Consider that the length of rectangle A is 21 cm and its width is 7 cm. Which rectangle is similar to rectangle A?

Answer:

Step-by-step explanation:

1.

3a+7=4a

a=7

2b=b+11

b=11

2.

y=101°

101+x=180

x=180-101=79°

3.

x+6=11

x=11-6=5

y-7=10

y=10+7=17

Answer:

C

Step-by-step explanation:

Since there is no relationship between the two , there exists no correlation between them.

This is simply because the effect of one is not felt on the other

Answer:

Step-by-step explanation:

total marbles=5+8+4+3=20

when he is drawing without replacing means red marble is drawn from 20 marbles.

Blue marble is drawn from 19 marbles.

when he is drawing with replacing means he draws one red marble from 20 marbles.Then he replaces it and draws blue marble from 20 marbles also.

We have a better chance of drawing a red and then a blue marble without replacing the first marble.

It is the ratio that shows the likelihood of a particular event happening from when many other events could also happen.

The total number of marbles = 5 + 8 + 4 +3

= 20 marbles.

P( Drawing a red marble ) = 5/20

Now draw a blue marble:

Total marbles = 20

P( Drawing a blue marble ) = 8/20

Joint probability = 5/20 * 8/20

= 0.1

Total marbles = 19

P( Drawing a blue marble ) = 8/19

Joint probability = 5/20 * 8/19

= 0.105

This means that there is a higher probability of drawing a blue marble after a red marble without replacement.

Thus we have found that we have a better chance of drawing a red and then a blue marble without replacing the first marble.

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Answer:

  (D) the square of a prime

Step-by-step explanation:

You want to know the kind of number that will have exactly two distinct positive divisors other than 1.

The number of divisors a number will have can be found from its prime factorization. If that is described by ...

  [tex]\displaystyle N=p_1^{e_1}\times p_2^{e_2}\times\dots=\prod\limits_n(p_i)^{e_i}\\ \\\text{\# of divisors of N}=\prod\limits_n (e_i+1)[/tex]

This count of divisors includes 1 and the number N. If there are 2 divisors other than 1, then we must have the product of all "bumped" exponents be 3. Since 3 is prime, its only factors are 1 and 3. That means there must be only one exponent, and its value must be 3-1 = 2.

That is, N = p², where p is a prime, has 2+1 = 3 divisors, including 1.

An integer with exactly 2 distinct divisors greater than 1 is the square of a prime, choice D.

Answer:

It will take 80 minutes!

Step-by-step explanation:

From the table we see that in 5 minutes we get 325 copies.

This means in one minute we get [tex]$ \frac{325}{5} $[/tex] = 65 copies.

So, assume we get 5200 copies in 'x' minutes.

So, we form the equation.

i.e., 65x = 5200

⇒ x = 80

This means it would take 80 minutes to get 5200 copies.

Answer:

Time for the object to get h(max)    s = 1.1875 sec

h (max)  = 1272.57 feet

Down time for the object to hit the ground   =  4.25 sec

Step-by-step explanation:

The relation

h(s)  =  -  16*s²  +  38* s  + 1250    (1)

Is equivalent to the equation for vertical shot

Δh = V(i)*t  -  1/2g*t²  (in this case we don´t have independent term since the shot is from ground level. We can see in (1), the independent term is 1250 feet ( the height of the empire state building), the starting point of the movement.

The description of the movement is:

V(s)  =  V(i)  - g*s     ⇒  V(s) = 38 - 32*s

At h(max)    V(s)  =  0      38/32  = s

So the maximum height is at  s = t = 1.1875 sec

The time for the object to pass for starting point is the same

t  =  1.1875 sec

h(max) is

h(max)  = - 16* (1.1875)² +  38 (1.1875) + 1250

h(max)  =  -  22,56  +  45.13  +  1250

h(max)  =  1272.57 feet

Time for the object to hit the ground is

h(s)  =  - 1250 feet

-1250  =  - 16 s² + 38*s  + 1250

-16s² +  38s  =  0

s ( -16s + 38 )  =  0

First solution for that second degree equation  is x = 0 which we dismiss

then  

( -16s + 38 )  =  0    ⇒ 16s   =  38     s  =  38/16

s =  2.375 sec    and  we have to add time between h (max) and to get to starting point  ( 1. 1875 sec)

total time is  = 2.375 + 1.875

Total time  =  4.25 sec

Answer:

40

Step-by-step explanation:

Let the number of boys participating in the quiz be b and the number of girls be g. Since the total number is 100, we have our first equation.

b + g = 100

The average score was 76 points. This means the total score was 76 * 100 = 7600

The average score for the boys was 80 meaning total scores for the boys was 80b while that of the girls was 70g

Hence, we have our second equation:

80b + 70g = 7600

Now let’s put the equations together and solve simultaneously to get g which is the number of girls:

b + g = 100

80b + 70g = 7,600

Let’s simply make a substitution. We can say b = 100 - g. Substituting this will yield:

80(100 - g) + 70g = 7,600

8000 - 80g + 70g = 7600

10g = 400

g = 400/10 = 40

Final answer:

By creating and solving two equations that represent the average scores and total number of students, it was determined that 40 girls participated in the quiz.

Explanation:

To solve this problem, we can create two equations using the information about the average scores of the boys and girls, and the overall average. Let's denote the number of girls as G and the number of boys as B. We are told that there are a total of 100 students, which means:

Equation 1: G + B = 100

We're also told the average scores for boys and girls separately, and the overall average score for the group. We can express this with the following equation:

Equation 2: (80B + 70G) / 100 = 76

Now we can solve these equations simultaneously. We already have the total number of students from Equation 1, so we can use that to express B in terms of G: B = 100 - G. Then we can substitute this into Equation 2:

(80(100 - G) + 70G) / 100 = 76

Expanding this, we get:

8000 - 80G + 70G = 7600

Combining like terms, we have:

-10G = -400

Dividing both sides by -10 gives us G = 40.

So 40 girls participated in the quiz.

Answer:

90k

Step-by-step explanation:

Taxable income is calculated by subtracting certain eligible deductions from gross income. In this scenario, a $10,000 investment in a 401k reduces the individual's taxable income from a $100,000 salary to $90,000.

When determining taxable income, it's important to subtract certain eligible deductions from the gross income. In this case, the individual earns a salary of $100,000 and invests $10,000 in a 401k plan. This investment is a pre-tax contribution, which means it lowers the amount of income that is subject to tax. Therefore, by investing $10,000 into a 401k, the individual's taxable income would be reduced to $90,000. So the correct answer is $90,000.

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Answer with explanation:

A salesperson can use probability to get an idea of his business as using probability he can estimate his sale of the next month as well, based on the present and previous months sales.

It can help him sort issues or errors he is facing in his business as he will get a complete idea of his business using probability.

Moreover, he can forecast future sales by using a technique which involves assigning percentages or weighting benchmarks in sales cycle, so that he can estimate the expected revenue generated.

For example:

A supermarket sales person can assign probabilities to benchmarks in sale cycle as providing needs analysis (25 % probability), adding new product (50%Probability) , Remove a product ( 75 % probability), closing sale (100% Probability) . If these probabilities are large, then forecast model can be objective.

_____________________________________________________

So just like that by assigning probabilities to benchmarks, a sales person can forecast future sales

Answer:

Probability can be used to help a sales person forecast future sales best my showing the likelihood of a certain event occurring. The sales person can then plan around the events that are deemed to be the most likely to occur.

Explanation:

100%Attempt 1 Complete

Answer:

A. 67°

Step-by-step explanation:

Since AC is tangent to the circle, ∠C must be 90°.

You know all angles of a triangle should add up to 180°, so with A given as 23°, that leaves 180-90-23 = 67° for O.

Answer: b. $22.75

Step-by-step explanation:

Given : A large pizza with no toppings costs $14.00. A large pizza with 2 toppings costs $17.50.

Let x denotes the number of toppings and y be the cost of that pizza.

Then, [tex]y=mx+c[/tex] , m= cost per topping  and c= cost of pizza without any topping.

From the given information.

c= $14

Function of cost becomes = [tex]y=mx+14[/tex]

For x= 2 and y= 17.50, we have

[tex]17.50=m(2)+14[/tex]

tex]3.50=m(2)[/tex]  [Subtract 14 from both sides]

[tex]m=\$ 1.75[/tex]  [Divide both sides by 2]

For c= 14 and m =1.75  , our function becomes.

[tex]y=1.75x+14[/tex]

Now, for x= 5

[tex]y=1.75(5)+14=8.75+14=22.75[/tex]

Hence, the cost of a pizza with 5 toppings =  $22.75

Answer:

The number of children attended the fair is 1520.

Step-by-step explanation:

We are given the following in the question:

Entry fee foe children = $1.50

Entry fee foe adult = $4.00

Total number of people in fair = 2200

Total money collected = $5000

Let x be the number of children and y be the number of adults in the fair.

Then, we can write the following equations:

[tex]x + y = 2200\\1.5x + 4y = 5000[/tex]

Solving the two equations, we have:

[tex]1.5x + 1.5y = 3300\\1.5x + 4y = 5000\\\Rightarrow 2.5y = 1700\\y = 680\\x = 2200-680 = 1520[/tex]

Thus, there were 1520 children and 680 adults in the fair.

Answer:

The equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

Step-by-step explanation:

Given:

Actual length of the tree = 5 cm

Current length of the tree = 65 cm

Per day growth Rate of plant = 2.5 cm

Let number of days she owned the plant be 'x'

Now We can say that,

Current length of the tree is equal to sum of Actual length of the tree and Per day growth Rate of plant multiplied by number of days she owned the plant.

Farming the above sentence in equation form we get;

[tex]5+2.5x=65[/tex]

Hence the equation to determine the number of days Margo has owned the plant is [tex]5+2.5x=65[/tex].

The concept in the question is about representing relations as matrices. In the matrices, the rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The positions in the matrices that are filled with 1s correspond to the numbers in the given relationships.

The relations can be represented on the set {1, 2, 3, 4} with a matrix as follows:

a) For this relationship, a 4x4 matrix can be created. The rows and columns correspond to the numbers in the set {1, 2, 3, 4}. The elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}[/tex] correspond to positions in the matrix that will be filled with 1s, while the rest will be filled with 0s.

b) A matrix for this relationship would look similar to the above matrix but with different elements in the set [tex]{(1, 1), (1, 4), (2, 2), (3, 3), (4, 1)}[/tex]. In this case, the position of 1s and 0s in the matrix changes.

c) The matrix corresponding to this relationship would have 1s in positions corresponding to the elements of the set [tex]{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}.[/tex]

d) The last matrix would have 1s only at the positions corresponding to the relationship {(2, 4), (3, 1), (3, 2), (3, 4)}.

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Answer:

H0:[tex]\mu_{N}\geq \mu_{C}[/tex]

H1:[tex]\mu_{N} < \mu_{C}[/tex]

[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}}=-0.759[/tex]  

[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]

So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .

Step-by-step explanation:

1) Data given and notation

[tex]\bar X_{N}=7880[/tex] represent the mean for the sample Nitrite

[tex]\bar X_{C}=8112[/tex] represent the mean for the sample control

[tex]s_{N}=115[/tex] represent the sample standard deviation for the sample Nitrite

[tex]s_{C}=1250[/tex] represent the sample standard deviation for the sample control

[tex]n_{N}=30[/tex] sample size for the group nitrite

[tex]n_{C}=30[/tex] sample size for the group control

t would represent the statistic (variable of interest)

[tex]\alpha=0.02[/tex] represent the significance level

Confidence =1-0.02=0.98 or 98%

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the nitrites decrease amino acid uptake , the system of hypothesis would be:

H0:[tex]\mu_{N}\geq \mu_{C}[/tex]

H1:[tex]\mu_{N} < \mu_{C}[/tex]

If we analyze the size for the samples both are equal to 30, but we don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{N}-\bar X_{C}}{\sqrt{\frac{s^2_{N}}{n_{N}}+\frac{s^2_{C}}{n_{C}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We can replace in formula (1) like this:

[tex]t=\frac{7880-8112}{\sqrt{\frac{1115^2}{30}+\frac{1250^2}{30}}}=-0.759[/tex]  

4) Statistical decision

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{N}+n_{C}-2=30+30-2=58[/tex]

Since is a left tailed test the p value would be:

[tex]p_v =P(t_{(58)}<-0.759)=0.225[/tex]

So the p value is a very High value and using any significance level given [tex]\alpha=0.02[/tex] we see that [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't conclude that the mean for the nitrite group is significantly lower than the mean for th control group .

Answer:

Option A - 10

Step-by-step explanation:

Given : There are 3 red chips and 2 blue chips. If they form a certain color pattern when arranged in a row, for example RBRRB.

To find : How many color patterns are possible?

Solution :

Total number of chips = 5

So, 5 chips can be arranged in 5! ways.

There are 3 red chips and 2 blue chips.

So, choosing 3 red chips in 3! ways

and choosing 2 blue chips in 2! ways.

As changing the places of similar chip will not create new pattern.

The total pattern is given by,

[tex]T=\frac{5!}{3!\times 2!}[/tex]

[tex]T=\frac{5\times 4\times 3!}{3!\times 2}[/tex]

[tex]T=10[/tex]

Therefore, color patterns are possible are 10.

Option A is correct.

Answer:

The probability of given event = [tex]\frac{1}{15}[/tex]

Step-by-step explanation:

Ten slips of paper labeled from 1 to 10 are placed in a hat. The first slip of paper is not replaced before selecting the second slip of paper.

We have to find the probability of selecting a number less than 3 and then a number greater than 4.

Probability of an event = [tex]\frac{number of favourable events}{total number of events}[/tex]

The probability of selecting number less than 3 = [tex]\frac{2}{10}[/tex] = [tex]\frac{1}{5}[/tex]

The probability of selecting number greater than 4 = [tex]\frac{3}{9}[/tex] = [tex]\frac{1}{3}[/tex]

Total probability = [tex]\frac{1}{5}\times \frac{1}{3}[/tex] = [tex]\frac{1}{15}[/tex]

The approximate height of the John Hancock replica is 2.33 meters.

Given that;

Willis Tower in Chicago is 1450 feet tall.

And, The John Hancock Center in Chicago is 1127 feet tall.

Let us assume that,

The approximate height of the John Hancock replica = x

Hence by using the definition of proportion, we get;

1450/3 = 1127/x

Cross multiplication,

1450x = 1127 × 3

x = 2.331

Round to the nearest hundredth;

x = 2.33

Thus, The approximate height of the John Hancock replica is 2.33 meters.

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Step-by-step explanation:

Total number of trees = 300

Given that for every two pine trees there will be 3 maple trees.

Let 2t be the total number of pine trees.

Then total number of maple trees is 3t.

Total number of trees = 2 t + 3 t  = 5 t

That is

              5t = 300

                 t = 60

Total number of pine trees = 2t = 2 x 60 = 120

Total number of maple trees = 3t = 3 x 60 = 180

There are 120 pine trees and 180 maple trees.

Answer:

The answer to your question is letter A

Step-by-step explanation:

                   Percent of blue pigment          Milliliters

 ink A                    10%                                        4

 ink B                    ---                                          10

Total volume        35%                                       14

Formula

Total percent x total volume = (percent ink A x A milliliters) +

                                                  (percent ink B x B milliliters)

Substitution

   (0.35 x 14) = ( 0.1 x 4) + (B x 10)

Solve for B

             4.9 = 0.4 + 10B

             10B = 4.9 - 0.4

             10B = 4.5

                 B = 4.5/10

                 B = 0.45 x 100

                 B = 45%

Answer:

612 feet

Step-by-step explanation:

LA is located at 330 feet ABOVE SEA LEVEL

Death Valley is located 282 feet BELOW SEA LEVEL

We let the sea level be at 0 (consider a number line).

So,

LA would be at +330 feet

and

Death Valley would be at -282 feet

The elevation change between the two would be the difference:

330 - (-282) = 330 + 282 = 612 feet

The difference in elevation = 612 feet

Answer:

D

Step-by-step explanation:

Answer:

At time t = 0.408 sec diver will be at maximum height

Step-by-step explanation:

We have given equation of the height [tex]f(t)=-4.9t^2+4t+9[/tex]

We know that velocity is the rate of change of distance with respect to time

So [tex]v=\frac{df(t)}{dt}=\frac{df(-4.9t^2+4t+10)}{dt}=-9.8t+4+0=-9.8t+4[/tex]

At maximum height velocity will be zero

So [tex]-9.8t+4=0[/tex]

t = 0.408 sec

So at time t = 0.408 sec diver will be at maximum height

Answer: 11

Step-by-step explanation:

Formula to find the sample size using sample standard deviation (s) :

[tex]n= (\dfrac{z^*\cdot s}{E})^2[/tex] , where z* = critical z-value and E = Margin of error.

As per given , we have

E= 7

s= 14 minutes

We know that the critical value for 90% confidence interval = z*=1.645

Then, the required sample size = [tex]n= (\dfrac{(1.645)\cdot (14)}{7})^2[/tex]

[tex]n= (1.645\cdot 2)^2=(3.29)^2=10.8241\approx11[/tex]

Hence, the required sample size = 11

To estimate the mean length of time it takes for buses to arrive and unload students, a sample size of 29 is needed to assert with 90% confidence that the sample mean is off by, at most, 7 minutes.

To determine the sample size needed to estimate the mean length of time it takes for buses to arrive and unload students, we can use the formula:

n = (Z * σ / E)^2

Where n is the required sample size, Z is the z-score corresponding to the desired confidence level (1.645 for 90% confidence), σ is the standard deviation (14 minutes), and E is the maximum error allowed (7 minutes).

Substituting the values into the formula:

n = (1.645 * 14 / 7)^2 = 5.3229^2 = 28.27.

Rounding up to the nearest whole number, the sample size needed is 29.

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Answer:

11 sections

Step-by-step explanation:

This problem is called the circle cutting or pancake cutting problem.

Let the number of cuts or divisions by straight line = n

With this information it is possible to calculate any number of pieces or section a circle will be divided into what straight lines are drawn (cut) across the circle.

When a straight line is drawn across the circle, it divides the circle into 2 sections or regions. The nth straight lines will divide the circle into n new sections or regions, so the progression is;

         f(1) = 2

         f(2) = 2 + f(1)

         f(3) = 3 + f(2)

         .

         .

         .

         f(n) = n + f(n-1)

Therefore,

         f(n) = n + [(n-1) + f(n-2)}

               = n + n-1 + ... + 2 + f(1)

               = f(1) + ∑[tex]_{i = 2}^{n}[/tex]i

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

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

When n = 4

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

              = 22/2

              = 11 sections

Answer:

Step-by-step explanation:

On Monday morning, Susan bought 2.5 pounds of grapes at the supermarket. That day, Susan ate some grapes and had 1.75 pounds of grapes left. This means that the amount of grapes that she ate would be 2.5 - 1.75 = 0.75

The percentage decrease of pounds of grapes on Monday would be the amount that she ate on Monday divided by the initial amount times 100. It becomes

0.75/2.5 × 100 = 30℅

Answer:

Step-by-step explanation:

it is given that Square contains a chord of of the circle equal to the radius thus from diagram

[tex]QR=chord =radius =R[/tex]

If Chord is equal to radius then triangle PQR is an equilateral Triangle

Thus [tex]QO=\frac{R}{2}=RO[/tex]

In triangle PQO applying Pythagoras theorem

[tex](PQ)^2=(PO)^2+(QO)^2[/tex]

[tex]PO=\sqrt{(PQ)^2-(QO)^2}[/tex]

[tex]PO=\sqrt{R^2-\frac{R^2}{4}}[/tex]

[tex]PO=\frac{\sqrt{3}}{2}R[/tex]

Thus length of Side of square [tex]=2PO=\sqrt{3}R[/tex]

Area of square[tex]=(\sqrt{3}R)^2=3R^2[/tex]

Area of Circle[tex]=\pi R^2[/tex]

Ratio of square to the circle[tex]=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }[/tex]

Answer:

It costs Lauren 14 dollars to ride 8 miles

Step-by-step explanation:

The equation for the price of the taxi ride is

y= 1.5x+2

where y is the price, and x is the number of miles driven. Lauren needs to ride 8 miles, so the price of her taxi ride is

y= 1.5*8 +2 =12+2=14

Answer:

Area of the walk = 110 square feet

Step-by-step explanation:

The rectangular yard measuring 24ft by 29ft

Area of the rectangle = length times width

Area of the rectangular yard = 24 times 29=696 square feet

Length of side walk is 2 feet wide

Length of the rectangular yard with walk = 24+2= 26 ft

Width of the rectangular yard with walk = 29+2=31 ft

Area of the rectangular yard with walk = 26 times 31=806 square feet

Area of the walk = [tex]806-696=110 squarefeet[/tex]

Answer:

Option D

Step-by-step explanation:

This are variables that have relationship with the outcome and exposure that is the confounding effect of alcohol on cancer is the fact that an alcohol consumers are more likely to smoke and smokers are likely to have cancer.