which pair or pairs of polygons are congruent ?

Which Pair Or Pairs Of Polygons Are Congruent ?

Answers

Answer 1

Answer:

E. 1, 2, 3, and 4

Step-by-step explanation:

Well all them are equal,

both rectangles in part 2 has a 3cm^2 area.

Both red and green in part 4 has 2 squares and 1 triangle or half of a square.

Both of part 3 have all the same shapes in them.

Same with part 1 both shapes have same area and perimeter.

Thus, answer choices E. 1,2,3, and 4 is correct.


Related Questions

Forty one people were riding bus number 527. At 8:45 am,it arrived at the 109th street stop. There,19 people got off and then 20 people boarded. How many riders were on the bus when it traveled to the next stop?

Answers

Answer:

1 because jahahdhekskdbsks

A trough of water is 8 meters deep and its ends are in the shape of isosceles triangles whose width is 5 meters and height is 2 meters. If water is being pumped in at a constant rate of 6 m3Isec. At what rate is the height of the water changing when the water has a height of 120 cm?

Answers

Answer:

0.3 m/s

Step-by-step explanation:

The first thing is to attach the allusive graphic to the question. Now yes, let's move on to the solution that would be:

If the through is completely filtered the its volume will:

V = l * [1/2 w * h] = 1/2 l * w * h

Now we derive with respect to time and we are left with:

dV / dt = 1/2 * l * w * dh / dt

We solve by dh / dt and we have:

dh / dt = (2 / (l * w)) * (dV / dt)

We know that l = 8 and w = 5, in addition to dV / dt = 6, we replace:

dh / dt = (2 / (8 * 5)) * (6)

dh / dt = 0.3

Therefore the rate at which the height of the water changes is 0.3 m / s

Figure ABCDE was reflected across the line y=x to create figure A’B’C’D’E’. What are the coordinates of the pre image of E?

Answers

Answer

so I need to know the coordinates for me to tell you the answer but I think I can still help you by explaining.

In order for E to become E' the rule for reflection over y=x is (y, x) so you basically switch the x and the Y to have E'. so for you to be able find out E, you need to witch the x and the y.

for example:

if E' was (-2, 3)

E in the pre image would be (3, -2)

hope this helps :)

Answer:

(-2,6)

Step-by-step explanation:

Just did it edge 2021

Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 fewer than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s−5)=9.45 for s to find the number of 49-cent stamps Travis bought.

Answers

Answer:

15 49-cent stamps

Step-by-step explanation:

We can solve this problem with the equations 0.49(x) + 0.21(y) = 9.45 and x - 5 = y. Well, 0.49(15) + 0.21(10) = 9.45, so we know that there are 15 49-cent stamps and 10 21-cent stamps. The question is asking for the number of 49-cent stamps, so we can tell Travis bought 15 49-cent stamps.

Hope this helps! Plz give me brainliest, it will help me achieve my next rank.

The number of 49-cent stamps that Travis bought given the equation is 15.

What he number of 49-cent stamps Travis bought?

Given this equation: 0.49s+0.21(s−5)=9.45 take the following steps to determine the value of s

Expand the bracket: 0.49s + 0.21s - 1.05 = 9.45Combine similar terms : 0.49s + 0.21s = 9.45 + 1.05Add similar terms: 10.50 = 0.70sDivide both sides of the equation by 0.70: s = 15

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Scott has eight CDs, and he picks two to take to work each day. How many different ways can Scott choose two CDs?

Answers

Answer:

The total number of ways to select 2 CDs from 8 CDs is 28.

He can choose them 28 different ways

A taxi company charges $2.25 per ride plus $0.30 per mile. Enter a linear model represents the cost, C, as a function of d, the number of miles of the ride.

Answers

Answer:

C(d) = d(2.25) + m(0.3)

Step-by-step explanation:

A taxi company charges $2.25 per ride plus $0.30 per mile.

Let d represent number of rides..

Let m represent number of Miles...

Then let C represent the total cost for each ride at a specific number of Miles.

The linear model representing the cost as a function of d the total ride

C(d) = d(2.25) + m(0.3)

The values stand independently because the customer can choose a different right and a different mile.

An object of height 2.50cm is placed 20.0cm from a converging mirror of focal length 10.0cm. What are the height and the magnification of the image formed?

Answers

First find the distance it is reflected:

D = 20.0 x 10.0 /(20-10) = 200/10 = 20cm away.

