what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?

Answers

Answer 1

Answer:

Approximately 3.05

Step-by-step explanation:

Using "compatible numbers" we can simply round these numbers to integer values.  Let's make 76.32 => 76 and 24.98 => 25

So from here let's do 76/25 to get 3 R 1/25

1/25 as a decimal is .04

So far, we have 3.04.  Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98.  So we should consider an extra value in our decimal.

Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.

Thus our number will be 3.04 + .01.

Making our quotient approximately 3.05.

Cheers.


Related Questions

What is the value of the product (3 – 2i)(3 + 2i)?

Answers

Answer:

13

Step-by-step explanation:

(3 - 2i)(3 + 2i)

Expand

(9 + 6i - 6i - 4i^2)

Add

(9 - 4i^2)

Convert i^2

i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1

(9 - 4(-1))

Add

(9 + 4)

= 13

Answer:

13.

Step-by-step explanation:

(3 - 2i)(3 + 2i)

= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)

= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]

= 9 - 4(-1)

= 9 + 4

= 13

Hope this helps!

evaluate the expression 4x^2-6x+7 if x = 5

Answers

Answer:

77

Step-by-step explanation:

4x^2-6x+7

Let x = 5

4* 5^2-6*5+7

4 * 25 -30 +7

100-30+7

7-+7

77

99 litres of gasoline oil is poured into a cylindrical drum of 60cm in diameter. How deep is the oil in the drum? ​

Answers

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

Given the sequence 38, 32, 26, 20, 14, ..., find the explicit formula. A. an=44−6n B. an=41−6n C. an=35−6n D. an=43−6n

Answers

Answer:

The answer is option A

Step-by-step explanation:

The sequence above is an arithmetic sequence

For an nth term in an arithmetic sequence

A(n) = a + ( n - 1)d

where a is the first term

n is the number of terms

d is the common difference

From the question

a = 38

d = 32 - 38 = - 6 or 20 - 26 = - 6

Substitute the values into the above formula

A(n) = 38 + (n - 1)-6

= 38 - 6n + 6

We have the final answer as

A(n) = 44 - 6n

Hope this helps you

Answer:

a

Step-by-step explanation:

you're welcome!

Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario

Answers

Answer:

The test statistic is [tex]t = 2.79[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 59.3[/tex]

    The sample size is  [tex]n = 79[/tex]

    The  sample mean is  [tex]\= x = 62.4[/tex]

    The  standard deviation is  [tex]\sigma = 9.86[/tex]

Generally the test statistics is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]

          [tex]t = 2.79[/tex]

A fair die is tossed once, what is the probability of obtaining neither 5 nor 2?​

Answers

Answer:

4/6 or 66.666...%

Step-by-step explanation:

If you want to find the probability of obtaining neither a 5 nor a 2 you find how many times they occur and add them together in this case 5 occurs once and 2 also occurs once out of 6 numbers so 1/6 + 1/6 equals 2/6, you now know that 4/6 of them won't be a 5 nor a 2 and because it is a fair die the likelihood of it falling on a number is the same for all sides so the answer is 4/6 or 66.67%.

AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?

Answers

Answer:

4

Step-by-step explanation:

Original coordinates:

A (0, 2)

B (2, 3)

The scale is what number the original coordinates was multiplied by to reach the new coordinates

1. Divide

(0, 8) ÷ (0, 2) = 4

(8, 12) ÷ (2, 3) = 4

AB was dilated by a scale factor of 4.

Researchers recorded that a certain bacteria population declined from 450,000 to 900 in 30 hours at this rate of decay how many bacteria will there be in 13 hours

Answers

Answer:

30,455

Step-by-step explanation:

Exponential decay

y = a(1 - b)^x

y = final amount

a = initial amount

b = rate of decay

x = time

We are looking for the rate of decay, b.

900 = 450000(1 - b)^30

1 = 500(1 - b)^30

(1 - b)^30 = 0.002

1 - b = 0.002^(1/30)

1 - b = 0.81289

b = 0.1871

The equation for our case is

y = 450000(1 - 0.1871)^x

We are looking for the amount in 13 hours, so x = 13.

y = 450000(1 - 0.1871)^13

y = 30,455

consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation

Answers

Answer:

Explained below.

Step-by-step explanation:

Enter the data in an Excel sheet.

(a)

Go to Insert → Chart → Scatter.

Select the first type of Scatter chart.

The scatter plot is attached below.

(b)

The scatter plot with the line of best fit is attached below.

