Chocolate sprinkles cost as much per pound as sugar. Find 1/10 the baker’s total cost for 100 pounds of chocolate sprinkles.

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

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The median for the given sample of data is A. 20.

To find the median for the given sample of data, we need to arrange the numbers in ascending order and then find the middle value.

Arranging the numbers in ascending order: 16, 17, 18, 18, 19, 19, 21, 22, 22, 23, 25

There are 11 numbers in the sample, so the middle value is the (11 + 1) / 2 = 6th value.

The 6th value in the ordered list is 19.

Therefore, the median for this sample of data is A. 20.

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Answer:

18.19

Step-by-step explanation:

15% of 20 = 3

20 - 3 = 17

7% of 17 = 1.19

17 + 1.19 = 18.19

Answer:

96/x

Step-by-step explanation:

When two variables x and y vary inversely, their product is a constant. Therefore, the function that models the inverse variation between x and y is:

x*y = k

where k is the constant of proportionality.

We can use the given information to find the value of k:

x = 12 when y = 8

so, k = xy = 128 = 96

Now we can use this value of k to write the function that models the inverse variation:

x*y = 96

To find the inverse variation, we divide both sides by y,

x = 96/y

Alternatively, we can write y = 96/x

So, the function that models the inverse variation between x and y is either x = 96/y or y = 96/x

Answer:

for every 5 roses there's 1 plant(s)

Step-by-step explanation:

For the multisets {3 · a, 2 · b, 1 · c} and {2 · a, 3 · b, 4 · d} the solutions are  A ∪ B is {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d},A ∩ B is {2 · a, 2 · b},A − B is {1 · a, 0 · b, 1 · c} ,B − A is {0 · a, 1 · b, 4 · d} and A + B is {5 · a, 5 · b, 1 · c, 4 · d}.

We will use the given multisets A and B:

A = {3 · a, 2 · b, 1 · c}
B = {2 · a, 3 · b, 4 · d}

a) A ∪ B (union): This operation combines all elements of both multisets.
A ∪ B = {3 · a, 2 · b, 1 · c, 2 · a, 3 · b, 4 · d}

b) A ∩ B (intersection): This operation finds the common elements between both multisets.
A ∩ B = {2 · a, 2 · b} (as a and b are the common elements)

c) A − B (difference): This operation removes elements in B from A.
A − B = {1 · a, 0 · b, 1 · c}

d) B − A (difference): This operation removes elements in A from B.
B − A = {0 · a, 1 · b, 4 · d}

e) A + B (sum): This operation adds the counts of the elements in both multisets.
A + B = {5 · a, 5 · b, 1 · c, 4 · d}

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The three necessary precautions for the distillation set-up are proper insulation, temperature control, and monitoring of pressure.

Distillation is a widely used technique for separating and purifying liquids based on their boiling points. To ensure the success and safety of the distillation process, several precautions must be taken during the set-up.

Firstly, proper insulation is crucial to maintain consistent and efficient distillation conditions. Insulation helps to minimize heat loss or gain from the surroundings, which can affect the accuracy of the boiling point and the separation efficiency. Insulation materials such as glass wool or insulating tape can be used to cover the distillation apparatus and prevent heat exchange with the environment.

Secondly, temperature control is essential to achieve the desired separation. Distillation involves heating the mixture to vaporize the more volatile component and then condensing it back into a liquid. Precise temperature control ensures that the desired compound vaporizes without excessive overheating or decomposition. This can be achieved by using a temperature-regulated heat source, such as a heating mantle or a water bath, along with a thermometer to monitor the temperature throughout the process.

Lastly, monitoring of pressure is crucial for safe and efficient distillation. Controlling the pressure inside the distillation apparatus helps to prevent excessive pressure buildup, which can lead to equipment failure or even explosion. Pressure can be controlled by adjusting the rate of vapor condensation or by using a pressure relief valve to maintain a safe operating pressure.

In summary, the three necessary precautions for the distillation set-up are proper insulation to minimize heat exchange, temperature control to achieve accurate separation, and monitoring of pressure to ensure safety and prevent equipment failure.

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Answer:

B.  p - 200

Step-by-step explanation:

Start with the original price, p.

When the price is reduced by $200, you are taking away $200 from the price, so you need to subtract $200 from the original price, p.

Answer:  B.  p - 200

Answer:

Assuming 4 laps=1 mile, a standard track, then for every 5 minutes she runs a mile. 20 miles time 5 minutes each equals 100 minutes, or 1 hour and 40 minutes

Twenty people are to be divided into two teams with ten players on each team, number of ways this be done is 92378  

Combinations:

In mathematics, combination is the process of choosing a number of items from a given group of objects.

The combination of n things in 'a' time without repetition is given by

Here we have,

Twenty people need to be divided into two teams with ten players on each team  

The total number of ways that can be chosen is 10 people from a group of 20 people = ²⁰C₁₀  

= 20!/10!(20 - 10)!

= 20!/ 10! 10!

= 184756  

As we know need to divide them into 2 groups

The number of ways that can be done = 184756/2 = 92378  

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Answer:

Construct a perpendicular bisector to line AB

The first option

Answer:

Construct a perpendicular bisector to line AB  the first one

Answer:

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): None

y-intercept(s): (0,5)

Step-by-step explanation:

1 cup = 8 ounces

64 ÷ 8 = 8

he adds two sets of 8 cups of grape juice so 16 total

20 cups of ginger ale + 16 cups of grape juice

36 cups total

Answer:

36 cups

Step-by-step explanation:

8 oz = 1 cup

64 oz / 8 oz = 8 cups

8 cups + 8 cups (due to 2 bottles of 64 oz)

16 cups+ 20 cups

36 cups

Answer:

7.7 is the answer

Step-by-step explanation:

(credit to manics.info)

Step 1:

Calculate the square root of 60 to be:

√60 = 7.74596669241483

Step 2:

Reduce the tail of the answer above to two numbers after the decimal point:

7.74

Step 3:

Round 7.74 so you only have one digit after the decimal point to get the answer:

7.7

To check that the answer is correct, use your calculator to confirm that 7.72 is about 60.

Hope this help and have a great day!

The sampling method described in which the population is first divided into groups and then random samples are drawn from each group is called stratified sampling. In this sampling method, the population is divided into homogeneous subgroups called strata, based on some characteristic of interest such as age, gender, income level, or geographic location. Random samples are then drawn from each stratum, and the data collected from each sample are combined to form the final sample.

Stratified sampling is often used when the population is heterogeneous, meaning that it has distinct subgroups with different characteristics that may affect the outcome of the study. By dividing the population into homogeneous subgroups, stratified sampling increases the precision of the estimates and reduces the sampling error, compared to simple random sampling. Stratified sampling also ensures that each subgroup of the population is represented in the sample, which may be important for making inferences about the entire population. However, stratified sampling can be more complex and time-consuming than simple random sampling, especially if the population has many subgroups.

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Answer:

i would say b

Step-by-step explanation: if they all slept 4 hours a night then all 9 would have a total of 36 and a night would be 1 so 36 to 1

3(a-4) + 1= 9 - a

3(a-4) = 8 - a

3a-12 = 8 - a

4a = 20

a=5

I hope this helps! :)

Answer:

a=5

Step-by-step explanation:

3(a-4)+1=9-a

3a-12+1=9-a

   3a-11=9-a

   3a+a=9+11

       4a=20

         a=20÷4

           =5

The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(a) Let X be the number of calls received in a 5-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, X follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The probability of receiving two calls in a 5-minute interval is:

P(X = 2) = (e^-4 * 4^2) / 2! = 0.0902

(b) Let Y be the number of calls received in a 15-minute interval. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Y follows a Poisson distribution with mean λ = 0.8 * 15 = 12. The probability of receiving exactly 10 calls in 15 minutes is:

P(Y = 10) = (e^-12 * 12^10) / 10! = 0.1143

(c) Let Z be the number of callers waiting after 5 minutes. The arrival rate of calls is 48/60 = 0.8 calls per minute. Then, Z follows a Poisson distribution with mean λ = 0.8 * 5 = 4. The expected number of callers waiting after 5 minutes is:

E(Z) = λ = 4

The probability that none will be waiting is:

P(Z = 0) = e^-4 = 0.0183

(d) Let W be the waiting time until the next call. The time between calls follows an exponential distribution with rate λ = 48/60 = 0.8 calls per minute. Then, the probability that the agent can take 2 minutes for personal time without being interrupted by a call is:

P(W > 2) = e^(-0.8 * 2) = 0.4493

Alternatively, we can use the memoryless property of the exponential distribution to calculate:

P(W > 2) = P(W > 1 + 1) = P(W > 1) * P(W > 1) = e^(-0.8 * 1) * e^(-0.8 * 1) = 0.4493.

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Answer:

\(\sqrt{\frac{x}{2} }\)

Key:

• \(\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\)

Step-by-step explanation:

\(\frac{\sqrt{x}}{\sqrt{2}}\\\)

\(\frac{\sqrt{x}}{\sqrt{2}}=\sqrt{\frac{x}{2}}\\\)

\(=\sqrt{\frac{x}{2}}\)

The fully factored form of 2x^2 + 10x - 12, both through grouping and factoring out the GCF, is 2(x + 6)(x - 1).

To find the greatest common factor (GCF) of the expression 2x^2 + 10x - 12, we need to identify the largest common factor among all the coefficients and variables. In this case, the GCF is 2.

To rewrite the expression with four terms, we can factor out the GCF from the first two terms and the last two terms. Here's the breakdown:

2x^2 + 10x - 12

First, let's factor out the GCF, which is 2:

2(x^2 + 5x - 6)

Now we have the expression written with four terms: 2x^2 + 10x - 12 becomes 2(x^2 + 5x - 6).

To factor the expression further using the method of grouping, we need to find two numbers that multiply to -6 and add up to 5 (the coefficient of the middle term, 5x).

The numbers that satisfy these conditions are 6 and -1 since 6 * (-1) = -6 and 6 + (-1) = 5.

We can now rewrite the middle term (5x) as the sum of these two numbers:

2(x^2 + 6x - x - 6)

Now we can group the terms:

2[(x^2 + 6x) + (-x - 6)]

Next, we factor out the common factors from each group:

2[x(x + 6) - 1(x + 6)]

Notice that both terms in the brackets have a common factor, which is (x + 6). We can factor it out:

2(x + 6)(x - 1)

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Answer:

Te conozco y sé qué

Como Nuevo de fabrica el otro

Answer:

834 chirps

Step-by-step explanation:

Given the data:

Chirps in 1 min Temperature (°F)

781 74

1039 85.9

1156 87.2

1218 87.8

1131 91.4

888 75.5

Using technology, the regression model obtained will be in the form :

y = bx + c

b = slope ; c = intercept

y = temperature ; x = chirps per minute

The regression model is :

ŷ= 43.28 + 0.0390x

If outside temperature, y = 76 ; x will be ;

76 = 43.28 + 0.0390x

76 - 43.28 = 0.0390x

32.72 = 0.0390x

x = 32.72 / 0.0390

x = 838.97435

x = 834 chirps per minute

To show that {1, 2, 3} is linearly independent, we need to prove that the only solution to the equation a11 + a22 + a3*3 = 0 is a1 = a2 = a3 = 0.

Suppose that there exist constants a1, a2, and a3 such that a11 + a22 + a33 = 0. Since 1, 2, and 3 are all in 5, we know that they are nonzero. If a3 = 0, then a11 + a2*2 = 0. Since 2 is not a multiple of 1, a2 must be 0, which means a1 = 0 as well. So we have a1 = a2 = a3 = 0 in this case, and {1, 2, 3} is linearly independent.

If a3 is nonzero, we can divide both sides of the equation by a3 to get a1/ a31 + a2/ a32 + 3 = 0. This means that 3 is a linear combination of 1 and 2, which contradicts the given condition that 3 is not a linear combination of 1 and 2. Therefore, a3 must be 0, and we are back to the previous case where a1 = a2 = a3 = 0.

Therefore, {1, 2, 3} is linearly independent. The conditions that 1, 2, and 3 are in 5, 2 is not a multiple of 1, and 3 is not a linear combination of 1 and 2 are sufficient to show this.

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Answer:

Step-by-step explanation:

x will be the original weight.

2x - 20 = 180

2x = 200

x = 100

Answer:

38°

Step-by-step explanation:

Complementary means that they add up to 90
So then to find the measure of angle 2, subtract the measure of angle 1 from 90.

90-52=38

Answer:

38°

Step-by-step explanation:

Complementary means that the two angles add up to 90 degrees.

m∠1 + m∠2 = 90°

Substitute using the given value of m∠1

52° + m∠2 = 90°

m∠2 = 38°

Hope this helps :)

Have a great day!

Answer:

b i think

Step-by-step explanation:

becuase 45f in total and for every hour it decreses 2f the anwser would be b but i may be wrong

This selection process is referred to as "systematic sampling"

Systematic sampling is the sampling method where samples are selected based on a systematic interval in a population. It is a type of probability sampling, where every kth element in the population is selected as a sample, where k is a constant value.

The interval k is calculated by dividing the population size N by the sample size n; hence, k = N/n. In this case, the sample size is 100, and the population size is 100,000, so the interval is k = 1000. The selection process involved in this question is an example of systematic sampling because the selection of the 100 sales invoices is based on a systematic interval of 1000. Starting at a random point, every, 1000th sale invoice is selected until 100 are chosen.

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Answer:

factorize 48 in root ans is _4root 6+11root3