Recipe for a dozen cookies calls for 2/4 cup of flour. How much flour would be needed to triple the recipe

Answer:

  0.46 seconds or 11.72 seconds

Step-by-step explanation:

Putting 87 for h in the height equation gives ...

  87 = -16t^2 +195t

Dividing by -16 puts this in a little nicer form for finding solutions.

  t^2 -(195/16)t = -87/16

To "complete the square", we can add the square of half the coefficient of t:

  t^2 -(195/16)t + (195/32)^2 = (195/32)^2 -87/16

  (t -195/32)^2 = 32457/1024

Taking the square root, we have ...

  t -195/32 = ±(1/32)√32457

  t = (195 ±√32457)/32 ≈ 0.4638 or 11.7237

The rocket is at a height of 87 feet after 0.46 seconds, and again after 11.72 seconds.

Answer: player A = 11/16 and player B = 5/16

Step-by-step explanation:

If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.

Player A needs 2 points = 11

Player B needs 3 points = 5

Total outcome of tossing a coin = 16

Player A = 11/16 = 0.6875

Player B = 5/16 = 0. 3125

Or

Using the fifth roll of the pascal triangle (2+3) outcome

( 1, 4, 6, 4, 1 )

Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11

And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning

Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16

Final answer:

The possible model for the number of incorrect questions that agree is a binomial distribution. The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers.

Explanation:

The possible model for the number of incorrect questions that agree is a binomial distribution because there are a fixed number of trials (the number of questions) and each trial has two possible outcomes (agree or disagree).

The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4, so the probability of agreeing on a particular question is 1/4. Since there are 20 questions, the probability that they agree on exactly 8 questions is given by the binomial probability formula: P(x = 8) = C(20, 8) * (1/4)^8 * (3/4)^12.

The teacher can use this model to calculate the probability of observing 8 or more agreed-upon answers by summing the probabilities of all possible outcomes with 8 or more agreed-upon answers: P(x ≥ 8) = P(x = 8) + P(x = 9) + ... + P(x = 20).

Answer:

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Step-by-step explanation:

Given;

Speed of sound v = 340 m/s

Frequency of sound f = 170 hz

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;

Length L = v/f = speed/frequency

L = 340/170

L = 2 m

The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m

Answer:

y = 1 + ¼x²

Step-by-step explanation:

Given

One more than one-fourth the square of a number x is y​

Required

Represent algebraically

We start by analysing the expression one after the other.

First, the two numbers to compare are represented by x and y.

Where y is the resulting number.

So, we start with y =;

Then we move backwards

- "the square of a number, x" can be represented with x²

- one-fourth "the square of a number, x".

The expression in quote has already been represented by x².

So, we can replace this expression with x².

This will give us: one-fourth of x²

One-fourth means ¼

Hence, one-fourth of x² = ¼ * x²

- "One more than" means 1 has to be added to the previous expression to give y.

In other words; 1 + ¼ * x²

Finally, we'll bring the expressions together to give

y = 1 + ¼ * x²

y = 1 + ¼x²

Hence, "One more than one-fourth the square of a number x is y​" is represented in algebra by y = 1 + ¼x²

Answer:

The volume of the sphere is 972π mm³

Step-by-step explanation:

To calculate the volume of a sphere we have to use the following formula:

V = volume

r = radius  = 9mm

π = pi

V = ⁴⁄₃πr³

we replace with the known values

V = ⁴⁄₃ * π * (9mm)³

V = π * ⁴⁄₃ *729mm³

V = π * 972mm³

V = 972π mm³

The volume of the sphere is 972π mm³

The cost of the fabric per yard is approximately $6.39.

To find the cost of the fabric per yard, we need to first calculate the cost per foot and then convert it to yards.

Step 1: Calculate the cost per foot of fabric.

[tex]Cost per foot = Total cost / Total feet[/tex]

[tex]Cost per foot = $9.60 / 4.5 feet[/tex]

[tex]Cost per foot = $2.13[/tex]

Step 2: Convert the cost per foot to cost per yard.

Since there are 3 feet in a yard, we can find the cost per yard by multiplying the cost per foot by 3.

[tex]Cost per yard = Cost per foot * 3[/tex]

[tex]Cost per yard ≈ $2.13 * 3[/tex]

[tex]Cost per yard = $6.39[/tex]

Complete correct question:

Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?

Answer:

The forumula for finding area of the circle is  \pi r^2.

Step-by-step explanation:

Let's find the radius of the mug:

r=\frac{d}{2}=\frac{8}{2}=4

Now, we can to express the area of each cookie in terms of pi:

Area= \pi *4^2=16\pi

Answer:

Number of students want to go to Theme Park = 75

Step-by-step explanation:

Note: The given question is incomplete. Complete question is as follow.

Given:

Number of sample student = 30

Place                 Number of students  want to go

Theme Park                          10

Theater                                  5

Sports Center                        8

Seaside                                  7

Find:

How many students want to go to Theme Park.

Computation:

⇒ Probability for  students want to go to Theme Park =  10 / 30

⇒ Probability for  students want to go to Theme Park =  1 / 3

⇒ Number of students want to go to Theme Park =  [1 / 3]225

⇒ Number of students want to go to Theme Park = 75

Final answer:

Using a sample proportion, if 12 out of 30 students chose the Theme Park, we estimate that 90 out of 225 students will want to go to the Theme Park.

Explanation:

To estimate how many of the 225 students will want to go to the Theme Park, we use the results from Sally's sample of 30 students. First, we need to know the number of students in the sample who chose the Theme Park. Suppose, for instance, that 12 out of the 30 sampled students chose the Theme Park. We can set up a proportion to find the estimated number of students out of 225 who would choose the same.

Here's the proportion based on the sample data:

Number of students who chose Theme Park in the sample / Total number of students in the sample = Estimated number of students who will choose Theme Park / Total number of students planning to go

In our example, this is 12/30 = x/225, where x is the estimated total.

We cross-multiply to solve for x:

12 × 225 = 30 × x

x = (12 × 225) / 30

x = 90

Thus, we estimate that 90 out of the 225 students will prefer to go to the Theme Park.

Answer:

4

Step-by-step explanation:

n/6+2

Let n = 12

12/6 +2

Division first

2 +2

4

Answer:

4

Step-by-step explanation:

plug in 12 for n and you get :: 12/6 + 2

PEMDAS says to divide first, 12/6 is 2. you add 2 next and you get 4

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Answer:

Step-by-step explanation: Opposite sides of a parallelogram are equal.

Answer:

The opposite sides of the parallelogram have equal lengths.

Step-by-step explanation:

PLATO SAMPLE

Answer:

Substitute the slope and the coordinate of D into the equations and solve for b for each equation

Step-by-step explanation:

The equation for a line is y = mx+b

where m is the slope and b is the y intercept

We know m

We have a point (x,y)

We can substitute into the equation and solve for b

Answer:

First option

Step-by-step explanation:

In y = mx + b, m is the slope and b is the y-intercept

Plug in m, and coordinates of D and solve for b

Answer:

its 6

just simplify the expression.

-Hops

Answer: 6

Divide

18÷9=2

Multiply

2×3=6

Answer:

13/15

Step-by-step explanation:

First, you find a common denominator. 10 x 3 and 6 x 5 both equal 30, so 30 can be used as a common denominator. You also have to multiply the numerator by the same number you multiplied in the denominator. Since we did 10 x 3, do 7 x 3, and with the other fraction we did 6 x 5, so do 1 x 5. You should get 21/30 + 5/30. Since they have the same denominator, you can add them. You'll get 26/30, which can still be simplified. 30 divided by 2 is 15, and 26 divided by 2 is 13. The final answer is 13/15.

Answer:

x = 36

Step-by-step explanation:

Given;

(8/9)x = 32

Solving for x

Multiply through by 9

(8/9)×9 ×x = 32×9

8x = 32×9

Divide through by 8

8x/8 = 32×9/8

x = 36

Answer:

INCORRECT: The range of the F value is (-[infinity], +[infinity])

Step-by-step explanation:

While it's true that there is no maximum value to an F value, you cannot have a negative F statistic and the lowest value you can have is zero.

The incorrect statement about ANOVA test is that the range of F value is (-∞, ∞).

ANOVA test is abbreviated for Analysis of Variance. This test is used to find whether there is a significant difference between the means of certain number of groups using variance.

Null hypothesis in an ANOVA test is that there is no difference in the mean of groups. Alternate hypothesis of ANOVA test is that at least one of the group has different mean than others.

In ANOVA test, an F value is the ratio of variation between sample means to the variation within sample means. So the first statement which says F value as a ratio of between-group mean square to within-group mean square is correct.

We have ANOVA test is an appropriate test for comparing three or more independent groups in a continuous variable. Second statement is also correct.

The value of F will always be positive. The range of F starts from 0. So the statement that range of F value is (-∞, ∞) is incorrect.

By the definition of ANOVA test itself, we can say that a significant test result in ANOVA means that means are not all equal. So fourth statement is also correct.

Hence the statement range of F value is (-∞, ∞) is incorrect.

Learn more about ANOVA here :

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We have been given that Regan sold 14 necklace and made a total of $210. Each necklace cost the same amount. We are asked to find the cost of one necklace.

To find the cost of one necklace, we will divide total cost by total number of necklaces as:

[tex]\text{Cost of one necklace}=\frac{\text{Total cost}}{\text{Total necklaces}}[/tex]

[tex]\text{Cost of one necklace}=\frac{\$210}{14}[/tex]

[tex]\text{Cost of one necklace}=\$15[/tex]

Therefore, the cost of one necklace is $15.

Answer:

a) At least 842 adults must be surveyed.

b) At least 1068 adults must be surveyed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

a) 73% of adults used the Internet.

At least n adults must be surveyed.

n is found when [tex]M = 0.03, \pi = 0.73[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]

[tex]n = 841.3[/tex]

Rounding up

At least 842 adults must be surveyed.

b. No known possible value of the proportion.

Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]

[tex]n = 1067.11[/tex]

Rounding up

At least 1068 adults must be surveyed.

To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.

To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:

n = (Z² * p(1-p)) / E^2

Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).

Plug in the values:

n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14

Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.

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Answer:

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Step-by-step explanation:

Suppose we have a quadratic equation in the following format:

[tex]y = f(x) = ax^{2} + bx + c[/tex]

The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which

[tex]x_{v} = -\frac{b}{2a}[/tex]

In this problem:

[tex]f(x) = x^{2} - x + 2[/tex]

This means that [tex]a = 1, b = -1, c = 2[/tex]

So

[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]

[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]

The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]

Answer: 105

Step-by-step explanation:

Answer:

105

Step-by-step explanation:

C

Answer:

63.

Step-by-step explanation:

To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:

8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8

Now, this will get rid of the fractions, giving us:

x-56= 7

Next, simply add 56 to both sides:

x-56+56= 7+56

This results in:

x=63.

Answer:

C=2πr

Step-by-step explanation:

Answer: y= -4x + 1

Step-by-step explanation:

(-1,5) (1,-3)

5-(-3)=8

-1-1=-2

8/-2=-4  negative 4 is the slope. Now find the y-intercept using the formula y=mx + b where b is the y intercept.

so we will plot the  y and x values plus the slope to find the y-intercept.

5=-4(-1) + b  solve for b

5=4 + b

b=1

so now will write the equation y = -4x +1

Answer:45=3x3x5

Step-by-step explanation:

prime factorization of 45

45 ➗ 3=15

15 ➗ 3=5

5 ➗ 5=1

45=3x3x5

Final answer:

The prime factorization of 45 is found by dividing it into prime numbers, leading to the result of 3² x 5.

Explanation:

The prime factorization of 45 is the process of breaking down the number 45 into a product of prime numbers.

To find the prime factorization, we can start by dividing 45 by the smallest prime number 2, but since 45 is not even, we move to the next prime number, which is 3. We find that 45 is divisible by 3 (45 ÷ 3 = 15).

We continue the process with the quotient. Since 15 is also divisible by 3 (15 ÷ 3 = 5), we divide it by 3 again.

Finally, we are left with the number 5, which is a prime number.

Therefore, the prime factorization of 45 is 3² x 5.

Answer:

I E I ≤ 0.0522

Step-by-step explanation:

See attached image file

Answer:

[tex]z=\frac{87.8-90.1}{\frac{17.3}{\sqrt{38}}}=-0.820[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z<-0.820)=0.412[/tex]  

Since the p value is very high ant any significance level we will have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the true mean is not significantly different from 90.1 and the method not shows a significantly effect in the scores.

Step-by-step explanation:

Information provided

[tex]\bar X=87.8[/tex] represent the sample mean for the scores on the standardized test in the general population of 6th graders    

[tex]\sigma=17.3[/tex] represent the population standard deviation

[tex]n=38[/tex] sample size  

[tex]\mu_o =90.1[/tex] represent the value that we want to verify

z would represent the statistic

[tex]p_v[/tex] represent the p value for the test

System of hypothesis

We want to verify if the new teaching method negatively affects reading comprehension scores, so then the system of hypothesis for this case are:

Null hypothesis:[tex]\mu =90.1[/tex]  

Alternative hypothesis:[tex]\mu \neq 90.1[/tex]  

Since we know the population deviation the statistic would be:

[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)  

Replacing the info given we got:

[tex]z=\frac{87.8-90.1}{\frac{17.3}{\sqrt{38}}}=-0.820[/tex]  

The p value for this case would be given by:

[tex]p_v =2*P(z<-0.820)=0.412[/tex]  

Since the p value is very high ant any significance level we will have enough evidence to FAIL to reject the null hypothesis, so then we can conclude that the true mean is not significantly different from 90.1 and the method not shows a significantly effect in the scores.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 90.1

For the alternative hypothesis,

µ < 90.1

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 90.1

x = 87.8

σ = 17.3

n = 38

z = (87.8 - 90.1)/(17.3/√38) = - 0.82

Looking at the normal distribution table, the probability corresponding to the z score is 0.21

Assume significant level = 0.05

Since alpha, 0.05 < than the p value, 0.21, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, there is not enough evidence to conclude that the new teaching method negatively affects reading comprehension scores.

Answer:

2y² -4y +5

Step-by-step explanation:

First you need to find the sum of y²+5y-1 and 3y²-2y+4

(y²+5y-1) + (3y²-2y+4) => y²+3y²+5y-2y-1+4

                                  =4y²+3y+3

Next is to subtract 2y²+7y-2 from the sum calculated above in order to  find the algebraic expression asked in the exercise

4y²+3y+3 -(2y²+7y-2) => 4y²-2y²+3y-7y+3+2

                                   =2y² -4y +5

Therefore, the algebraic expression asked must be 2y² -4y +5

Answer:

5x+4y=85-

 Slope = -2.500/2.000 = -1.250

 x-intercept = 85/5 = 17

 y-intercept = 85/4 = 21.25000

2x+3y=41-

 Slope = -1.333/2.000 = -0.667

 x-intercept = 41/2 = 20.50000

 y-intercept = 41/3 = 13.66667

Answer:

-3/4

Step-by-step explanation:

(3 - 0)/(1 - 5) =

3/-4 =

-3/4

Answer:

-3/4

Step-by-step explanation:

This question is actually quite easy and can be done through the process of elimination. We are going from x=1 to x=5, so we are going right. We are going from y=3 to y=0, so we are going down. Because we are going down as we move right, the slope must be negative.

The actual equation for slope is:

(y2-y1)/(x2-x1) for (x1, y1), (x2, y2)