Now calculate the magnification: -20/ 20 = -1

Now calculate the height:

-1 x 2.50 = -2.50

The negative sign means the image is inverted.

The mirrored image would be inverted, 2.50 cm tall and 20 cm in front of the mirror.

a patient is taking 65 grams of medicine if it is increased by 20% how many grams are they taking

Answers

Answer:

78 grams

Step-by-step explanation:

20% is 1/5

1/5 of 65 is 13

65 + 13 = 78

brainliest?

is -17 a natural number

Answers

━━━━━━━☆☆━━━━━━━

▹ Answer

-17 isn't a natural number

▹ Step-by-Step Explanation

Positive integers are only natural numbers, meaning negative numbers aren't natural numbers.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Write the equation in the form Ax + By = C. Find an equation of a line passing through the pair of points (4,7) and (3,4).

Answers

Answer:

[tex] 3x - y = 5 [/tex]

Step-by-step explanation:

The two pint equation of a line:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

We have

[tex] x_1 = 4 [/tex]

[tex] x_2 = 3 [/tex]

[tex] y_1 = 7 [/tex]

[tex] y_2 = 4 [/tex]

[tex] y - 7 = \dfrac{4 - 7}{3 - 4}(x - 4) [/tex]

[tex] y - 7 = \dfrac{-3}{-1}(x - 4) [/tex]

[tex] y - 7 = 3(x - 4) [/tex]

[tex] y - 7 = 3x - 12 [/tex]

[tex] 5 = 3x - y [/tex]

[tex] 3x - y = 5 [/tex]

The table shows claims and their probabilities for an insurance company.
O A. (a)
O B. (a)
Amount of Claim
$0
$50,000
$100,000
$150,000
$200,000
$250,000
Probability
0.60
0.25
0.09
0.04
0.01
0.01
O c. (a) $
OD. (a) $
(a) Calculate the expected value.
(b) How much should the company charge as an average premium so that it breaks even on its claim
costs?
(c) How much should the company charge to make a profit of $60 per policy?

Answers

Answer:

a) Expected Value of Claims = $32,000

b) Average premium per claim, in order to break-even on claim costs

= $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

= $5,393.33 per policy

Step-by-step explanation:

a) Data and Calculations:

Amount of Claim      Probability   Expected Value

$0                               0.60             $0

$50,000                     0.25             $12,500

$100,000                   0.09                 9,000

$150,000                   0.04                 6,000

$200,000                  0.01                 2,000

$250,000                 0.01                 2,500

Expected Cost of claims =          $32,000

b) Average premium per claim, in order to break-even on claim costs

= Total Claim cost divided by number of policies

= $32,000/6 = $5,333.33

c) To make a profit of $60 per policy (i.e. a total profit of $360 ($60 x 6), it must charge:

Total Claim cost + Total profit / 6 or Average Premium plus Profit per policy =

= ($32,000 + $360)/6 or $5,333.33 + $60

= $32,360/6 or $5,393.33

= $5,393.33

The total expected value is $32000, the average premium so that it breaks even on its claim  costs are $5333.33 and the company charge to make a profit of $60 per policy is $5393.33.

Given :

The table shows claims and their probabilities for an insurance company.

Amount of Claim          Probability               Expected Value

$0                                      0.60                             0

$50000                             0.25                            $12500

$100000                            0.09                            $9000

$150000                            0.04                             $6000

$200000                           0.01                              $2000

$250000                            0.01                             $2500

A) So, the total expected value is = 12500 + 9000 + 6000 + 2000 + 2500

                                                   =  $32000

B) The average premium is given by:

[tex]=\dfrac{32000}{6}[/tex]

= $5333.33

C) The company charge to make a profit of $60 per policy is:

[tex]= \dfrac{32000+360}{6}[/tex]

[tex]=\dfrac{32360}{6}[/tex]

= $5393.33

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a coin will be tossed 10 times. Find the chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses

Answers

Answer:

The chance that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses is P=0.0488.

Step-by-step explanation:

To solve this problem we divide the tossing in two: the first 5 tosses and the last 5 tosses.

Both heads and tails have an individual probability p=0.5.

Then, both group of five tosses have the same binomial distribution: n=5, p=0.5.

The probability that k heads are in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{5}{k}\cdot0.5^k\cdot0.5^{5-k}[/tex]

Then, the probability that exactly 2 heads are among the first five tosses can be calculated as:

[tex]P(x=2)=\dbinom{5}{2}\cdot0.5^{2}\cdot0.5^{3}=10\cdot0.25\cdot0.125=0.3125\\\\\\[/tex]

For the last five tosses, the probability that are exactly 4 heads is:

[tex]P(x=4)=\dbinom{5}{4}\cdot0.5^{4}\cdot0.5^{1}=5\cdot0.0625\cdot0.5=0.1563\\\\\\[/tex]

Then, the probability that there will be exactly 2 heads among the first five tosses and exactly 4 heads among the last 5 tosses can be calculated multypling the probabilities of these two independent events:

[tex]P(H_1=2;H_2=4)=P(H_1=2)\cdot P(H_2=4)=0.3125\cdot0.1563=0.0488[/tex]

George has opened a new store and he is monitoring its success closely. He has found that this store’s revenue each month can be modeled by r(x)=x2+5x+14 where x represents the number of months since the store opens the doors and r(x) is measured in hundreds of dollars. He has also found that his expenses each month can be modeled by c(x)=x2−3x+4 where x represents the number of months the store has been open and c(x) is measured in hundreds of dollars. What does (r−c)(3) mean about George's new store?

Answers

This is a great question!

When we are given ( r - c )( 3 ), we are being asked to take 3 as x in the functions r( x ) and c( x ), taking the difference of each afterwards -

[tex]r( 3 ) = ( 3 )^2 + 5( 3 ) + 14,\\x( 3 ) = ( 3 )^2 - 3( 3 ) + 4[/tex]

____

Let us calculate the value of each function, determine their difference, and multiply by 100, considering r( x ) and c( x ) are measured in hundreds of dollars,

[tex]r( 3 ) = 9 + 15 + 14 = 38,\\x( 3 ) = 9 - 9 + 4 = 0 + 4 = 4\\----------------\\( r - c )( 3 ) = 38 - 4 = 34,\\34 * 100 = 3,400( dollars )\\\\Solution = 3,400( dollars )[/tex]

Therefore, ( r - c )( 3 ) " means " that George's new store will have a profit of $3,400 after it's third month in business, given the following options,

( 1. The new store will have a profit of $3400 after its third month in business.  

( ​​2. The new store will have a profit of $2400 after its third month in business.

( 3. ​The new store will sell 2400 items in its third month in business.

( 4. The new store will sell 3400 items in its third month in business.

The required answer is , [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

Substitution:

The substitution method is the algebraic method to solve simultaneous linear equations.

Given function is,

[tex]r(x) = x^2+5x+14[/tex]...(1)

And [tex]c(x) = x^2-4x+5[/tex]...(2)

Now, substituting the value into the equation (1) and (2).

[tex]r(5) = (5)^2+5(5)+14=64[/tex]

[tex]c(5) = (5)^2-4(5)+5=10[/tex]

Therefore,

[tex](r-c)(5)=r(5)-c(5)\\=64-10\\=54[/tex]

Now, [tex](r-c)(5)[/tex] means the revenue less expenses in 5 months i.e. the new store will have a profit of $ 5400 after 5 months.

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The number 128 is divided into two parts in the ratio 7:9. Find the absolute difference between the two parts.

Answers

7+9=16
128/16 =8

7x 8 = 56
9x 8 = 72

72-56 = 16

16 is the absolute difference between the 2 parts

The formula to convert Fahrenheit to Celsius is C - 5 (F - 32). Convert 30°C to
Fahrenheit. Round to the nearest degree.
A. 30°F
B. -1°F
C. 112°F
D. 86°F

Answers

Answer:

D. *6F

Step-by-step explanation:

C=(F-32)*5/9

30=(F-32)*5/9

F = (30*9)/5+32

F = 86

Find the length of KC

Answers

Answer:

54

give me brainliest please please please and follow my page

Step-by-step explanation:

To find length of KC...we need to find the length of HM and MU first ...

so....HM= 96- 78 = 14

JU = 96 + HM = 96 + 14 = 110

....

KU = 110 - JK = 110 - 82 = 28

....

UN = 105+ 82 -( 96 + 14 )

187 - 110

= 77

UC = 77 - 51 = 26

KC = UC + KU = 26 + 28 = 54

The length of [tex]\overline{KC}[/tex] along line [tex]\overline{JN}[/tex] is given as 54 (Option A) See the computation below.

How do you compute the length of [tex]\overline{KC}[/tex]?

To determine the length of [tex]\overline{KC}[/tex], the length of [tex]\overline{HM}[/tex] and [tex]\overline{MU}[/tex]must first be derived.