The line of best fit is:

[tex]y=-0.8046x+103.56[/tex]

(c)

Compute the value of x for y = 30 as follows:

[tex]y=-0.8046x+103.56[/tex]

[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]

Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.

(d)

The Pearson's Correlation Coefficient is:

[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]

  [tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]

Thus, the Pearson's Correlation Coefficient is -0.71.

(e)

A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.

The correlation between Advanced Mathematics and English results is -0.71.

This implies that there is a strong negative correlation.

anyone can help me with these questions?
please gimme clear explanation :)​

Answers

Step-by-step explanation:

The limit of a function is the value it approaches.

In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1.  As x approaches negative infinity (far to the left), the curve f(x) approaches -1.

lim(x→∞) f(x) = 1

lim(x→-∞) f(x) = -1

In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2.  As x approaches negative infinity (far to the left), the curve f(x) approaches -3.

lim(x→∞) f(x) = 2

lim(x→-∞) f(x) = -3

Two fraction have the same denominator, 8.the some of two fraction is 1/2.if one of the fraction is added to five times the order, the result is 2,find the number.

Answers

Answer:

  1/8, 3/8

Step-by-step explanation:

Let x and y represent the two fractions. Then we are given ...

  x + y = 1/2

  x + 5y = 2

Subtracting the first equation from the second, we get ...

  (x +5y) -(x +y) = (2) -(1/2)

  4y = 3/2 . . . . . simplify

  y = 3/8 . . . . . . divide by 4

  x = 1/2 -3/8 = 1/8

The two numbers are 1/8 and 3/8.

A raffle offers one $8000.00 prize, one $4000.00 prize, and five $1600.00 prizes. There are 5000 tickets sold at $5 each. Find the expectation if a person buys one ticket.

Answers

Answer:

The expectation is  [tex]E(1 )= -\$ 1[/tex]

Step-by-step explanation:

From the question we are told that  

     The first offer is  [tex]x_1 = \$ 8000[/tex]

     The second offer is  [tex]x_2 = \$ 4000[/tex]

      The third offer is  [tex]\$ 1600[/tex]

      The number of tickets is  [tex]n = 5000[/tex]

      The  price of each ticket is  [tex]p= \$ 5[/tex]

Generally expectation is mathematically represented as

             [tex]E(x)=\sum x * P(X = x )[/tex]

     [tex]P(X = x_1 ) = \frac{1}{5000}[/tex]    given that they just offer one

    [tex]P(X = x_1 ) = 0.0002[/tex]    

 Now  

     [tex]P(X = x_2 ) = \frac{1}{5000}[/tex]    given that they just offer one

     [tex]P(X = x_2 ) = 0.0002[/tex]    

 Now  

      [tex]P(X = x_3 ) = \frac{5}{5000}[/tex]    given that they offer five

       [tex]P(X = x_3 ) = 0.001[/tex]

Hence the  expectation is evaluated as

       [tex]E(x)=8000 * 0.0002 + 4000 * 0.0002 + 1600 * 0.001[/tex]

      [tex]E(x)=\$ 4[/tex]

Now given that the price for a ticket is  [tex]\$ 5[/tex]

The actual expectation when price of ticket has been removed is

      [tex]E(1 )= 4- 5[/tex]

      [tex]E(1 )= -\$ 1[/tex]

You are going to your first school dance! You bring $20,
and sodas cost $2. How many sodas can you buy?
Please write and solve an equation (for x sodas), and
explain how you set it up.

Answers

Answer:

10

Step-by-step explanation:

Let the no. of sodas be x

Price of each soda = $2

Therefore, no . of sodas you can buy = $2x

2x=20

=>x=[tex]\frac{20}{2}[/tex]

=>x=10

you can buy 10 sodas

Answer: 10 sodas

Step-by-step explanation:

2x = 20       Divide both sides by 2  

x = 10

If I brought 20 dollars and I  want to by only sodas and each sodas cost 2 dollars, then I will divide the total amount of money that I brought  by 2 to find out how many sodas I could by.

Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k)left parenthesis, k, right parenthesis she can drive with 12 liters of fuel. She assumes the relationship between kilometers and fuel is proportional.


How many kilometers can Pamela drive with 12 liters of fuel?

Answers

Answer:

132 kilo meters

Step-by-step explanation:

Pro por tions:

9 lite rs ⇒ 99 km

12 lite rs  ⇒  P km

P = 99*12/9

P = 132 km

Answer:

132

Step-by-step explanation:

give person above brainliest :))

Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure. Question 9 options:
A) (x, y) → (x, y – 6)
B) (x, y) → (x – 6, y)
C) (x, y) → (x, y + 6)
D) (x, y) → (x + 6, y)

Answers

Answer:

  B) (x, y) → (x – 6, y)

Step-by-step explanation:

Each x-value in the image is 6 less than in the pre-image. Each y-value is the same. That means x gets mapped to x-6, and y gets mapped to y:

  (x, y) → (x – 6, y)

Which graph shows the polar coordinates (-3,-) plotted

Answers

Graph 1 would be the answer

A Markov chain has 3 possible states: A, B, and C. Every hour, it makes a transition to a different state. From state A, transitions to states B and C are equally likely. From state B, transitions to states A and C are equally likely. From state C, it always makes a transition to state A.

(a) If the initial distribution for states A, B, and C is P0 = ( 1/3 , 1/3 , 1/3 ), find the distribution of X2

(b) Find the steady state distribution by solving πP = π.

Answers

Answer:

A) distribution of x2 = ( 0.4167 0.25 0.3333 )

B) steady state distribution = [tex]\pi a \frac{4}{9} , \pi b \frac{2}{9} , \pi c \frac{3}{9}[/tex]

Step-by-step explanation:

Hello attached is the detailed solution for problems A and B

A) distribution states for A ,B, C:

Po = ( 1/3, 1/3, 1/3 )  we have to find the distribution of x2 as attached below

after solving the distribution

x 2 = ( 0.4167, 0.25, 0.3333 )

B ) finding the steady state distribution solving

[tex]\pi p = \pi[/tex]

below is the detailed solution and answers

Which of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7

Answers

Answer:

f(x) = 7

Step-by-step explanation:

f(x) = f(-x) it is even

-f(x)=f(-x) it is odd

f(x) = (x – 1)^2 neither even nor odd

f(x) = 8x   this is a line  odd functions

f(x) = x^2 – x  neither even nor odd

f(x) = 7  constant  this is an even function

Answer:

answer is f(x)= 7

Step-by-step explanation:

just took edge2020 test

The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.

Answers

Answer:

7/11 = 0.6363...

Step-by-step explanation:

7 + 4 = 11

probability of winning: 7/11 = 0.6363...

The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]

Given that the odds  of the horse winning the race is 7:4

Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:

[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]

From the given question;

The probability of the horse winning the race is:

[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]

[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]

Learn more about probability here:

https://brainly.com/question/11234923?referrer=searchResults

Consider the surface f(x,y) = 21 - 4x² - 16y² (a plane) and the point P(1,1,1) on the surface.

Required:
a. Find the gradient of f.
b. Let C' be the path of steepest descent on the surface beginning at P, and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane.
c. Find parametric equations for the path C' on the surface.

Answers

Answer:

A) ( -8, -32 )

Step-by-step explanation:

Given function : f (x,y) = 21 - 4x^2 - 16y^2

point p( 1,1,1 ) on surface

Gradient of F

attached below is the detailed solution

A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.​

Answers

Answer:

109

Step-by-step explanation:

Use a chart or calculator to find the z-score corresponding to a probability of 1%.

P(Z > z) = 0.01

P(Z < z) = 0.99

z = 2.33

Now find the sample standard deviation.

z = (x − μ) / s

2.33 = (30.5 − 30) / s

s = 0.215

Now find the sample size.

s = σ / √n

s² = σ² / n

0.215² = 5 / n

n = 109

Brainliest! Jared uses the greatest common factor and the distributive property to rewrite this sum: 100 + 75 Drag one number into each box to show Jared's expression. Brainliest!

Answers

Answer:

25(4 + 3)

Step-by-step explanation:

100 = 2^2 + 5^2

75 = 3 * 5^2

GCF = 5^2 = 25

100 + 75 =

= 25 * 4 + 25 * 3

= 25(4 + 3)

Which function below has the following domain and range?
Domain: { -6, -5,1,2,6}
Range: {2,3,8)
{(2,3), (-5,2), (1,8), (6,3), (-6, 2)
{(-6,2), (-5,3), (1,8), (2,5), (6,9)}
{(2,-5), (8, 1), (3,6), (2, - 6), (3, 2)}
{(-6,6), (2,8)}​

Answers

Answer:

{(2,3), (-5,2), (1,8), (6,3), (-6, 2)

Step-by-step explanation:

The domain is the input and the range is the output

We need inputs of -6 -5 1 2 6

and outputs of 2 3 and 8

Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.

Answers

Answer:

the equation is not correct, u have to write like

ax'3+bx'2+cx+d

Answer:

x=-2 and x=0

Step-by-step explanation:

So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.

