A type of bacteria doubles in number every 12 hours after 2 days there are 48 bacteria how many bacteria were there at the beginning of the first day

To calculate milk needed for a different number of pancakes and determine the amount of butter for a varied pancake quantity.

To calculate the amount of milk needed for 4 pancakes that Simon is making:

Divide the amount of milk needed for 8 pancakes (250ml) by 2 since 4 is half of 8. 250ml ÷ 2 = 125ml.

To determine the amount of butter for the 12 pancakes that Craig is making:

Since the recipe calls for 5g of butter for 8 pancakes, we can calculate the amount needed for 12 pancakes by setting up a proportion: (5g/8 pancakes) = (x/12 pancakes). Solving for x gives x = 7.5g.

Answer:

1. There are 648 total combinations that can be chosen.

2. After she choses two possiblilities the total number changes to 108 total posibilities to chose from

Step-by-step explanation:

possibility: 1/2 x 1/3 x 1/2 x 1/6 x 1/9 = 648

then you remove the first two because she chose those ones

1/2 x 1/6 x 1/9 = 108 possibilities left

Answer:

Step-by-step explanation:

1.       C

2.        C

3.         B

The question is a college-level mathematics problem focusing on statistics related to normal distribution, particularly the calculation of probabilities, defining a random variable, and understanding hypothesis testing and p-values.

The student's question pertains to the concept of normal distribution and statistics as applied to biological data. Specifically, it involves analysis using the mean and standard deviation of a dataset, and proper understanding of hypothesis testing and p-values in scientific research.

Understanding the Random Variable X

The random variable X, in this context, represents the duration of criminal trials. The question requires defining X and calculating related probabilities using the normal distribution properties. A probability statement and sketching of the graph would aid in visual understanding of the probabilities in question.

In statistical hypothesis testing, a p-value less than the level of significance (e.g., 0.01) typically leads to rejection of the null hypothesis, indicating evidence supporting the alternative hypothesis. The data on fruit flies' fecundity and genetic traits provided is an example of such an analysis.

Answer:

  y = -2

Step-by-step explanation:

The equation of a horizontal line is ...

  y = constant

In order to make it go through a point with a y-coordinate of -2, the value of the constant must be -2.

Your line is y = -2.

Answer:

The answer to the nearest foot is = 15 feet

Step-by-step explanation:

Solution

The first set taken is to  Compute L for a 55-mph speed limit

Given that

L =(θ2 -θ1)/200 (h +S Tan ∝) =

= ( u + 5) 336²/200 (1.9 +336 tan 0.7°)

= 9° (336)²/200 (1.9 +336 tan 0.7°) = 14.7652094

= 15 feet  { 9° = 9*π/180 = π/20}

Note: Kindly find an attached image for the complete question given and answered

Answer:

14 sq cm

Step-by-step explanation:

7 × 4 = 28

28 ÷ 2 = 14

brainliest?

Answer:

0.3876<p<0.4389

Step-by-step explanation:

-Given [tex]n=2472, \ x=1022 , \ CI=0.99[/tex]

-We calculate the proportion of surveys returned:

[tex]\hat p=\frac{1022}{2472}\\\\=0.4134[/tex]

For a 99% confidence interval:

[tex]z_{\alpha/2}=2.576[/tex]

#The margin of error is calculated as;

[tex]ME=z_{0.005}\times \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\=2.576\times \sqrt{\frac{0.4134(1-0.4134)}{2472}}\\\\=0.0255[/tex]

The confidence interval are then:

[tex]CI=\hat p\pm ME\\\\=0.4134\pm 0.0255\\\\=[0.3876,0.4389][/tex]

Hence, the confidence interval is 0.3876<p<0.4389

Final answer:

None of the provided expressions have a greatest common factor of 3xy² with 42xy⁴ because they do not contain the necessary factors of 3, x, and y².

Explanation:

The student is asking for expressions that have a greatest common factor (GCF) of 3xy² with 42xy⁴. To find expressions with a GCF of 3xy², we need to look for expressions that include multiples of 3xy² in their factorization.

Looking at the provided expressions:

Therefore, none of the provided expressions have a GCF of 3xy² with 42xy⁴.

Answer:

(a)[tex]\frac{7}{25}[/tex]

(b)[tex]\frac{19}{116}[/tex]

(c)[tex]\frac{28}{125}[/tex]

Step-by-step explanation:

Number of juniors who attended prom,n(J)=28

Number of seniors who attended prom,n(S)=97

Number of juniors who did not attend prom,n(J')=56

Number of seniors who did not attend prom,n(S')=19

(a) P (a junior who did not attend prom)

[tex]P(J')=\frac{56}{200}= \frac{7}{25}[/tex]

(b)

[tex]P(Senior)=\frac{116}{200}[/tex]

[tex]P ($did not attend prom$ | senior)=\frac{\text{P(seniors who did not attend prom)}}{P(Senior)} \\=\frac{19/200}{116/200} \\=\frac{19}{116}[/tex]

(c)P (junior | attended prom)

[tex]P(Senior)=\frac{84}{200}[/tex]

[tex]P (Junior|$ attended prom$)=\frac{\text{P(juniors who attended prom)}}{P(\text{those who attended prom)}} \\=\frac{28/200}{125/200} \\=\frac{28}{125}[/tex]

Answer:

A. P = 7/25

B. P = 19/116

C. P = 28/125

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly this way:

      Juniors  Seniors   Totals

Yes       28         97          125

No       56         19           75

Totals   84        116          200

2. Find the probability of each of the events.

Let's recall that the formula of probability is:

P = Number of favorable outcomes/Total number of possible outcomes

A. P (a junior who did not attend prom)

P = Juniors who did not attend prom/Total number of students surveyed

P = 56/200

P = 7/25 (Diving by 8 numerator and denominator)

B. P (did not attend prom | senior)

P = Seniors who did not attend prom/Total number of seniors surveyed

P = 19/116

C. P (junior | attended prom)

P = Juniors who attend prom/Total number of students attended prom

P = 28/125

The null hypothesis will be rejected if the test statistic is: greater than -2.33

The null hypothesis will be rejected if the test statistic falls within the critical region, which is determined by the significance level (0.01 in this case).

To determine the test statistic, calculate the z-score for the sample proportion and compare it to the critical value.

The formula to calculate the z-score for the sample proportion is:

[tex]z = (\hat{p} - p) / \sqrt(p * (1 - p) / n)[/tex]

Where:

[tex]\hat{p}[/tex] is the sample proportion (230/1189 = 0.193)

p is the population proportion (0.22)

n is the sample size (1189)

Calculating the z-score:

z = (0.193 - 0.22) / [tex]\sqrt[/tex](0.22 * (1 - 0.22) / 1189)

z = -2.25

To determine if the null hypothesis is rejected or not, compare the absolute value of the z-score to the critical value for a one-tailed test at a 0.01 significance level.

The critical value for a one-tailed test at a 0.01 significance level is approximately -2.33.

If the absolute value of the calculated z-score is greater than 2.33, we reject the null hypothesis.

Since absolute value of the calculated z-score is not greater than 2.33, null hypothesis is not rejected.

Answer:

a) [tex]P(E) = \frac{6}{8}[/tex]

b) [tex]P(F|E) = \frac{5}{7}[/tex]

c) [tex]P(E \cap F) = \frac{15}{28}[/tex]

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

We have that:

8 vehicles, of which 6 are vans.

a.) Let E denote the event that the first vehicle assigned is a van. What is P(E) ?

8 vehicles, of which 6 are vans.

So

[tex]P(E) = \frac{6}{8}[/tex]

b.) Let F denote the probability that the second vehicle assigned is a van. What is P(F|E)?

P(F|E) is the probability that the second vehicle assigned is a van, given that the first one was.

