Which expression represents the area of the base of the cone? A cone with diameter 12 inches, height 8 inches, and slant height 10 inches. B = pi r squared (pi) (5 squared) (pi) (6 squared) (pi) (10 squared) (pi) (12 squared)

4. 1<x<5

5. 23<y

6. x=y÷2+1

Answer:

quadratic

Step-by-step explanation:

The slοpe οf the line passing thrοugh the pοints (-2,-4) and (3,-4) is 0.

In mathematics, slοpe refers tο the measure οf the steepness οf a line. It is defined as the ratiο οf the vertical change (rise) between twο pοints.

Tο find the slοpe οf the line passing thrοugh the pοints (-2,-4) and (3,-4), we can use the slοpe fοrmula:

slοpe = (change in y) / (change in x)

Let's call the first pοint (-2,-4) "pοint 1" and the secοnd pοint (3,-4) "pοint 2". Then, we have:

change in y = y2 - y1 = (-4) - (-4) =

change in x = x2 - x1 = 3 - (-2) = 5

Substituting these values intο the slοpe fοrmula, we get:

slοpe = (change in y) / (change in x) = 0 / 5 = 0

Hence, the slοpe οf the line passing thrοugh the pοints (-2,-4) and (3,-4) is 0.

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Answer:

x = 4\(\sqrt{6}\) , y = 8\(\sqrt{2}\)

Step-by-step explanation:

Using the sine ratio in the right triangle on the left and the exact value

sin45° = \(\frac{\sqrt{2} }{2}\)

let the altitude of the outer triangle be h ( common to both right triangles )

sin45° = \(\frac{opposite}{hypotenuse}\) = \(\frac{h}{8}\) = \(\frac{\sqrt{2} }{2}\) ( cross- multiply )

2h = 8\(\sqrt{2}\) ( divide both sides by 2 )

h = 4\(\sqrt{2}\)

----------------------------------------------------------------

Using the tangent ratio in the right triangle on the right and the exact value

tan30° = \(\frac{1}{\sqrt{3} }\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{h}{x}\) = \(\frac{4\sqrt{2} }{x}\) = \(\frac{1}{\sqrt{3} }\) ( cross- multiply )

x = 4\(\sqrt{6}\)

--------------------------------------------------------------------

Using the sine ratio in the right triangle on the right and the exact value

sin30° = \(\frac{1}{2}\) , then

sin30° = \(\frac{h}{y}\) = \(\frac{4\sqrt{2} }{y}\) = \(\frac{1}{2}\) ( cross- multiply )

y =8\(\sqrt{2}\)

The number of non-zero values in a tridiagonal matrix increases with the size of the matrix.

A tridiagonal matrix is a type of matrix that consists of three diagonals. The main diagonal is the diagonal that runs from the top left corner of the matrix to the bottom right corner. The secondary diagonal is the diagonal that runs from the top right corner of the matrix to the bottom left corner. The third diagonal is the diagonal that runs from the top left corner of the matrix to the bottom right corner, one row above the main diagonal. The number of non-zero values in a tridiagonal matrix of size n x n can be calculated using the formula: Nnz = 2n + (n-2). For example, for a tridiagonal matrix of size 4 x 4, the number of non-zero values would be 2 x 4 + (4-2) = 10. In general, the number of non-zero values in a tridiagonal matrix increases with the size of the matrix.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

q1 (1,-3)

r1 (3,3)

s1 (0,2)

t1 (-2,-1)

Step-by-step explanation:

When a shape is reflected, it must be reflected across a line

The vertices for \(\mathbf{rx-axis}\) of qrst are:

The given parameters are:

\(\mathbf{q = (1,3)}\)

\(\mathbf{r = (3,-3)}\)

\(\mathbf{s = (0,-2)}\)

\(\mathbf{s = (-2,1)}\)

The transformation rule is given as:

\(\mathbf{rx-axis}\)

The above rule means that the vertices are reflected over the x-axis

The rule of the transformation is:

\(\mathbf{(x,y) \to (x,-y)}\)

So, we have:

\(\mathbf{q(1,3) \to q'(1,-3)}\)

\(\mathbf{r(3,-3) \to r'(3,3)}\)

\(\mathbf{s(0,-2) \to s'(0,2)}\)

\(\mathbf{t(-2,1) \to t'(-2,-1)}\)

Hence, the vertices for \(\mathbf{rx-axis}\) of qrst are:

\(\mathbf{q'(1,-3)}\)

\(\mathbf{ r'(3,3)}\)

\(\mathbf{ s'(0,2)}\)

\(\mathbf{t'(-2,-1)}\)

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a) The initial population is \(N_0\) = 125 / \(e^{(2k)}\).

b) The exponential growth model for the bacteria population is N = \(N_0\) × \(e^{(kt)}\).

c) The number of bacteria after 8 hours is N = \(N_0\) × \(e^{(8k)}\).

d) After t = ln(25,000 / \(N_0\)) / k hours the bacteria count will be 25,000.

(a) To calculate the beginning population, we must first establish the bacterium population's exponential growth rate. Assume that the initial bacterial population is \(N_0\). The exponential growth model is given by:

N = \(N_0\) × \(e^{(kt)}\)

Where N is the number of bacteria at time t, \(N_0\) is the starting population, e is the natural logarithm base, k is the growth rate constant, and t is time in hours.

We have two data sets: N = 125 after two hours and N = 350 after four hours. We can solve using these two equations \(N_0\) and k.

(125) = \(N_0\) × \(e^{(2k)}\)

(350) = \(N_0\) × \(e^{(4k)}\)

Dividing the second equation by the first equation:

(350/125) = \(e^{(2k)}\)

Taking the natural logarithm of both sides:

ln(350/125) = 2k

Solving for k:

k = ln(350/125) / 2

Now that we have k, we can plug it into either equation and solve for it. \(N_0\):

\(N_0\) = 125 / \(e^{(2k)}\)

(b) The bacterium population's exponential growth model is:

N = \(N_0\) × \(e^{(kt)}\)

Where \(N_0\) = 125 / \(e^{(2k)}\) and k = ln(350/125) / 2

(c) To calculate the number of bacteria present after 8 hours, we use the exponential growth model with t = 8:

N = \(N_0\) × \(e^{(8k)}\)

(d) To calculate the time when the bacterium count reaches 25,000, enter N = 25,000 into the exponentially growing model and solve for t:

25,000 = \(N_0\) × \(e^{(kt)}\)

t = ln(25,000 / \(N_0\)) / k

However, in the absence of a specified growth rate constant (k) and starting population (\(N_0\)), we are unable to determine a precise value for t.

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The question is -

The number of bacteria in the culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours.

(a) Find the initial population.

(b) Write an exponential growth model for the bacteria population. (Let t represent time in hours)

(c) Use the model to determine the number of bacteria after 8 hours.

(d) After how many hours will the bacteria count be 25,000?

The actual quotient and the estimated quotient of 78,070÷37 is 2110 , so the difference between them is 0.

On dividing 78,070 by 37 ,

we get

78,070 /37

=2110

Since , the number gets divided completely

therefore the estimated quotient and the actual quotient will be 2110.

We first round the dividend and the divisor to the closest tens, hundreds, or thousands, and then divide the rounded figures to approximate the quotient. When the divisor in a division sum has two or more digits, it is helpful to first estimate the quotient before attempting to discover the exact number.

The outcome of dividing two numbers is known as the quotient. Divided divisor = quotient + remainder is the formula for expressing the terms of division.

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According to the information, we can infer that the number of ounces of water, x, that Will could have put in each cup is 8 ounces.

Will initially had a cooler filled with 144 ounces of water. After using 16 ounces to fill his water bottle, there were 144 - 16 = 128 ounces of water remaining in the cooler.