[tex]\overline{HM}[/tex] = 96 - 78

[tex]\overline{HM}[/tex] = 14

[tex]\overline{JU}[/tex] = 96 + [tex]\overline{HM}[/tex]

= 96 + 14

[tex]\overline{JU}[/tex]= 110

[tex]\overline{KU}[/tex] = 110 - [tex]\overline{JK}[/tex]

= 110 - 82

[tex]\overline{KU}[/tex]= 28

[tex]\overline{UN}[/tex] = 105+ 82 -( 96 + 14 )

=187 - 110

[tex]\overline{UN}[/tex]= 77

[tex]\overline{UC}[/tex] = 77 - 51

[tex]\overline{UC}[/tex]= 26

Thus,

[tex]\overline{KC}[/tex] = [tex]\overline{UC}[/tex] + [tex]\overline{KU}[/tex]

[tex]\overline{KC}[/tex]= 26 + 28

[tex]\overline{KC}[/tex]= 54

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This is not an incomplete question, it has come from a very reliable source, please dont delete. If 60% of the students in Mr. Bobby's class are bio majors, which of the following could be the total number of students in his class? 28 32 35 39 PLZHELPTHANKS

Answers

Answer:

35 students

Step-by-step explanation:

Take the number of students in the class and multiply by 60% and see if you get an integer number

28 * .60 =16.8  not an integer

32 * .6 =19.2

35 * .6 =21  yes

39*.6 =23.4

Galina had two boxes with pieces of paper in each. In the first box, each piece of paper had one possible outcome from flipping a coin 4 times (e.g. HHTH). There was one piece of paper for every possible outcome.
How many pieces of paper were in the first box?

Answers

Answer:

B

Step-by-step explanation:

If A and B are independent events, P(A) = 0.25, and P(B) = 0.3, what is P(AB)?
O A. 0.25
B. 0.3
C. 0.15
O D. 0.075

Answers

Answer:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Step-by-step explanation:

For this case we have the following events A and B and we also have the probabilities for each one given:

[tex] P(A) = 0.25, P(B= 0.3[/tex]

And if we want to find [tex] P(A \cap B)[/tex] we can use this formula from the definition of independent events :

[tex] P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075[/tex]

And the best option would be:

[tex] P(A \cap B) =0.075[/tex]

Periodically, customers of a financial services company are asked to evaluate the company's financial consultants and services. Higher ratings on the client satisfaction survey indicate better service, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use
α = 0.05
and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16
n2 = 10
x1 = 6.82
x2 = 6.28
s1 = 0.65
s2 = 0.75
(a)
State the null and alternative hypotheses.
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 > 0
Ha:
μ1 − μ2 ≤ 0
H0:
μ1 − μ2 ≠ 0
Ha:
μ1 − μ2 = 0
H0:
μ1 − μ2 ≤ 0
Ha:
μ1 − μ2 > 0
H0:
μ1 − μ2 = 0
Ha:
μ1 − μ2 ≠ 0
(b)
Compute the value of the test statistic. (Round your answer to three decimal places.)
(c)
What is the p-value? (Round your answer to four decimal places.)
p-value =
(d)
What is your conclusion?
Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Do not reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating. Do not Reject H0. There is sufficient evidence to conclude that the consultant with more experience has a higher population mean rating.Reject H0. There is insufficient evidence to conclude that the consultant with more experience has a higher population mean rating.

Answers

Answer:

A) Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Test statistic = t = 1.878

C) p-value is 0.038823.

D) Reject the Null hypothesis H0

Step-by-step explanation:

We are given;

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

A) The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

B) Formula yo determine the test statistic is;

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

Plugging in the relevant values, we have;

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

C) The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Plugging in the relevant values, we have;

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value;

From online p-value calculator from t-score and DF which i attached, we have the p-value as;

The p-value is 0.038823.

D) The p-value result is significant at p < 0.05

Thus, we reject the Null hypothesis H0

A) Null hypothesis: μ1 − μ2 ≤ 0

B) Test statistic = t = 1.878

C) The p-value is 0.038823.

D) Reject the Null hypothesis H0.

Hypothesis

What all information we have ?

α = 0.05

n1 = 16

n2 = 10

bar x1 = 6.82

bar x2 = 6.28

s1 = 0.65

s2 = 0.75

Part A)

The hypothesis is as follows;

Null hypothesis; H0: μ1 − μ2 ≤ 0

Alternative hypothesis; Ha: μ1 − μ2 > 0

Part B)

The formula to determine the test statistic is :

t = ((bar x1) - (bar x))/√((s1)²/n1) + (s2)²/n2))

t = (6.82 - 6.28)/√((0.65)²/16) + (0.75)²/10))

t = 0.54/√(0.02640625 + 0.05625)

t = 0.54/0.2875

t = 1.878

The formula to determine the test statistic is t = 1.878.

Part C)

The formula for the degree of freedom is;

Δ = [(s1)²/n1) + (s2)²/n2))]²/[((s1²/n1)²/(n1 - 1)) + ((s2²/n2)²/(n1 - 1))  

Δ = [(0.65)²/16) + (0.75)²/10))]²/[((0.65²/16)²/(16 - 1)) + ((0.75²/10)²/(10 - 1))  

Δ = 0.00683205566/(0.000046486 + 0.0003515625)

Δ ≈ 17

Thus, the P-value is 0.038823.

Part D)

The p-value result is significant at p < 0.05 is :

Thus, we reject the Null hypothesis H0.

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A sample of size 42 college students produced a 95% confidence interval of (3.1, 5.2) for the mean number of coats owned. Then there is a 95% chance that these 42 students own on average between 3.1 and 5.2 coats.

a. True
b. False

Answers

Answer:

b. False.

Step-by-step explanation:

According to the presented information, at the 95% confidence level, the mean number of coats owned will be between 3.1 and 5.2. That does not mean that there is a 95% chance that they will own that many coats; just that you are 95% confident that they will own the coats.

Hope this helps!

According to the Stack Overflow Developers Survey of 20184 , 25.8% of developers are students. The probability that a developer is a woman given that the developer is a student is 7.4%, and the probability that a developer is a woman given that the developer is not a student is 76.4%. If we encounter a woman developer, what is the probability that she is a student

Answers

Answer:

3.26%

Step-by-step explanation:

The computation of the probability that she is a student is shown below:

Percentage of student developers = 25.8% = SD

The Percentage of the developer is student = 7.4% = DS

The percentage of the developer is not student = 76.4% = ND

Based on this, the probability is

[tex]= \frac{SD \times DS}{SD \times DS + DS \times ND}[/tex]

[tex]= \frac{25.8\% \times 7.4\%}{25.8\% \times 7.4\% + 7.4\% \times 76.4\%}[/tex]

=3.26%

we simply considered all the elements

Express it in slope-intercept form.

Answers

Hey there! :)

Answer:

y = 1/4x - 3.

Step-by-step explanation:

Use the slope-formula to find the slope of the line:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points from the line. Use the points (-4, -4) and (0, 3):

[tex]m = \frac{-3 - (-4)}{0 - (-4)}[/tex]

Simplify:

m = 1/4.

Slope-intercept form is y = mx + b.

Find the 'b' value by finding the y-value at which the graph intersects the y-axis. This is at y = -3. Therefore, the equation is:

y = 1/4x - 3.

Find a solution to the linear equation y=12x−24

Answers

Answer:

I didn't know which one you wanted...

Step-by-step explanation:

1. Finding the x an y-intercepts

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (2,0)

y-intercept(s): (0,−24)

2. Finding the slope and y-intercept

Use the slope-intercept form to find the slope and y-intercept.

Slope: 12

y-intercept: −24

Charlotte is running at a rate of 9 (km)/(h) what is charlotte speed in (m)/(s)

Answers

Answer:

2.5 meters per second

Step-by-step explanation:

9x1000=9000m/h

9000/60/60=2.5m/s

Answer:

2.5 m/s

Step-by-step explanation:

convert kilometers to meters and then use a conversion calc to do the rest

perform the indicated operations a. 3/10+6/10. b. 1/3+2/4+1/6. c. 5/6-3/6 d. 2/3-6/10 e. 4/10×3/7 f. 1/6x6/15 g. 1/8÷4/9 h. 1/5÷3/4​

Answers

Answer:

A. [tex]\frac{9}{10}[/tex]

B. 1

C. [tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]

D. [tex]\frac{2}{30}[/tex] or [tex]\frac{1}{15}[/tex]

E. [tex]\frac{12}{70}[/tex] or [tex]\frac{6}{35}[/tex]

F. [tex]\frac{6}{90}[/tex] or [tex]\frac{1}{15}[/tex]

G. [tex]\frac{9}{32}[/tex]

H. [tex]\frac{4}{15}[/tex]

Answer:

Step-by-step explanation:

Reducing the given expressions to the lowest terms:

A. 3/10 + 6/10:

B. 1/3 + 1/4 + 1/6:

C. 5/6-3/6:

D. 2/3-6/10:

E. 4/10*3/7:

F. 1/6*6/15:

G. 1/8 divided by 4/9:

H. 1/5 divided by 3/4:

Not sure how to solve

Answers

Answer:

  (x, y, z) = (13/7, 19/7, 25/7)

Step-by-step explanation:

You know that the vector whose components are the coefficients of the equation of the plane is perpendicular to the plane. That is (1, 2, 3) is a vector perpendicular to the plane.

The parametric equation for a line through (1, 1, 1) with this direction vector is ...

  (x, y, z) = (1, 2, 3)t +(1, 1, 1) = (t+1, 2t+1, 3t+1)

The point of intersection of this line and the plane will be the point in the plane closest to (1, 1, 1). That point has a t-value of ...

  (t +1) +2(2t +1) +3(3t +1) = 18

  14t +6 = 18

  t = 12/14 = 6/7

The point in the plane closest to (1, 1, 1) is ...

  (x, y, z) = (6/7+1, 2(6/7)+1, 3(6/7)+1)

  (x, y, z) = (13/7, 19/7, 25/7)

A man is twice the age of his son,in 20 years time, the son's age will be 2/3 of that his father. what is the son's present age?​

Answers

Answer:

20 years old.

Step-by-step explanation:

Let us say that the man's age is represented by x and the son's age is represented by y.

As of now, x = 2y.

In 20 years, both ages will increase by 20. We can have an equation where the son's age increased by 20 equals 2/3 of the man's age plus 20.

(y + 20) = 2/3(x + 20)

Since x = 2y...

y + 20 = 2/3(2y + 20)

3/2y + 30 = 2y + 20

2y + 20 = 3/2y + 30

1/2y = 10

y = 20

To check our work, the man's age is currently double his son's, so the man is 40 and the son is 20. In 20 years, the man will be 60 and the son will be 40. 40 / 60 = 2/3, so the son's age is 2/3 of his father's.

So, the son's present age is 20 years old.

Hope this helps!

A particular fruit's weights are normally distributed, with a mean of 476 grams and a standard deviation of 36 grams. The heaviest 19% of fruits weigh more than how many grams? Give your answer to the nearest gram.

Answers

Answer:

Step-by-step explanation:

Given that:

mean (μ) = 476 grams, standard deviation (σ) = 36 grams. P(z) = 19%

The z score shows by how many standard deviation the raw score is above or below the mean. It is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Since the 19% weigh more, therefore 81% (100% - 19%) weigh less.

From the normal distribution table, the z score that corresponds to a probability of 81%(0.81) = 0.87

We substitute z = 0.88 in the z score equation to find the raw score. Therefore:

[tex]z=\frac{x-\mu}{\sigma}\\0.87=\frac{x-476}{36}\\ x-476=31.32\\x=31.32+476\\x=507.32\\[/tex]

x ≅ 507 grams

Therefore 19% of fruits weigh more than 507 grams

Which are the roots of the quadratic function f(b) = 62 – 75? Select two options.

b=573

Ob= -573

b=35

b= -35

Ob= 253

Answers

Answer:

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

Step-by-step explanation:

Given

[tex]f(b) = b^2 - 75[/tex]

Required

Determine the roots

To get the root of the function, then f(b) must be 0;

i.e. f(b) = 0

So, the expression becomes

[tex]0 = b^2 - 75[/tex]

Add 75 to both sides

[tex]75 + 0 = b^2 - 75 + 75[/tex]

[tex]75 = b^2[/tex]

Take square roots of both sides

[tex]\sqrt{75} = \sqrt{b^2}[/tex]

[tex]\sqrt{75} = b[/tex]

Reorder

[tex]b = \sqrt{75}[/tex]

Expand 75 as a product of 25 and 3

[tex]b = \sqrt{25*3}[/tex]

Split the expression

[tex]b = \sqrt{25} *\sqrt{3}[/tex]

[tex]b = \±5 *\sqrt{3}[/tex]

[tex]b = \±5 \sqrt{3}[/tex]

[tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

The options are not clear enough; however the roots of the equation are [tex]b = 5 \sqrt{3} \ or\ b = -5 \sqrt{3}[/tex]

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