When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be measured by the following piecewise defined function: S of t is equal to the piecewise function of 140 minus 5 times t if 0 is less than or equal to t is less than or equal to 5 and 115 if 5 is less than t is less than 8 and 43 plus 9 times t if 8 is less than or equal to t is less than or equal to 12 where t is the time, in hours, since taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 9 a.m., in which interval will their systolic pressure be lowest?

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The 95% confidence interval for the difference between the proportion of the population who would survive at least 15 years can be used to estimate the range within which the true difference lies.

It provides a measure of uncertainty around the point estimate. The confidence interval can be interpreted as follows: we are 95% confident that the true difference in proportions of the population who would survive at least 15 years falls within the calculated interval. To construct the confidence interval, we first need to obtain sample data from the population. Let's assume we have collected data from two independent samples. From Sample 1, we find that out of n1 individuals, x1 survive at least 15 years. Similarly, from Sample 2, we have n2 individuals, with x2 surviving at least 15 years. To calculate the confidence interval, we use the formula: CI = (p1 - p2) ± Z * sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)) Where p1 = x1 / n1 and p2 = x2 / n2 are the sample proportions, and Z is the critical value corresponding to the desired confidence level (in this case, 95%). The critical value is determined based on the standard normal distribution. Once we have the confidence interval, let's say [lower limit, upper limit], we can interpret it as follows: We are 95% confident that the true difference in proportions between the two populations who would survive at least 15 years lies between the lower limit and the upper limit. In other words, there is a high likelihood that the actual difference falls within this range. The confidence interval allows us to make inferences about the population based on our sample data. It provides a range of plausible values for the difference in proportions, taking into account the variability of the sample. The wider the confidence interval, the greater the uncertainty in our estimate. Conversely, a narrower interval indicates a more precise estimation.

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Answer:

X=3

Step-by-step explanation:

5x - 2 = 13

5x = 15

x = 3

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Answer:

3

Step-by-step explanation:

5x-2=13

5x=13+2

5x=15

x=15/5

x=3

If we test H₀ : μ = 16 versus H₁ : μ ≠ 16 at α = 0.01, reject H₀ in favor of H₁. The correct answer is (a)

If the confidence interval for the population mean does not contain the hypothesized value in the null hypothesis, then we can reject the null hypothesis in favor of the alternative hypothesis.

In this case, the confidence interval is centered around 10.15, and it does not contain the hypothesized value of 16. Therefore, we can conclude that we have evidence to reject the null hypothesis at a significance level of 0.01 and accept the alternative hypothesis that the population mean is not equal to 16.

It is important to note that this decision is based on the confidence interval and significance level given in the question. If the confidence level or significance level were different, the decision might be different as well.

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the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined which shape is formed as Square

When the coordinates (1,1), (7,3), (8,0) and (2,-2) are joined, a square is formed. The sides are equal length and the angles are all 90 degrees.The coordinates (1,1), (7,3), (8,0) and (2,-2) are points on a two-dimensional plane. When the points are connected, a square is formed. A square is a four sided shape with four 90 degree angles and four equal length sides. The length of each side can be calculated by finding the distance between the two points. For example, the distance between (1,1) and (7,3) is 6 units. Therefore, the length of each side of the square is 6 units.

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Answer:

3

Step-by-step explanation:

The answer should be 3? Geometry.

Answer:

(3 x + 4) (x - 1) (x + 3)

Step-by-step explanation:

Factor the following:

3 x^3 + 10 x^2 - x - 12

The possible rational roots of 3 x^3 + 10 x^2 - x - 12 are x = ± 1/3, x = ± 2/3, x = ± 4/3, x = ± 1, x = ± 2, x = ± 3, x = ± 4, x = ± 6, x = ± 12. Of these, x = -4/3, x = 1 and x = -3 are roots. This gives 3 x + 4, x - 1 and x + 3 as all factors:

Answer: (3 x + 4) (x - 1) (x + 3)

Answer:

2 ounces

Step-by-step explanation:

2 pounds and 2 tons are a lot of weight to assume the weight of a pen.

Answer:

D.)

Step-by-step explanation:

To be proportional from one thing to another means to have the same relationship between the two and in this case, the same relationship between the height and the base. The relationship between the height and base in the triangle is 1.6 to 2.5, and to have a proportional relationship, you need to have the same relationship. The option D.) has the same relationship between the height and base as the relationship 1.6 to 2.5 is the same as 0.8 to 1.25, because it's the same thing, just divided by 2 in both parts.

Hope this helped you understand!

Answer:

$0.75

Step-by-step explanation:

$4.50 divided by 6 equals $0.75.

To find the eigenvalues of a symmetric matrix, we can first compute the characteristic polynomial, which is the determinant of the matrix minus λ times the identity matrix.

For the given matrix, the characteristic polynomial is λ^2 - 6λ + 8, which can be factored as (λ - 2)(λ - 4). Thus, the eigenvalues are λ = 2 and λ = 4. Since the matrix is symmetric, we know that its eigenvalues are real and its eigenvectors can be chosen to be orthogonal. This property makes symmetric matrices particularly useful in many applications, such as in linear algebra, physics, and engineering.

To find the eigenvalues of the symmetric matrix:

| 3 1 |

| 1 3 |

We can start by finding the characteristic polynomial, which is the determinant of the matrix minus the eigenvalue λ times the identity matrix:

| 3-λ 1 |

| 1 3-λ |

(3-λ)(3-λ) - 1 = λ^2 - 6λ + 8 = (λ-2)(λ-4)

Setting this polynomial equal to zero, we get the two eigenvalues:

λ = 2, 4

Therefore, the eigenvalues of the symmetric matrix are 2 and 4.

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Answer:

178m squared

Step-by-step explanation:

make 3 rectangular shapes

shape 1 ) 18×5=90

shape 2) 13×6= 78

shape 3) 5×2=10

Add up all the answers and that's the ans

90+78+10=178

Answer:

x=85/11

Step-by-step explanation:

\(\frac{x}{5}= \frac{17}{11} \\\\5*\frac{x}{5} =\frac{17}{11} \\\\x=\frac{85}{11}\)

Answer:

99 and 33

Step-by-step explanation:

let x and y be the 2 numbers, with x being the larger of the 2, then

x + y = 132 → (1)

x - y = 66 → (2)

add (1) and (2) term by term to eliminate y

(x + x) + (y - y) = 132 + 66

2x + 0 = 198

2x = 198 ( divide both sides by 2 )

x = 99

substitute x = 99 into (1) and solve for y

99 + y = 132 ( subtract 99 from both sides )

y = 33

the 2 numbers are 99 and 33

12 square inches is the area of base with volume of 36 cubic inches; height of 9 inches

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Given that volume of a cone is 36 cubic inches.

Height of the cone is 9 inches.

We need to find the area of the base of each cone.

V=Ah/3

Where A is the Area of base

Plug in the values of volume and height to find the base area

36=A×9/3

36=3A

Divide both sides by 3

A=12

Hence, if volume is 36 cubic inches and height is  9 inches then the area of the base of cone is 12 square inches.

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Answer:

3

Step-by-step explanation:

it's three because ur trying to find the median so if u put it together it will be -18,-13,-6,-6,3,4,11,13,20 and to find whats between those numbers it will be 3

Answer:     -3

Step-by-step explanation:

Hence option b is the correct option i.e The sample mean's sampling distribution will be roughly normal.

The appropriate response to the question about Sampling Distributions is The sample mean will have a sampling distribution mean that is identical to the population mean.

The sampling distribution must then resemble the normal distribution as the sample size grows.

According to this, if the sample size is large enough, the sampling distribution of the mean will always be normally distributed. The sampling distribution of the mean will be normal regardless of whether the population has a normal, Poisson, binomial, or any other distribution.

A bell-shaped, symmetrical distribution known as a normal distribution has fewer observations the farther out from its center.

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Answer: nope!

Step-by-step explanation: there are 4 quarts in a gallon and we can see by adding the mango juice, there will be no space!

Water (2 quarts) mango juice (2 quarts) equals a gallon

Ginger ale = one gallon

That’s already 2 gallons and we still have the 2 pints of pineapple juice!

Answer:

Yes, the expression can be factored to give:

\(( {x}^{2} + 4)(x + 2)(x - 2).\)

The number of 10 chips stacks that Dave can make if two stacks are not considered distinct is 110.

To get the symmetric stacks, one has to subtract the symmetric stacks to know the ones that are asymmetric.

The symmetric are flipped. Given that they are double counted what we have to do is to divide through by 2.

6/2 = 3

10/2 = 5

4/2 = 2

1/2(10C6) - (5C3) + (5C3)

0.5(210-10+10)

= 110

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The null and alternative hypotheses are H₀: μ = 3.50, H₁: μ ≠ 3.50. Test statistic is t ≈ -1.387, P-value is approximately 0.169, there is not enough evidence to conclude that the population mean.

To test the claim that the population mean of student course evaluations is equal to 3.50, we can set up the following hypotheses:

Null hypothesis (H₀): The population mean is equal to 3.50.

Alternative hypothesis (H₁): The population mean is not equal to 3.50.

H₀: μ = 3.50

H₁: μ ≠ 3.50

Given summary statistics: n = 86, x' = 3.41, s = 0.65

To perform the hypothesis test, we can use a t-test since the population standard deviation is unknown. The test statistic is calculated as follows:

t = (x' - μ₀) / (s / √n)

Where μ₀ is the population mean under the null hypothesis.

Substituting the values into the formula:

t = (3.41 - 3.50) / (0.65 / √86)

t = -0.09 / (0.65 / 9.2736)

t ≈ -1.387

Next, we need to calculate the P-value associated with the test statistic. Since we have a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than -1.387.

Using a t-distribution table or statistical software, the P-value is approximately 0.169.

Since the P-value (0.169) is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, there is not enough evidence to conclude that the population mean of student course evaluations is significantly different from 3.50 at the 0.05 significance level.

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Answer:

i got a orange

Step-by-step explanation:

Answer:

35y2+13y−12

                       =35y2+28y−15y−12

                       =7y(5y+4)−3(5y+4)

                       =(7y−3)(5y+4)

Therefore, the possible length and breadth are 7y-3 units and 5y+4 units

Answer:

1000000

Step-by-step explanation:

Answer: 1000000

Step

no

step

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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The explicit equation of the function is t(n) = 5 * 8^(n-1)

The function definition is given as:

t(1)=5

t(n+1)=8t(n)

Let n = 1

So, we have:

t(2) = 8t(1)

Divide through by t(1)

t(2)/t(1) = 8

The common ratio of the function is:

r = t(2)/t(1) = 8

The explicit rule is then calculated as:

t(n) = t(1) * r^(n-1)

So, we have:

t(n) = 5 * 8^(n-1)

Hence, the explicit equation of the function is t(n) = 5 * 8^(n-1)

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Option A is correct, the most general antiderivative is \(\frac{7}{3}. e^{\:3x}\:dx+6e^-^x+C\).

To find the antiderivative of the given function, we can apply the power rule for integration.

The power rule states that if f(x) is of the form f(x)=axⁿ.

where a is a constant and  n is a real number (except -1), then the antiderivative of f(x) with respect to x is given by \(\frac{a}{n+1}x^{n+1}+C\).

Applying the power rule to each term in the given function, we have:

\(\int \:\left(7e^{3x}\:-6e^{-x}\:\right)dx=\int \:\:7e^{\:3x}\:dx-\int 6e^{\:-x}\:dx\)

Integrating each term individually:

\(\:\int \:7e^{\:3x}\:dx=\:\frac{7}{3}e^{\:3x}+C_1\)

\(\:\int \:6e^{\:-x}\:dx=\:-6e^{\:-x}+C_2\\\)

Combining the results, we get:

\(\int \:\left(7e^{3x}\:-6e^{-x}\:\right)dx=\frac{7}{3}. e^{\:3x}\:dx+6e^-^x+C\)

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Answer:

The answer is C: 2.9 seconds.

Step-by-step explanation:

To solve this problem, you can set up an equation representing the distance each balloon travels over time, and then solve for the time at which they will be at the same height.

The equation for the first balloon is:

70 - 6t = h (h is the height of the first balloon at time t)

The equation for the second balloon is:

10 + 15t = h (h is the height of the second balloon at time t)

If we set the two equations equal to each other and solve for t, we get:

70 - 6t = 10 + 15t

16t = 60

t = 60/16 = 3.75 seconds

The two balloons will be at the same height after approximately 3.75 seconds. Therefore, the answer is C: 2.9 seconds.

Answer:

true

Step-by-step explanation:

Answer: True

Step-by-step explanation: