

Cross Multiplying

=> x * 6 = 8*3

=> 6x = 24

Dividing both sides by 6

=> x = 4

Answer:

4

Step-by-step explanation:

ΔABC ~ ΔDEF

AB/DE = BC/EF

x/3 = 8/6

Cross multiply.

6 × x = 3 × 8

6x = 24

Divide both sides by 6.

(6x)/6 = 24/6

x = 4

Answer:

[tex]\overrightarrow{AB}=\frac{-9}{-4}[/tex]

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Step-by-step explanation:

A vector quantity is represented by [tex](\frac{y}{x})[/tex]

where y = y-coordinate and x = x-coordinate

Since vector AB represents a vector in 3rd quadrant,

It starts from point A and ends at B,

Therefore, coordinates of B are (-9, -4)

[tex]\overrightarrow{AB}[/tex] = [tex](\frac{-9}{-4})[/tex]

Similarly vector CD starts with C and ends at D in the 2nd quadrant,

Therefore coordinates of D will be (-5, 4)

[tex]\overrightarrow{CD}=\frac{-5}{4}[/tex]

Answer:

Step-by-step explanation:

No, it is not an even function.  The graph is not symmetric about the y-axis.

Answer:

40 /9 or also can be written as 4 4/9

Step-by-step explanation:

hope this helps

Answer:

120

Step-by-step explanation:

As we can see that if we divide 120 by the 24, the remainder would be zero and the quotient be 5

As if we multiply 24 with the 5 it gives 120

And, the 4 is not a digit as it smaller than 24 so we have to carry the amount

Therefore if we insert 120 and divisible by 24 than it gives quotient 5 and the remainder is zero as it is completely divisible

Answer:

m^4+(1/m^4)= 123.4641 or 118.6

Step-by-step explanation:

m-(1/m)=3

m² - 1= 3m

m² -3m -1= 0

m = (3-√13)/2 = -0.3

Or

m =( 3+√13)/2= 3.3

m^4+(1/m^4) for m = -0.3

= (-0.3)^4 + (1/(0.3)^4)

= 0.0081 + 123.456

= 123.4641

m^4+(1/m^4) for m = 3.3

= (3.3)^4 + (1/(3.3)^4)

= 118.5921 + 0.008432

= 118.6

Answer:

16x^2 + 8x.

Step-by-step explanation:

To find the area of the walkway, you need to do the area of the whole thing minus the area of the pool.

The area of the whole thing is (8x - 3)(2x + 7) = 16x^2 - 6x + 56x - 21 = 16x^2 + 50x - 21.

The area of the pool is (8x - 3 - x - x)(2x + 7 - x - x) = (6x - 3)(7) = 42x - 21.

So, the area of the walkway is 16x^2 + 50x - 21 - (42x - 21) = 16x^2 + 50x - 21 - 42x + 21 = 16x^2 + 8x.

If you want, you can factor that and make it 8x(2x + 1).

Hope this helps!

Answer:

56% shaded

Step-by-step explanation:

if there are 100 boxes, then every box it 1%

5 rows (50%) + 6 extra boxes (6%) = 56%

Answer:

A) [tex]a_{1}[/tex] = 1, [tex]a_{2}[/tex] = 4

B) [tex]a_{n}[/tex] = 2[tex]a_{n-1}[/tex] + 2

C)    [tex]a_{n} = 2^{n-1} + 2^n -2\\a_{n} = 2^n + 2^{n-1} -2[/tex]

Step-by-step explanation:

For n ≥ 1 ,

S is a set containing 2^n distinct real numbers

an = no of comparisons to be made between pairs of elements of s

A)

[tex]a_{1}[/tex] = no of comparisons in set (s)

that contains 2 elements = 1

[tex]a_{2}[/tex] = no of comparisons in set (s) containing 4 = 4

B)  an = 2a[tex]_{n-1}[/tex] + 2

C) using the recurrence relation

a[tex]_{n}[/tex] = 2a[tex]_{n-1}[/tex] + 2

substitute the following values  2,3,4  .......... for n

a[tex]_{2}[/tex] = 2a[tex]_{1}[/tex] + 2

a[tex]_{3}[/tex] = 2a[tex]_{2}[/tex] + 2 = [tex]2^{2} a_{1} + 2^{2} + 2[/tex]

a[tex]_{4}[/tex] = [tex]2a_{3} + 2 = 2(2^{2}a + 2^{2} + 2 ) + 2[/tex]

    = [tex]2^{n-1} a_{1} + \frac{2(2^{n-1}-1) }{2-1}[/tex]   ---------------- (x)

since  2^1 + 2^2 + 2^3 + ...... + 2^n-1 =  [tex]\frac{2(2^{n-1 }-1) }{2-1}[/tex]

applying the sum formula for G.P

[tex]\frac{a(r^n -1)}{r-1}[/tex]

Note ; a = 2, r =2 , n = n-1

a1 = 1

so equation x becomes

[tex]a_{n} = 2^{n-1} + 2^n - 2\\a_{n} = 2^n + 2^{n-1} - 2[/tex]

Answer:

1) 2/9

2)3/9

Step-by-step explanation:

sorry,thats what i know so far

Answer:

Step-by-step explanation:

a) From the information given, we can state the hypothesis as follows:

For null hypothesis,

p = 0.9

Or

p ≤ 0.9

For alternative hypothesis,

p > 0.9

Because of the greater than inequality symbol in the alternative hypothesis, it means that it is a right tailed test.

b) Since z = 2.31, we would determine the p value by looking at the probability corresponding to the area above the z score from the normal distribution table. Thus

P value = 1 - 0.9896 = 0.0104

Using a significance level of alpha equals 0.10, since alpha, 0.10 is > p value, 0.0104, then we would reject the null hypothesis.

===================================================

Explanation:

Let's say the lawn is 120 square feet. I picked 120 as it is the LCM (lowest common multiple) of 60 and 40.

Since Wilma can mow the lawn in 60 minutes, her rate is 120/60 = 2 sq ft per minute. In other words, each minute means she gets 2 more square feet mowed. Rocky can do the full job on his own in 40 minutes, so his rate is 120/40 = 3 sq ft per minute.

Their combined rate, if they worked together (without slowing each other down), would be the sum of the two rates. So we get 2+3 = 5 sq ft per minute as the combined rate. The total time it would take for this 120 sq ft lawn is 120/5 = 24 minutes.

--------------------------

Another approach

Wilma takes 60 minutes to do the full job, so her rate is 1/60 of a lawn per minute. Rocky's rate is 1/40 of a lawn per minute. Their combined rate is

1/60 + 1/40 = 2/120 + 3/120 = 5/120 = 1/24 of a lawn per minute

x = number of minutes

(combined rate)*(time) = number of jobs done

(1/24)*x = 1

x = 1*24

x = 24 is the time it takes if they worked together without getting in each other's way.

Effectively, we are solving the equation

1/A + 1/B = 1/C

with

A = time it takes Wilma to do the job on her own

B = time it takes Rocky to do the job on his own

C = time it takes the two working together to get the job done

The equation above is equivalent to C*(1/A + 1/B) = 1 or (1/A + 1/B)*C = 1.

So basically you find the value of 1/A + 1/B, then find the reciprocal of this to get the value of C.

Together they can mow the lawn in 24 minutes.

Time and efficiency are inversely proportional to each other.

Time and work are directly proportional to each other.

Given, Wilma can mow a lawn in 60 minutes. Rocky can mow the same lawn in 40 minutes.

Assuming total work to be 120 as it is the LCM of 40 and 60.

So, The efficiency of Wilma is (120/60) = 2 and the efficiency of Rocky is

(120/40) = 3.

Now together their efficiency is (2 + 3) = 5.

∴ Together they can complete the work in (120/5) = 24 minutes.

learn more about time and work here :

https://brainly.com/question/3854047

#SPJ2

Answer:

A

Step-by-step explanation:

9-2x≤3x+24

-15≤5x

-3≤x

so it's:

[-3,∞)

Hey there! :)

Answer:

To graph y = -3x - 2, we can start by solving for some points. Plug in x values for x in the equation to solve for the y value:

X                   Y

-2                  4

-1                    1

0                   -2

1                     -5

2                    -8

Use these points to graph the line (Graphed below)

Answer:

Step-by-step explanation:

672532 to nearest thousand = 673000

hope this helps

plz mark as brainliest!!!!!!!!!

Find the number in the thousand place 2 and look one place to the right for the rounding digit 5.

Round up if this number is greater than or equal to 5 and round down if it is less than 5.

So, 673000 is your answer.

Answer:

Step-by-step explanation:

Looking at the Venn diagram,

The total number of students surveyed is 7 + 5 + 8 + 6 + 2 + 4 + 3 + 6 = 41

The number of children that studies none of the subjects is 6

The number of children that study only biology is 7

The number of children that study only physics is 5

The number of children that study only physics and biology is 2

Therefore, the number of students that do not study chemistry is 6 + 7 + 2 + 5 = 20

Probability = number of favorable outcomes/total number of outcomes

Therefore, the probability that a child chosen at random does not study chemistry is 20/41 = 0.49

Answer:

P(X < 80) = 0.89435.

Step-by-step explanation:

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.

In this question, we have that:

[tex]\mu = 60, \sigma = 16[/tex]

P(X < 80)

This is the pvalue of Z when X = 80. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{80 - 60}{16}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.89435.

So

P(X < 80) = 0.89435.

Answer:

option 3 is the answer.

Answer:

x is 64 and y is 16 but if you can't comprehend thats 64/16 = 4

Step-by-step explanation:the power is the number multiplied by it self so 8 to the power if 2 is 8 x 8 and 2 to the power of four is 2 x 2 x 2 x 2= 16

Answer:

Step-by-step explanation:

Mean = (29.7 + 29.4 + 31.7 + 29.0 + 29.1 + 30.5 + 29.1 + 29.8)/8 = 29.7875

Mean = 29.7875 × 1000 = $29787.5

Standard deviation = √(summation(x - mean)²/n

n = 8

Summation(x - mean)² = (29.7 - 29.7875)^2 + (29.4 - 29.7875)^2 + (31.7 - 29.7875)^2 + (29.0 - 29.7875)^2 + (29.1 - 29.7875)^2 + (30.5 - 29.7875)^2 + (29.1 - 29.7875)^2 + (29.8 - 29.7875)^2 = 5.88875

Standard deviation = √(5.88875/8

s = 0.88

s = 0.88 × 1000 = $880

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0:µ ≤ 30000

For the alternative hypothesis,

H1:µ > 30000

This is a right tailed test.

b) The decision rule is to reject the null hypothesis if the significance level of 0.05 is greater than the probability value. If it is otherwise, we would fail to reject the null hypothesis.

c) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 8

Degrees of freedom, df = n - 1 = 8 - 1 = 7

t = (x - µ)/(s/√n)

Where

x = sample mean = 29787.5

µ = population mean = 30000

s = samples standard deviation = 880

t = (29787.5 - 30000)/(880/√8) = - 0.68

We would determine the p value using the t test calculator. It becomes

p = 0.26

d) Since alpha, 0.1 < the p value, 0.26, then we would fail to reject the null hypothesis.

Answer:

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 100, p = 0.42[/tex]

92% confidence level

So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.3336[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.42 - 1.75\sqrt{\frac{0.42*0.58}{100}} = 0.5064[/tex]

The 92% confidence interval for the true proportion of customers who click on ads on their smartphones is (0.3336, 0.5064).

Answer:

A.

Step-by-step explanation:

When we multiply the 2 negatives together, we will get a positive number. Since choice A, when you multiply them together, you will get a positive number. Therefore, your answer choice is A.

Answer:

A. [tex]- \frac{-19}{-8} (-50)[/tex]

Step-by-step explanation:

Answer:

To construct a confidence interval, Normal distribution should be used since the sample size is quite large (n > 30)

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

Step-by-step explanation:

We are given the following information:

The sample size is

[tex]n = 235[/tex]

The mean weight is

[tex]\bar{x}= 33.7 \: hg[/tex]

The standard deviation is

[tex]s = 7.3 \: hg[/tex]

Since the sample size is quite large (n > 30) then according to the central limit theorem the sampling distribution of the sample mean will be approximately normal, therefore, we can use the Normal distribution for this problem.

The correct option is (b)

The critical value corresponding to 95% confidence level is given by

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

From the z-table, at α = 0.025 the critical value is

[tex]z_{\alpha/2} = 1.96[/tex]

What is Normal Distribution?

A Normal Distribution is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.

Answer:

Correct option: C.

Step-by-step explanation:

(Assuming the correct function is R(x) = 2x^2 + 3x + 5)

To find the input value that gives the value of R(x) = 19, we just need to use this output value (R(x) = 19) in the equation and then find the value of x:

[tex]R(x) = 2x^2 + 3x + 5[/tex]

[tex]19 = 2x^2 + 3x + 5[/tex]

[tex]2x^2 + 3x -14 = 0[/tex]

Solving this quadratic function using the Bhaskara's formula (a = 2, b = 3 and c = -14), we have:

[tex]\Delta = b^2 - 4ac = 9 + 112 = 121[/tex]

[tex]x_1 = (-b + \sqrt{\Delta})/2a = (-3 + 11)/4 = 2[/tex]

[tex]x_2 = (-b - \sqrt{\Delta})/2a = (-3 - 11)/4 = -3.5[/tex]

So looking at the options, the input to the function is x = 2

Correct option: C.

Answer:

Option A

Step-by-step explanation:

Given equation is

=> 3y = 6x + 3

In slope-intercept form, it becomes

=> 3y = 3(2x+1)

=> y = 2x+1

So, Slope = m = 2

Parallel lines have equal slope, So any line parallel to the above line would have its slope equal to 2

=> Line parallel to 3y = 6x + 3 is y = 2x + 10

Hey there! :)

Answer:

Choice C: x + 8 = 3x.

Step-by-step explanation:

Solve this question by simplifying each answer choice:

a) 4x = 20

Divide both sides by 4:

4x/4 = 20/4

x = 5. This is incorrect.

b) x/2 = 8

Multiply both sides by 2:

x = 16. This is incorrect.

c) x + 8 = 3x

Subtract x from both sides:

8 = 2x

Divide 2 from both sides:

x = 4. This is correct.

d) x = x+5 /2

Multiply both sides by 2:

2x = x + 5

Subtract x from both sides:

x = 5. This is incorrect.

Therefore, choice C is the correct answer.

Answer:

C . x+8=3x

Step-by-step explanation:

[tex]x +8 = 3x\\Collect-like-terms\\8=3x-x\\8=2x\\\frac{2x}{2} =\frac{8}{2} \\x =4[/tex]

Answer:

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Step-by-step explanation:

Let X the random variable that represent the respiratory rate of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(50,5)[/tex]  

Where [tex]\mu=50[/tex] and [tex]\sigma=5[/tex]

We are interested on this probability

[tex]P(40<X<55)[/tex]

And since we need to use excel the code in order to find the answer would be:

=NORM.DIST(55,50,5,TRUE)-NORM.DIST(40,50,5,TRUE)

And the answer would be:

[tex]P(40<X<55)=0.819[/tex]

Answer:

Pr(Three 2's) = 1/27

Step-by-step explanation:

Let's assume the die is a fair die, on the first roll of the die, the child has a 1/6 chance of getting any number, including 6.

Second roll, the child has a 1/36 chance of getting any two numbers, including two 6's.

And on the third roll, the child has a 1/36×1/6=1/216 chance of getting any three numbers, including three 6's. And this is due to the fact that the rolls are independent, so the total possible outcomes multiply each roll with each roll's probability. Since each roll's probability is 1/6.

The probability of the child rolling no more than three twos will be =2/6×2/6×2/6

=1/3×1/3×1/3

=1/27

Therefore, the chances of three twos will be 1/27

Answer:

The variance for the number of correct answers is 4.5.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the correct answer is guessed, or it is not. Questions are independent of each other, so we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The variance of the binomial distribution is:

[tex]V(X) = np(1-p)[/tex]

24 questions

This means that [tex]n = 24[/tex]

Each question has four possible answers one of which is correct

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

Find the variance for the number of correct answers

[tex]V(X) = np(1-p) = 24*0.25*0.75 = 4.5[/tex]

The variance for the number of correct answers is 4.5.

Answer:

-189

Step-by-step explanation:

(63) -3

Calculate the product

-3(63)

Multiply both numbers

-3 × 63

= -189