First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x

Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in

So, in conclusion I believe the answer to be x=-2 and x=0

Simplify . 7+ the square root of 6(3+4)-2+9-3*2^2 The solution is

Answers

Answer:

7+sqrt(37)

Step-by-step explanation:

7+sqrt(6*(3+4)-2+9-3*2^2)=7+sqrt(6*7+7-3*4)=7+sqrt(42+7-12)=7+sqrt(37)

Please Solve
F/Z=T for Z

Answers

Answer:

F /T = Z

Step-by-step explanation:

F/Z=T

Multiply each side by Z

F/Z *Z=T*Z

F = ZT

Divide each side by T

F /T = ZT/T

F /T = Z

Answer:

[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]

Step-by-step explanation:

[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]

solve the equation ​

Answers

Answer:

x = 10

Step-by-step explanation:

2x/3 + 1 = 7x/15 + 3

(times everything in the equation by 3 to get rid of the first fraction)

2x + 3 = 21x/15 + 9

(times everything in the equation by 15 to get rid of the second fraction)

30x+ 45 = 21x + 135

(subtract 21x from 30x; subtract 45 from 135)

9x = 90

(divide 90 by 9)

x = 10

Another solution:

2x/3 + 1 = 7x/15 + 3

(find the LCM of 3 and 15 = 15)

(multiply everything in the equation by 15, then simplify)

10x + 15 = 7x + 45

(subtract 7x from 10x; subtract 15 from 45)

3x = 30

(divide 30 by 3)

x = 10

If f(x) = 2x2 – 3x – 1, then f(-1)=

Answers

ANSWER:
Given:f(x)=2x^2-3x-1
Then,f(-1)=2(-1)^2-3(-1)-1
f(-1)=2(1)+3-1
f(-1)=5-1
f(-1)=4


HOPE IT HELPS!!!!!!
PLEASE MARK BRAINLIEST!!!!!

The value of function at x= -1 is f(-1) = 4.

We have the function as

f(x) = 2x² - 3x -1

To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:

f(-1) = 2(-1)² - 3(-1) - 1

      = 2(1) + 3 - 1

      = 2 + 3 - 1

      = 4.

Therefore, the value of function at x= -1 is f(-1) = 4.

Learn more about Function here:

https://brainly.com/question/32020999

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Evaluate integral _C x ds, where C is
a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)
b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Answers

Answer:

a.    [tex]\mathbf{36 \sqrt{5}}[/tex]

b.   [tex]\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]

Step-by-step explanation:

Evaluate integral _C x ds  where C is

a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)

i . e

[tex]\int \limits _c \ x \ ds[/tex]

where;

x = t   , y = t/2

the derivative of x with respect to t is:

[tex]\dfrac{dx}{dt}= 1[/tex]

the derivative of y with respect to t is:

[tex]\dfrac{dy}{dt}= \dfrac{1}{2}[/tex]

and t varies from 0 to 12.

we all know that:

[tex]ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt[/tex]

[tex]\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt[/tex]

[tex]= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt[/tex]

[tex]= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0[/tex]

[tex]= \dfrac{\sqrt{5}}{4}\times 144[/tex]

= [tex]\mathbf{36 \sqrt{5}}[/tex]

b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Given that:

x = t  ; y = 3t²

the derivative of  x with respect to t is:

[tex]\dfrac{dx}{dt}= 1[/tex]

the derivative of y with respect to t is:

[tex]\dfrac{dy}{dt} = 6t[/tex]

[tex]ds = \sqrt{1+36 \ t^2} \ dt[/tex]

Hence; the  integral _C x ds is:

[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]

Let consider u to be equal to  1 + 36t²

1 + 36t² = u

Then, the differential of t with respect to u is :

76 tdt = du

[tex]tdt = \dfrac{du}{76}[/tex]

The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145

Thus;

[tex]\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt[/tex]

[tex]\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}[/tex]

[tex]= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}[/tex]

[tex]\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}[/tex]

[tex]\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}[/tex]

Figure out if the figure is volume or surface area.​

(and the cut out cm is 4cm)

Answers

Answer:

Surface area of the box = 168 cm²

Step-by-step explanation:

Amount of cardboard needed = Surface area of the box

Since the given box is in the shape of a triangular prism,

Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides

Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]

                                                           = [tex]\frac{1}{2}(6)(4)[/tex]

                                                           = 12 cm²

Surface area of the rectangular side with the dimensions of (6cm × 9cm),

= Length × width

= 6 × 9

= 54 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Surface area of the prism = 2(12) + 54 + 45 + 45

                                           = 24 + 54 + 90

                                           = 168 cm²

Other Questions
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