At first, a tank was completely filled with water. A pump was turned on for some time to drain water from the tank. The line graph shows the volume of water in the tank over 40 minutes.
a)how much water was drained out of the tankin one minute
b)how long will it take for the water to be drained out of the tank completely?
see the attachment below.​

The function has three x-intercepts: x=0, x=4, and x=5. The graph of f(x) has three x-intercepts in the xy-plane.

To find the x-intercepts of a function, we need to set the value of y to zero and solve for x. In this case, the function is f(x) = x(x-4)^2(x-5)^3. To find the x-intercepts, we set f(x) = 0 and solve for x.
First, we notice that each factor is squared or cubed, which means that they cannot be negative. Therefore, we only need to consider the positive values of x.
Next, we see that the factor x will make the whole expression zero when x=0.
The factors (x-4)^2 and (x-5)^3 will make the expression zero when x=4 and x=5, respectively.
Therefore, the function has three x-intercepts: x=0, x=4, and x=5.
In conclusion, the graph of f(x) has three x-intercepts in the xy-plane. Includes the terms "parenthesis" and "squared."

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Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents

. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.

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The final calculation revealed that the height of the mountain was approximately 350.1 meters.

Back in their workshop, Alex applied the tangent function to find the mountain's height. They knew that tangent is the ratio of the opposite side (the height) to the adjacent side (the horizontal distance). Setting up the equation, they plugged in the known values:

tangent(35 degrees) = height / 500 meters

Using trigonometric tables or a calculator, they found that the tangent of 35 degrees is approximately 0.7002. Now they could solve the equation:

0.7002 = height / 500 meters

To isolate the height, they multiplied both sides of the equation by 500:

0.7002 * 500 meters = height

The final calculation revealed that the height of the mountain was approximately 350.1 meters.

With this crucial information, Alex and Sarah could now design the bridge

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The HCF of the given expression is (x + 2y).

To find the highest common factor (HCF) of the given expression, [tex]X^2 + 2xy^2 + 4y^3[/tex], we need to factorize it. However, the given expression seems to contain some typographical errors or inconsistencies, as it is not a valid mathematical expression.

If you meant to write the expression as , [tex]X^2 + 2xy^2 + 4y^3[/tex]we can proceed with finding the HCF.

The expression can be factored as follows:

[tex]X^2 + 2xy^2 + 4y^3 = (x + 2y)(x^2 - 2xy + 2y^2)[/tex]

To find the HCF, we look for the common factors among the terms. In this case, the common factor is (x + 2y). Therefore, the HCF of the given expression is (x + 2y).

Please note that if there was an error in the original expression you provided, and it differs from what was assumed here, please correct it so that a more accurate response can be given

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Note the full question is ;

Xsquare_2x_ysquare +4y_3

hcf of the given term is ?

The only odd integer among the choices is 5mn.

To determine which expression is an odd integer,

we need to know that the sum of an even integer and an odd integer is always odd, and the product of an even integer and an odd integer is always even.

A: 3m + 4n = 2m + m + 4n is even

since it's the sum of two even integers.

B: 5mn is odd since it's the product of an odd and an even integer.

C: (m + 3n)² = m² + 6mn + 9n² is odd since it's the sum of two odd integers and an even integer.

D: m³n² = m * m² * n² is even since it's the product of an even integer and two odd integers.

E: 5m + 6n = 2(2m + 3n) + m is odd since it's the sum of two even integers and an odd integer.

Therefore, the only odd integer among the choices is 5mn.

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True. The double integral can be used to compute the area of a region d in a plane by integrating the function f(x,y). In fact, the double integral of f(x,y) over a region D in the xy-plane gives the volume of the solid between the surface z=f(x,y) and the xy-plane over the region D.

However, if we take the function f(x,y) to be the constant function 1, then the double integral of f(x,y) over the region D is simply the area of the region D. Therefore, we can compute the area of a region D in a plane by integrating the constant function 1 over the region D using the double integral. Integrating over two variables requires calculating two separate integrals, so the answer is more than 100 words.
True. A double integral can be used to compute the area of a region D in a plane by integrating the function f(x, y). To find the area, you would integrate the function f(x, y) = 1 over the region D, as the double integral represents the sum of the function values over the entire area. The double integral can be thought of as a generalization of single-variable integration, allowing us to find the area in two dimensions.

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Answer:

90 nickels, 72 pennies

Step-by-step explanation:

0.05n+0.01p= 5.22

n+p=162

0.05(162-p)= 5.22

p= 72

n+72= 162

n=90

Answer:

10c a - 3; b = 4

10d See below

Step-by-step explanation:

10c

The problem asks about

3² × 4² = 12²

The given rule is

a² × b² = (a × b)²

Match each number in the problem to each variable or expression in the given rule.

a = 3; b = 4; a × b = 3 × 4 = 12

Answer: a = 3; b = 4

10d

Let's use two sets of number for the formula.

a = 2; b = 5

a² × b² = (a × b)²

2² × 5² = 4 × 25 = 100

(2 × 5)² = 10² = 100

100 = 100

a = 6; b = 8

a² × b² = (a × b)²

6² × 8² = 36 × 64 = 2304

(6 × 8)² = 48² = 2304

2304 = 2304

The formula works every time.

The formula shows you that if you have to multiply the squares of two numbers, you can also multiply the numbers first, then square the product. The result is the same.

a) