In Mary's first math test she scored 87%. The mean and standard deviation for the class were 71% and 18% respectively. In her second math test, Mary scored 66%. The mean and standard deviation for the class were 53% and 14% respectively. In which test did Mary do better relative to the rest of the class? Explain your reasoning. (Hint: find the z-scores corresponding to her two test scores.)

Answer:

One proof can be as follows:

Step-by-step explanation:

We have that [tex]g.c.d(a,b)=1[/tex] and [tex]a=cp, b=dq[/tex] for some integers [tex]p, q[/tex], since [tex]c[/tex] divides [tex]a[/tex] and [tex]d[/tex] divides [tex]b[/tex].  By the Bezout identity two numbers [tex]a,b[/tex] are relatively primes if and only if there exists integers [tex]x,y[/tex] such that

[tex]ax+by=1[/tex]

Then, we can write

[tex]1=ax+by=(cp)x+(dq)y=c(px)+d(qy)=cx'+dy'[/tex]

Then [tex]c[/tex] and [tex]d[/tex] are relatively primes, that is to say,

[tex]g.c.d(c,d)=1[/tex]

Answer:

There is a 35.7% probability that this deal will not materialize.

Step-by-step explanation:

This problem can be solved by a simple system of equations.

-I am going to say that x is the probability that this deal materializes and y is the probability that this deal does not materialize.

The sum of all probabilities is always 100%. So

[tex]1) x + y = 100[/tex].

Bob, the proprietor of Midland Lumber, believes that the odds in favor of a business deal going through are 9 to 5.

Mathematically, this means that:

[tex]2) \frac{x}{y} = \frac{9}{5}[/tex]

We want to find the value of y. So, we can write x as a function of y in equation 2), and replace it in equation 1).

Solution:

[tex]\frac{x}{y} = \frac{9}{5}[/tex]

[tex]x = \frac{9y}{5}[/tex]

[tex]x + y = 100[/tex]

[tex]\frac{9y}{5} + y = 100[/tex]

[tex]\frac{14y}{5} = 100[/tex]

[tex]14y = 500[/tex]

[tex]y = \frac{500}{14}[/tex]

[tex]y = 35.7[/tex]

There is a 35.7% probability that this deal will not materialize.

(n+4) +7 remove the parenthesis

n+4+7 add the same number answer is n +11

Answer:

The man had a displacement of 12.88 m southeastward

Step-by-step explanation:

The path of man forms a right triangle. The first two magnitudes given in the problem form the legs and the displacement that we must calculate forms the hypotenuse of the triangle. To do this we will use the equation of the pythagorean theorem.

H = magnitude of displacement

[tex]H^2 = \sqrt{L_1^2 + L_2^2} = \sqrt{6.70^2 + 11.0^2} = \sqrt{165.89}   =12.88 m[/tex]

using the graphic method, we will realize that the displacement is oriented towards the southeast

Answer:

Step-by-step explanation:

The given information can be tabulated as follows:

                          Graphics G     Printing P            Total

X                                      3                 2                    5

Y                                      1                  1                      2

Available                       21                19

We have the constraints as

[tex]3x+y\leq 21\\2x+y\leq 19\\x\leq 2\\y\leq 15[/tex]

Thus we have solutions as

[tex]0\leq x\leq 2\\0\leq y\leq 15[/tex]

Answer: 0.0011

Step-by-step explanation:

By using the standard normal distribution table , the probability that Z is to the left of 3.05 is [tex]P(z<3.05)= 0.9989[/tex]

We know that the probability that Z is to the right of z is given by :-

[tex]P(Z>z)=1-P(Z<z)[/tex]

Similarly,  the probability that Z is to the right of 3.05 will be :-

[tex]P(Z>3.05)=1-P(Z<3.05)=1-0.9989=0.0011[/tex]

Hence, the probability that Z is to the right of 3.05 = 0.0011

Answer:

66.11

Step-by-step explanation:

We are given that  a number

66.1086

We have to round the number to hundredths

Place of 6=One;s

Place of second 6=Tens

Place of 1=Tenths

Place of 0=Hundredths

Place of 8=Thousandths

Place of 6=Ten thousandths

Thousandths place is 8 which is greater than 5 therefore, one will be added to hundredth place and other number on the left side of  hundredth place remain same and the numbers on the right side of hundredth place will be replace by zero.

Therefore, the given number round to hundredths=66.11

Answer: (A) 30%

Step-by-step explanation:

Given : The probability that a bird will lay an egg =0.75

The probability that the egg will hatch  =0.50

Now, the probability that the egg will lay an egg and hatch = [tex]0.75\times0.50[/tex]

Also,The probability that the chick will be eaten by a snake before it fledges =0.20

Then, the probability that the chick will not  be eaten by a snake before it fledges : 1-0.20=0.80

Now, the probability that a parent will have progeny that survive to adulthood will be :-

[tex]0.75\times0.50\times0.80=0.30=30\%[/tex]

Hence, the probability that a parent will have progeny that survive to adulthood =  30%

Answer:  10

Step-by-step explanation:

The formula to find the sample size is given by :-

[tex]n=(\dfrac{z_{\alpha/2}\ \sigma}{E})^2[/tex]

Given : Significance level : [tex]\alpha=1-0.99=0.1[/tex]

Critical z-value=[tex]z_{\alpha/2}=2.576[/tex]

Margin of error : E=5

Standard deviation : [tex]\sigma=6[/tex]

Now, the required sample size will be :_

[tex]n=(\dfrac{(2.576)\ 6}{5})^2=9.55551744\approx10[/tex]

Hence, the final sample required to be of 10 .

Answer:

Protein

Step-by-step explanation:

According to U.S. Food and Drug Administration (FDA) information, the current scientific evidence indicates that protein intake is not a matter of public concern, this is why the FDA does not request to add a % Daily Value on the Nutrition Facts panel, unless if the product is made for protein such as 'high protein' products or if this food is meant for use by childrend under 4 years old.

Answer:Protein

Step-by-step explanation: took quiz :)

Answer:

Ben must make at least 14 deliveries to reach his goal.

Step-by-step explanation:

The problem states that Ben earns $9 per hour and $6 for each delivery he makes. So his daily earnings can be modeled by the following function.

[tex]E(h,d) = 9h + 6d[/tex],

in which h is the number of hours he works and d is the number of deliveries he makes.

He wants to earn more than $155 in an 8 hour work day.What is the least number of deliveries he must make to reach his goal?

This question asks what is the value of d, when E = $156 and h = 8. So:

[tex]E(h,d) = 9h + 6d[/tex]

[tex]156 = 9*8 + 6d[/tex]

[tex]156 = 72 + 6d[/tex]

[tex]6d = 84[/tex]

[tex]d = \frac{84}{6}[/tex]

d = 14

Ben must make at least 14 deliveries to reach his goal.

Answer: 10gtt/ml means that in 10 drops there is a ml of the solution.

Now, you need 1000ml in 8 hours, and want to know the correct rate of flow in drops per minute.

first, 8 hours are 8*60 = 480 minutes.

then you need to infuse 1000ml in 480 minutes, so if you infuse at a constant rate, you need to infuse 1000/480 = 2.083 ml/min.

And we know that 10 drops are equivalent to 1 ml, then 2.083*10= 20.8 drops are equivalent a 2.083 ml, rounding it up, you get 21 drops for the dose.

So the correct rate of flow will be 21 drops per minute.

To find the correct rate of flow for an IV infusion, convert the time to minutes, divide the total volume by the total time to find the rate in ml/min, then multiply by the drip factor to convert to drops/min. Rounding to the nearest drop, we get 21 gtt/min.

To calculate the correct rate of flow for an IV infusion, we need to use the given information: the volume of the IV infusion (D5W 1000 ml), the time over which it must infuse (8 hours), and the IV tubing drip factor (10 gtt/ml).

First, convert the time from hours to minutes as we're interested in drops per minute: 8 hours * 60 minutes/hour = 480 minutes.

Next, we divide the total volume by the total time: 1000 ml / 480 minutes = ~2.08 ml/min. This is the rate in ml/min.

Finally, we multiply by the drip factor to get the rate in drops per minute: 2.08 ml/min * 10 gtt/ml = 20.8 gtt/min.

Rounding to the nearest drop gives us a rate of 21 gtt/min.

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Answer:

There are 100 milligrams of metoclopramide HCl in each milliliter of the prescription

Step-by-step explanation:

When the prescription says Purified water qs ad 100 mL means that if we were to make this, we should add the quantities given and then, fill it up with water until we have 100 mL of solution, being the key words qs ad, meaning sufficient quantity to get the amount of mixture given.

Then, knowing there is 10 grams of metoclopramide HCl per 100 mL of prescription, that means there is (1 gram = 1000 milligrams) 10000 milligrams of metoclopramide HCl per 100 mL of prescription. That is a concentration given in a mass/volume way.

Knowing the concentration, we can calculate it per mL instead of per 100 mL

[tex]Concentration_{metoclopramide HCL}= \frac{10000mg}{100mL} =100 \frac{mg}{mL}[/tex]

Answer: There is increase of 4.255 in the amount of carbon in the atmosphere.

Step-by-step explanation:

Since we have given that

Concentration of carbon in Earth's atmosphere in 1800 = 280 ppm

Concentration of carbon in Earth's atmosphere in 2015 = 399 ppm

We need to find the percentage increase in the amount of carbon in the atmosphere.

So, Difference = 399-280 = 119 ppm

so, percentage increase in the amount of carbon is given by

[tex]\dfrac{Difference}{Original}\times 100\\\\=\dfrac{119}{280}\times 100\\\\=\dfrac{11900}{280}\\\\=42.5\%[/tex]

Hence, there is increase of 4.255 in the amount of carbon in the atmosphere.

Answer:

Sample space = {(T,T), (T,H), (HT), (HH)}

Step-by-step explanation:

We are given a fair coin which when tossed one times either gives heads(H) or tails(T).

Now, the same coin is tossed two times.

1) All the possible outcomes

Tails followed by tails

Rails followed by heads

Heads followed by a tail

Heads followed by heads

2) Sample space

{(T,T), (T,H), (HT), (HH)}

3) Formula:

[tex]Probability = \displaystyle\frac{\text{Favourable outcome}}{\text{Total number of outcome}}[/tex]

Using the above formula, we can compute the following probabilities.

Probability((T,T)) =[tex]\frac{1}{4}[/tex]

Probability((T,H)) =[tex]\frac{1}{4}[/tex]

Probability((H,T)) =[tex]\frac{1}{4}[/tex]

Probability((H, H)) =[tex]\frac{1}{4}[/tex]

Probability(Atleast one tails) = [tex]\frac{3}{4}[/tex]

Probability(Atleast one heads) = [tex]\frac{3}{4}[/tex]

Probability(Exactly one tails) = [tex]\frac{2}{4}[/tex]

Probability(Exactly one heads) = [tex]\frac{2}{4}[/tex]

Answer:

[tex]1\,\,cm/min[/tex]

Step-by-step explanation:

Let V be the volume of cube and x be it's side .

We know that volume of cube is [tex]\left ( side \right )^{3}[/tex] i.e., [tex]x^3[/tex]

Given :

[tex]\frac{\mathrm{d} V}{\mathrm{d} t}=1200\,\,cm^3/min[/tex]

[tex]x=20\,\,cm[/tex]

To find : [tex]\frac{\mathrm{d} x}{\mathrm{d} t}[/tex]

Solution :

Consider equation [tex]V=x^3[/tex]

On differentiating both sides with respect to t , we get

[tex]\frac{\mathrm{d} V}{\mathrm{d} t}=3x^2\left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )\\1200=3(20)^2\left ( \frac{\mathrm{d} x}{\mathrm{d} t} \right )\\\frac{\mathrm{d} x}{\mathrm{d} t} =\frac{1200}{3(20)^2}=\frac{1200}{3\times 400}=\frac{1200}{1200}=1\,\,cm/min[/tex]

So,

Length of the side is increasing at the rate of [tex]1\,\,cm/min[/tex]

Answer:

The cost is $9.70 per kilogram.

Step-by-step explanation:

This can be solved by a rule of three.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.

In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.

Solution:

The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:

1 pound - xkg

2.2 pound - 1 kg

[tex]2.2x = 1[/tex]

[tex]x = \frac{1}{2.2}[/tex]

[tex]x = 0.45[/tex]kg

Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?

$4.40 - 0.45kg

$x - 1kg

[tex]0.45x = 4.40[/tex]

[tex]x = \frac{4.40}{0.45}[/tex]

[tex]x = 9.70[/tex]

The cost is $9.70 per kilogram.

"The cost per kilogram of cheese is approximately $2.00.

To find the cost per kilogram, we need to convert the cost from dollars per pound to dollars per kilogram using the conversion factor between pounds and kilograms. Given that 1 kilogram is equal to 2.2 pounds, we can set up the following conversion:

Cost per pound of cheese = $4.40

Conversion factor = 2.2 pounds/kilogram

Now, to find the cost per kilogram, we divide the cost per pound by the conversion factor:

Cost per kilogram = Cost per pound / Conversion factor

Cost per kilogram = $4.40 / 2.2 pounds/kilogram

Performing the division, we get:

Cost per kilogram ≈ $2.00

Answer:

[tex]q=9\,,\,r=6[/tex]

Step-by-step explanation:

Division Algorithm :

As per division algorithm , for numbers a and b , there exist numbers q and r such that [tex]a=bq+r\,\,,0\leq r< b[/tex]

Here ,

a = Dividend

b = Divisor

q = quotient

r = remainder

Given : 105 = 11q + r such that [tex]0 \leq r < 11[/tex]

Here, clearly a = 105 , b = 11

To find : q and r

Solution : On dividing 105 by 11 , we get [tex]105=11\times 9+6[/tex]

On comparing [tex]105=11\times 9+6[/tex] with [tex]a=bq+r\,\,,0\leq r< b[/tex] , we get [tex]q=9\,,\,r=6[/tex]

Answer:

12

Step-by-step explanation:

The greatest common divisor(gcd) is also known by the name highest common factor(hcf), greatest common factor(gcf).

Greatest common factor of two number can be defined as the highest  integer that divides both the number.

We have to find greatest common divisor of 252 and 60.

The prime factorization of 252 is:

252 = 2×2×3×3×7

The prime factorization of 60 is:.

60 = 2×2×3×5

Common factors are: 2×2×3

Hence, greatest common divisor of 252 and 60 = 2×2×3 = 12

Answer:

Taking into account the information presented in the image attached for this food.  

Naturally sugar are

2 g

Step-by-step explanation:

Information presented regarding to the composition of this food is attached.

One serving has a weight of 55 g.

Total carbohydrates in one serving are 37 g. This value includes fiber and sugars.

If we detail sugars, it has 12 g of total sugars (St), where 10 g are added sugars (Sa) and all the rest Natural sugars (Sn).

Expressing sugars as an equation

St = Sa + Sn

Isolating Sn value

Sn = St - Sa

Sn = 12 g - 10 g  

Sn = 2 g

Finally, Natural sugars (Sn) is 2 g.  

All 22 grams of total sugars per serving in the food are naturally occurring, as the label specifies there are 0g of added sugars.

To determine the grams of naturally occurring sugar in a serving of food, we need to examine the nutritional information provided.

According to the label, it includes 0g added sugars, which implies that all of the sugars listed are naturally occurring.

Therefore, if there are 22g total sugars in one serving of the food, and none of these are added sugars, then all 22 grams can be attributed to naturally occurring sugars.

Step-by-step explanation:

For each case we have the next step by step solution.

Answer: P means "This statement is false"

then, P is a "function" of some statement,

if i write P( 3> 1932) this could be read as:

3>1932, this statement is false.

You could see that 3> 1932 is false, so P( 3>1932) is true.

Then you could se P(x) at something that is false if x is true, and true if x is false, so p is a negation.

Answer:

160 lbs = 72.57kg

Step-by-step explanation:

This can be solved as a rule of three problem.

In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.

When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too.

When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease.

Unit conversion problems, like this one, is an example of a direct relationship between measures.

Each lb has 0.45kg. How many kg are there in 160lbs. So:

1lb - 0.45kg

160 lbs - xkg

[tex]x = 0.45*160[/tex]

[tex]x = 72.57[/tex] kg

160 lbs = 72.57kg

Answer:

The expectation is -$0.189.

Step-by-step explanation:

Consider the provided information.

In European roulette, the wheel is divided into 37 compartments numbered 1 through 36 and 0.

One-half of the numbers 1 through 36 are red, the other half are black, and the number 0 is green.

We need to find the expected value of the winnings on a $7 bet placed on black in European roulette.

Here the half of 36 is 18.

That means 18 compartments are red and 18 are black.

The probability of getting black in European roulette is 18/37

The probability of not getting black in European roulette is 19/37. Because 18 are red and 1 is green.

If the ball lands on a black number, the player wins the amount of his bet.

The bet is ball will land on a black number.

The favorable outcomes are 18/37 and unfavorable are 19/37.

Let S be possible numerical outcomes of an experiment and P(S) be the probability.

The expectation can be calculated as:

E(x) = sum of S × P(S)

For[tex] S_1 = 7[/tex]

[tex]P(S_1) = \frac{18}{37}[/tex]

For [tex]S_2 = -7[/tex](negative sign represents the loss)

[tex]P(S_2) = \frac{19}{37}[/tex]

Now, use the above formula.

[tex]E(x) = 7\times \frac{18}{37}-7\times \frac{19}{37}\\E(x) = -0.189[/tex]

Hence, the expectation is -$0.189.

The given sequence is convergent with a limit of -3/2, while the series is divergent since its terms do not approach zero

The sequence in question is An = [6*n/(-4*n + 9)]. To find out if this sequence is convergent or divergent, we need to take the limit as n approaches infinity. As n approaches infinity, the 'n' in the numerator and the 'n' in the denominator will dominate, making the sequence asymptotically equivalent to -6/4 = -3/2. Thus, the sequence is convergent, and its limit is -3/2.

On the other hand, the series ∑n=1[infinity]( An ) is the sum of the terms in the sequence. We can see that as n approaches infinity, the terms of this series do not approach zero, which is a necessary condition for a series to be convergent (using the nth term test). Therefore, the series is divergent.

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Answer: There are 3.36 ounces of ground almonds in 1 cup.

Step-by-step explanation:

Since we have given that

1 pint = 0.42 pounds

As we know that

1 cup = 0.5 pints

1 pound = 16 ounces

So, We need to find the number of ounces.

As 1 pint = 0.42 pounds = 0.42 × 16 = 6.72 ounces

0.5 pints is given by

[tex]6.72\times 0.5\\\\=3.36\ ounces[/tex]

Hence, there are 3.36 ounces of ground almonds in 1 cup.

To find out how many ounces are in one cup of ground almonds if 1 pint (2 cups) weighs 0.42 pounds, you divide 0.42 pounds by 2 to get the weight per cup, then multiply by 16 to convert pounds to ounces, resulting in 3.36 ounces per cup.

The question involves converting weight measurements from one unit to another, specifically from pounds to ounces. To do this, you use the conversion factor of 16, because there are 16 ounces in 1 pound. Applying this to the recipe question:

1 pint of ground almonds weighs 0.42 pounds. Since 1 pint equals 2 cups, this weight corresponds to 2 cups of ground almonds.

To find out how many ounces 1 cup of ground almonds weighs, first divide the total weight by the number of cups:

0.42 pounds ÷ 2 cups = 0.21 pounds per cup.

Then, convert pounds to ounces:

0.21 pounds × 16 ounces/pound = 3.36 ounces.

So, for the recipe, you should use 3.36 ounces of ground almonds.

Answer: [tex]8.76\%[/tex]

Step-by-step explanation:

The formula to find the final amount after getting simple interest :

[tex]A=P(1+rt)[/tex], where P is the principal amount , r is rate of interest ( in decimal )and t is time(years).

Given : Justin deposited $2,000 into an account 5 years ago.

i.e. P = $2,000 and  t= 5 years

He has just withdrawn $2,876.

i.e. we assume that A = $2876

Now, Put all the values in the formula , we get

[tex](2876)=(2000)(1+r(5))\\\\\Rightarrow\ 1+5r=\dfrac{2876}{2000}\\\\\Rightarrow\ 1+5r=1.438\\\\\Righhtarrow\ 5r=0.438\\\\\Rightarrow\ r=\dfrac{0.438}{5}=0.0876[/tex]

In percent, [tex]r=0.0876\times100=8.76\%[/tex]

hence, He earned [tex]8.76\%[/tex] of interest on account.

Answer:

59 coins

Step-by-step explanation:

The number of coins in Anthony's collection is 294

Using the parameters given for our Calculation;

Total number of coins now :

Six times as many coins can be calculated thus :

Therefore, the number of coins in Anthony's collection is 294

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Answer:

2.68

Step-by-step explanation:

We are given that [tex]x_0=7,x_1=7.1,x_2=7.2,x_3=7.3,x_4=7.4,x_5=7.5[/tex]

h=0.1

y'=2x-y

y(7)=0,f(x,y)=2x-y

[tex]x_0=7,y_0=0[/tex]

We have to find the approximate solution to the initial problem at x=7.1

[tex]y_1=y_0+hf(x_0,y_0)[/tex]

Substitute the value then, we get

[tex]y_1=0+(0.1)(2(7)-0)=0+(0.1)(14)=1.4[/tex]

[tex]y_1=1.4[/tex]

[tex]x_1=x_0+h=7+0.1=7.1[/tex]

[tex]y_2=y_1+hf(x_1,y_1)[/tex]

Substitute the values then, we get

[tex]y_2=1.4+(0.1)(2(7.1)-1.4)=1.4+(0.1)(14.2-1.4)=1.4+(0.1)(12.8)=1.4+1.28[/tex]

[tex]y_2=1.4+1.28=2.68[/tex]

Hence, the approximation solution to the initial problem at x=7.1 is =2.68

Step-by-step explanation:

We want to show that

[tex]=A \setminus (B \cup C) = (A\setminus B) \cap (A\setminus C)[/tex]

To prove it we just use the definition of [tex]X\setminus Y = X \cap Y^c[/tex]

So, we start from the left hand side:

[tex]=A \setminus (B \cup C) = A \cap (B \cup C)^c[/tex] (by definition)

[tex]=A \cap (B^c \cap C^c)[/tex] (by DeMorgan's laws)

[tex]=A \cap B^c \cap C^c[/tex] (since intersection is associative)

[tex]=A \cap B^c \cap A \cap C^c[/tex] (since intersecting once or twice A doesn't make any difference)

[tex]=(A \cap B^c) \cap (A \cap C^c)[/tex] (since again intersection is associative)

[tex]=(A\setminus B) \cap (A \setminus C)[/tex] (by definition)

And so we have reached our right hand side.