In this case, there are 7 vehicles, of which 5 are vans. So

[tex]P(F|E) = \frac{5}{7}[/tex]

c.) Use the results of parts(a) and (b) to calculate P(E and F)

[tex]P(F|E) = \frac{P(E \cap F)}{P(E)}[/tex]

[tex]P(E \cap F) = P(F|E)P(E)[/tex]

[tex]P(E \cap F) = \frac{6}{8}\frac{5}{7}[/tex]

[tex]P(E \cap F) = \frac{15}{28}[/tex]

The probability of the first vehicle assigned being a van is 3/4, and the conditional probability of the second vehicle being a van given the first was a van is 5/7. The probability that both vehicles assigned are vans is 15/28.

The subject of this question is probability, a topic in Mathematics. We are asked to find the probability of a certain event occurring under certain conditions.

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Answer:

it equals 1

Step-by-step explanation:

(5)(2)+2x−7=5

Step 1: Simplify both sides of the equation.

(5)(2)+2x−7=5

10+2x+−7=5

(2x)+(10+−7)=5(Combine Like Terms)

2x+3=5

2x+3=5

Step 2: Subtract 3 from both sides.

2x+3−3=5−3

2x=2

Step 3: Divide both sides by 2.

2x

2

=

2

2

x=1

Answer:

the interval would get bigger.

Step-by-step explanation:

if you wanted to be more confident in the interval you're giving, you would make more of the answers fit under the umbrella you're hypothetically creating.

Answer:

The value of t test statistics is 4.518.

Step-by-step explanation:

We are given that director of a radio broadcasting company wants to determine whether the mean length of commercials on his station is equal to 24 seconds.

He samples 200 commercials, and finds that the average length of these commercials is 26.3 seconds, with a standard deviation of 7.2 seconds.

Let [tex]\mu[/tex] = mean length of commercials on his station.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 24 seconds     {means that the mean length of commercials on his station is equal to 24 seconds}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 24 seconds     {means that the mean length of commercials on his station is different from 24 seconds}

The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;

                        T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average length of these commercials = 26.3 seconds

            s = sample standard deviation = 7.2 seconds

            n = sample of commercials = 200

So, test statistics  =  [tex]\frac{26.3-24}{\frac{7.2}{\sqrt{200} } }[/tex]  ~ [tex]t_1_9_9[/tex]  

                               =  4.518

The value of t test statistics is 4.518.

Answer:

90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

Step-by-step explanation:

We are given that a sample of 37 cars traveling on a particular stretch of highway revealed an average speed of 70.7 miles per hour with a standard deviation of 6.3 miles per hour.

Firstly, the pivotal quantity for 90% confidence interval for the true mean is given by;

                            P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average speed of cars = 70.7 miles per hour

             s = sample standard deviation = 6.3 miles per hour

             n = sample of cars = 37

             [tex]\mu[/tex] = true mean speed

Here for constructing 90% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 90% confidence interval for the true mean, [tex]\mu[/tex] is ;

P(-1.688 < [tex]t_3_6[/tex] < 1.688) = 0.90  {As the critical value of t at 36 degree of

                                 freedom are -1.688 & 1.688 with P = 5%}  

P(-1.688 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 1.688) = 0.90

P( [tex]-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

P( [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.90

90% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.688 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+1.688 \times {\frac{s}{\sqrt{n} } }[/tex] ]

                    = [ [tex]70.7-1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] , [tex]70.7+1.688 \times {\frac{6.3}{\sqrt{37} } }[/tex] ]

                    = [68.9517 miles per hour , 72.4483 miles per hour]

Therefore, 90% confidence interval for the true mean speed of all cars on this particular stretch of highway is [68.9517 miles per hour , 72.4483 miles per hour].

The interpretation of the above interval is that we are 90% confident that the true mean speed of all cars will lie between 68.9517 miles per hour and 72.4483 miles per hour.

Answer:

-4

Step-by-step explanation:

Each term is 4 less than the term before it, so the common difference is -4.

Answer:

B. -4 on edge !!

Step-by-step explanation:

Got it right :)

Answer:

Barney 145 3 Days 310 Miles

Mary   250 5 Days 600 Miles

A)  3 D + 310 M = 145

B) 5 D + 600 M = 250

Multiplying A) by -5/3

A) -5 D - 516.6666M = -241.66666666

B) 5D + 600M = 250

Adding A) and B)

83.3333 M = 8.3333333333

M = .10 per mile

3 D = 114

Daily Rate = 38 dollars per day

Step-by-step explanation:

Answer:

i believe the answer is 1/27

Step-by-step explanation:

you take the fractions and multiply them all together.

1x1x1 equals 1

and 3x3x3 equals 27

meaning the answer is 1/27 :)

To calculate 1/3 x 1/3 x 1/3, you're effectively cubing 1/3, which results in (1/3)^3 or 1^3/3^3, simplifying to 1/27.

The student is asking about the multiplication of fractions and exponentiation rules in algebra. To solve 1/3 x 1/3 x 1/3, you multiply the fractions normally. When multiplying identical fractions, we simply raise the fraction to the power of the number of times it is being multiplied by itself. So 1/3 x 1/3 x 1/3 is equivalent to (1/3)^3. When you raise a fraction to an exponent, you raise both the numerator and the denominator to that power. Therefore, (1/3)^3 equals 1^3/3^3, which simplifies to 1/27.

The example given with 3².35 relates to the rules of exponents, which state that when multiplying exponential terms with the same base, you can add the exponents (x^p x x^q = x^(p+q)). For the concept of cubing of exponentials, you would cube the base and multiply the existing exponent by 3 to execute the operation effectively.

Answer:

12.

Step-by-step explanation:

Given that,

Number of while balls are 3

Number of green balls are 4

Number of red balls are 5

We need to find the total number of outcomes. We know the total number of outcomes in is number of choices.

In this case, total number of outcomes are the sum of all color balls i.e. 3 + 4 + 5 = 12 balls.

Hence, the total number of outcomes are 12.

Final answer:

The total number of outcomes when one ball is drawn at random from a bag containing 3 white, 4 green, and 5 red balls is 12.

Explanation:

A bag contains 3 white balls, 4 green balls, and 5 red balls. The total number of possible outcomes when a ball is drawn at random is simply the sum of all the balls in the bag. Since each ball can be selected in one distinct way, we calculate the total number of outcomes by adding the number of white balls, the number of green balls, and the number of red balls.

So, the total number of outcomes is:

3 (white) + 4 (green) + 5 (red) = 12 (total outcomes)

Therefore, there are 12 different possible outcomes when one ball is drawn at random from this bag.

Answer:

The model car is 10 inches long

Step-by-step explanation:

To solve this question, we use conversion of units

Feet to inches.

Each feet has 12 inches.

The car is 15ft long.

So the car has 15*12 = 180 inches.

.5 inches = 9 in.

Rule of three

.5 inches - 9 inches

x inches - 180 inches

[tex]9x = 180*0.5[/tex]

[tex]9x = 90[/tex]

[tex]x = \frac{90}{9}[/tex]

[tex]x = 10[/tex]

The model car is 10 inches long

To find the length of Uni's model car, we convert the actual car's length to inches, set up a proportion with the given scale, and cross-multiply to solve for the model car's length, resulting in a model that is 10 inches long.

The subject matter of the question is related to scale models, which falls under the field of Mathematics. To solve this problem, we need to find the length of the model car based on the given scale and the actual length of the car.

The scale given is 0.5 inches = 9 inches. Firstly, we need to convert the actual length of the car from feet to inches, so we can work in the same units. There are 12 inches in a foot, so a 15 feet long car is 15 x 12 inches long, which is 180 inches. Now, we need to set up a proportion to find the length of the model car:

Actual car length (inch) : Model car length (inch) = Actual scale (inch) : Model scale (inch) 180 inches (actual car length) : x inches (model car length) = 9 inches (actual scale) : 0.5 inches (model scale)

By cross-multiplying, we get:

(180 inches x 0.5 inches) = (x inches x 9 inches)

Dividing both sides by 9 inches, we get:

x inches = (180 inches x 0.5 inches) / 9 inches

So, the length of the model car is:

x inches = 10 inches.

Therefore, Uni's model car is 10 inches long.

Answer:

3

Step-by-step explanation:

Answer:

The calculated value z = 1.3145 < 2.326 at  0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Step-by-step explanation:

Step(i):-

An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

The mean of the Population 'μ' = 28.0miles/gallon

Given data after testing 270 cars, they found a mean MPG of 27.8. Assume the variance is known to be 6.25.

The sample size 'n' = 270

Mean of the sample 'x⁻' = 27.8

Given Population variance 'σ² = 6.25

The standard deviation of Population 'σ' = √6.25 = 2.5

Step(ii):-

Null hypothesis :H₀: 'μ' = 28.

Alternative hypothesis :H₁: 'μ' ≠28.

The test statistic

[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]

[tex]Z = \frac{27.8-28 }{\frac{2.5}{\sqrt{270} } } = \frac{-0.2}{0.15214}[/tex]

Z = -1.3145

|Z| = |-1.3145|= 1.3145

Step(iii):-

The tabulated value  of z-score at 0.02 level of significance = 2.326

The calculated value z = 1.3145 < 2.326 at a t 0.02 level of significance

The null hypothesis is accepted

Hence An automobile manufacturer claims that its car has a 28.0 miles/gallon (MPG) rating.

Answer:

Weight of mixing water=224.541 lb

Step-by-step explanation:

Taking 1 cubic yard of concrete

Mass of gravel = 2314 lb

Moisture content = 3.5% Absorption 4.2%

Extra water needed = (4.2-3.5)*2314/100= 16.198 lb

Mass of sand= 899 lb

Moisture content = 5.7% Absorption =1.4%

Water released = (5.7-1.4)*899/100= 38.657 lb

Free water = 244 lb

Weight of mixing water = free water + extra water needed-water released = 244+16.198-38.657=224.541 lb

Weight of mixing water=224.541 lb

Answer:

24 324

Step-by-step explanation:

21334 fda  adf

Answer: 24, 324

Step-by-step explanation:

Find the perimiter of both sides

Answer:

  7 is located to the right of -2

Step-by-step explanation:

Larger numbers are to the right on a number line, so the statement that 7 is larger than -2 means ...

  7 is located to the right of -2

Final answer:

The question involves Mathematics and requires understanding of statistics and normal distribution to find z-scores for designing helmets to fit a specific range of male head breadths, accommodating all except the smallest and largest 4.3%.

Explanation:

The subject of this question is Mathematics, specifically focusing on statistics and the concept of normal distribution. Engineers designing helmets need to consider the breadths of male heads, which are normally distributed with a given mean and standard deviation. The design requirements stipulate that the helmets should fit all men except for those in the extremities of the distribution (smallest 4.3% and largest 4.3%).

To address such a problem, one would typically use the z-score to identify the cutoff points on a standard normal distribution that correspond to these percentages. The z-score represents the number of standard deviations a data point is from the mean. Therefore, the engineers must calculate the z-scores that correspond to the smallest and largest 4.3% of the distribution to determine the range of head breadths the helmets must accommodate.

Answer:

the answer is container c

b=11.14in2

12in

Step-by-step explanation:

Answer:

Answer is C

Step-by-step explanation:

Answer:

(-0.5,-2.5)

Step-by-step explanation:

(x1 + x2) / 2 = x midpoint

(y1 + y2) / 2 = y midpoint

x)

2 + -3 = 5

5 / 2 = -0.5

y)

4 + -9 = -5

-5 / 2 = -2.5

= (-0.5, -2.5)

The midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.

We have to find the midpoint of A and B where A has coordinates (2, 4)

and B has coordinates (-3, -9).

Midpoint = (2-3/2, 4-9/2)

=(-1/2, -5/2)

Hence, the midpoint of A and B where A has coordinates (2, 4) and B has coordinates (-3, -9) is (-1/2, -5/2)

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Answer: gang in la

Step-by-step explanation:

Answer:

15/56

Step-by-step explanation:

Total = 8

3/8 × 5/7

15/56