Will then took out 16 plastic cups for his teammates. Since the same amount of water was put in each cup, the remaining amount of water, 128 ounces, needs to be divided equally among the cups.

Dividing 128 ounces by 16 cups gives us 8 ounces of water for each cup.

So, Will could have put 8 ounces of water in each cup.

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Answer:

Some factors of 9 are 9,18,27,36,45,54,63,72,81,90,99,108 so the first multiple of 9 would be 9

Answer:

C. 21^10

Step-by-step explanation:

(3 * 7)^10 = 16679880978201

Correct option is (IV). kurtosis measure of the normal distribution = 3

Kurtosis is frequently defined as a measure of peakedness or flatness. However, this is deceptive. It is a measure of the distribution's tail heaviness (and skewness measure whether one tail is heavier than the other).

Normal distribution curve determines the skewness of the data as to what extent is is disoriented from the normal distribution curve. Also, it is the probability distribution curve that determines whether the data set is two legged, one legged or it lies under which probability curve.

Because these parameters are purely shape-related, they should not be affected by the mean or standard deviation. Pearson's measures use moments about the mean to avoid relying on the mean and scale the variables to eliminate the standard deviation. Because the normal distribution has only two parameters, the skewness and kurtosis are constants. The kurtosis value is 3.

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Answer:

- Mean of sampling distribution = 55%

- Standard deviation of the sampling distribution = 7%

- 68% of the distribution (about 136 of the 200 samples have sample proportions that) lie within 1 standard deviation of the mean, that is, within (55% ± 7%) = (48%, 62%).

- 95% of the distribution (about 190 of the 200 samples have sample proportions that) lie within 2 standard deviations of the mean, that is, within (55% ± 14%) = (41%, 69%).

- 99.7% of the distribution (almost all of the 200 samples have sample proportions that) lie within 3 standard deviations of the mean that is, within (55% ± 21%) = (34%, 76%).

Step-by-step explanation:

Population proportion = 55% = 0.55

Mean proportion of the sampling distribution too = 0.55

For a binomial distribution to approximate a normal distribution,

np ≥ 10

n(1-p) ≥ 10

np(1-p) ≥ 10

Note that n = sample size

p = proportion of medical doctors at the hospital that have prescribed a particular medication.

np = 50 × 0.55 = 27.5 ≥ 10

n(1-p) = 50×0.45 = 22.5 ≥ 10

np(1-p) = 50×0.55×0.45 = 12.375 ≥ 10

Hence, this sampling distribution is approximately normal.

Standard deviation of the sampling distribution is given as

σₓ = √[p(1-p)/n] = √[0.55×0.45/50] = 0.0703562364 = 0.0704 = 7.04% ≈ 7%

The empirical law for normal distributions explains that 68% of the distribution (about 136 of the 200 samples have sample proportions that) lie within 1 standard deviation of the mean, that is, within (55% ± 7%) = (48%, 62%).

95% of the distribution (about 190 of the 200 samples have sample proportions that) lie within 2 standard deviations of the mean, that is, within (55% ± 14%) = (41%, 69%).

99.7% of the distribution (almost all of the 200 samples have sample proportions that) lie within 3 standard deviations of the mean that is, within (55% ± 21%) = (34%, 76%).

Hope this Helps!!!

Answer:

Its correct I took the test!

Step-by-step explanation:

!!

The remainder when x³ - 1 is divided by (x + 3) is  -28

The functions are given as

x 3 1 is divided by x 3

Rewrite them as

f(x) = x³ - 1 is divided by (x + 3)

Set the divisor to 0

So, we have

x + 3 = 0

Determine the value of x

This gives

x = -3

By the remainder theorem

Substitute x = -3 in the function f(x)

So, we have

f(-3) = (-3)³ - 1

Evaluate the expression

f(-3) = -28

By the remainder theorem, this represents the remainder

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the probability that he found his dog. alive is 15%.

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Probability theory is a branch of mathematics that focuses on calculating the likelihood that an event will occur. Probability measures how likely something is to happen.

if he searched in a for two days and b for two days

P(A) = 0.4

P(B) = 0.6

P(Dn D-1 F-1)= n n+2

P(FnA, Sn, F-1) = 0.25

P(FB, S, F-1) = 0.15

Hence the probability that he found his dog. alive is 15%.

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Answer: it’s 40

hope this helps :)

Step-by-step explanation:

Just substitute the variable with the number and use pemdas.

First you have to multiply 5/13 by -26, then add 50 to what you get.

The correct inverse of the function \(f(x) = -3\sqrt[3]{4x}\) is \(f^{-1}(x) = \frac{-x^3}{108}\), not \(-\frac{x^2}{4}\).

To find the inverse of a function, we usually follow the steps of swapping the variables and solving for the new dependent variable. Let's apply these steps to the function \(f(x) = -3\sqrt[3]{4x}\) to find its inverse.

1. Swap the variables:

Swap \(x\) and \(y\) to obtain \(x = -3\sqrt[3]{4y}\).

2. Solve for the new dependent variable:

Start by isolating the cube root term:

\[\frac{x}{-3} = \sqrt[3]{4y}\]

Next, cube both sides to eliminate the cube root:

\[\left(\frac{x}{-3}\right)^3 = (4y)\]

Simplify and solve for \(y\):

\[\frac{x^3}{-27} = 4y\]

\[y = \frac{-x^3}{108}\]

Hence, the inverse of the function \(f(x) = -3\sqrt[3]{4x}\) is \(f^{-1}(x) = \frac{-x^3}{108}\), not \(-\frac{x^2}{4}\). It seems there might have been an error in the given answer.

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Based on the information provided, Jameela, who lives in poverty and has a diet mainly consisting of legumes, whole-grain breads and rice, fruits, and a few vegetables, is most at risk of nutrient deficiencies.

Jameela's limited access to a varied and balanced diet puts her at risk of nutrient deficiencies. While legumes, whole-grain breads, rice, fruits, and vegetables can provide essential nutrients, it is important to have a diverse range of food sources to ensure an adequate intake of all necessary vitamins, minerals, and other nutrients.

The heavy veils worn by Jameela may further contribute to her risk of nutrient deficiencies. The veils may limit her approach to sunlight, which is an important source of vitamin D synthesis in the body. Vitamin D is crucial for bone health and overall immune function. If Jameela does not have alternative sources of vitamin D in her diet or through supplements, she may be at risk of deficiency.

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\(2y = 3x + 6\\y = \frac{3}{2}x + \frac{6}{2} = \frac{3}{2}x + 3\)

The correct property of the quadratic parent function is given by:

B. Its vertex is at the origin.

The quadratic parent function is modeled by:

y = x².

It has the vertex at the origin and increases to the left and to the right, into quadrants I and II, forming a function that is graphed by a parabola.

Hence the correct option regarding a property of the quadratic parent function is given by:

B. Its vertex is at the origin.

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The probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.

The probability is a metric for determining how likely an event is to occur. It assesses the event's certainty. P(E) = Number of Favorable Outcomes / Number of Total Outcomes is the probability formula.

To calculate the probability of a Type I error, we first need to specify the null and alternative hypotheses.

Null hypothesis: The true mean weight of cereal in the boxes is equal to or greater than 520 grams.

Alternative hypothesis: The true mean weight of cereal in the boxes is less than 520 grams.

Let's denote the true mean weight of cereal in the boxes as μ. Under the null hypothesis, we have μ ≥ 520.

We can use the fact that the distribution of fills is normal with a known standard deviation of 3 grams to find the sampling distribution of the sample mean weight of cereal in a sample of size 3. Since we are sampling without replacement, we need to use the formula for a finite population:

Standard error of the sample mean = standard deviation / sqrt(sample size) * sqrt(N-n/N-1)

where N is the population size (the total number of boxes filled), n is the sample size (3 in this case), and N-1 is the degrees of freedom.

We know that the population mean is μ and the population standard deviation is 3 grams. We also know that the machine is set to put 523 grams in each box, so N (the population size) is equal to 515 / 523 times the number of boxes filled. Let's assume that the machine fills 10,000 boxes per day, so N = 9,856.

Plugging in the values, we get:

Standard error of the sample mean = 3 / √(3) * √(9,856-3/9,855) = 1.539 grams

Next, we need to find the critical value of the sample mean weight that separates the rejection region (when we reject the null hypothesis) from the acceptance region (when we fail to reject the null hypothesis).

Since the alternative hypothesis is one-tailed (we are only interested in the left tail), we can use a one-tailed t-test with a significance level of 0.05. The degrees of freedom is n-1 = 2.

Using a t-table or a calculator, we find the critical value to be -2.353.

Finally, we can calculate the probability of a Type I error as follows:

Probability of Type I error = P(reject null | null is true)

= P(sample mean < critical value | μ ≥ 520)

= P(z < (critical value - μ) / standard error of the sample mean | μ ≥ 520)

= P(z < (-2.353 - 520) / 1.539 | μ ≥ 520)

= P(z < -9.747 | μ ≥ 520)

= extremely small (close to 0)

Therefore, the probability of a Type I error is extremely small, which means that the workers are unlikely to make a mistake by shutting down the machine too often when the true mean weight of cereal in the boxes is equal to or greater than 520 grams.

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Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

The difference in magnitude between Tallahassee and Bascom is approximately 2.2475.

Let's use the formula for the magnitude of population, which is given by:

magnitude = log(P)

where P is the population.

For Tallahassee, the population is about 188,000, so we have:

magnitude of Tallahassee = log(188000)

Using a calculator, we can find that the magnitude of Tallahassee is approximately 5.2745.

For Bascom, the population is about 1065, so we have:

magnitude of Bascom = log(1065)

Using a calculator, we can find that the magnitude of Bascom is approximately 3.0270.

To find the difference in magnitude between the two cities, we simply subtract the magnitude of Bascom from the magnitude of Tallahassee:

difference in magnitude = magnitude of Tallahassee - magnitude of Bascom

Substituting the values we found, we get:

difference in magnitude = 5.2745 - 3.0270

Simplifying, we get:

difference in magnitude ≈ 2.2475

Therefore, the difference in magnitude between Tallahassee and Bascom is approximately 2.2475.

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Answer:

72°

Step-by-step explanation:

Given

Zy = 108°

Zx = ?

We know

Zx + Zy = 180° {being supplementary angles }

Zx + 108° = 180°

Zx = 180° - 108°

Zx = 72°

Hope it will help :)

It would take 10 gardeners to plant 45 trees in 45 minutes.

It's a math tool for solving problems about proportion. You can relate more than 2 variables and from the proportion, it's possible to find an unknown number.

The question gives:

6 gardeners can plant 18 trees in 30 minutes.

?  gardeners can plant 45 trees in 45 minutes.

6 gardeners can plant \(\frac{18\; tree}{30\; min}=\frac{3}{5}\) trees/min. You can calculate the second rate from   \(\frac{45\; tree}{45\; min}=\frac{1}{1}=1\) tree/min.

Write the previous text information in form of proportion.

6 gardeners  ----------- 3/5 trees/min

x gardeners  ----------- 1 tree/min

Then, applying cross multiplication:

\(\frac{3x}{5}=6\\ \\ 3x=30\\ \\ x=10\)

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Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

Answer:

the answer is 3.6

can you also please mark me as brainliest?

thanks

The height of the screw = 16 inches.

The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.

Given that,

Diameter of a bicycle = 16 inches

The distance the bike moves (forward) after the screw punctures the tire = 56π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16π inches

Therefore,

\(\frac{56\pi }{16\pi }\) = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A cos(Bx - C) + D

Where

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2π/B

Bx = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The mid line = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

Hence, After the bike moves forward another 56π inches the height of the screw = 16 inches.

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Answer:

16 on edge

Step-by-step explanation: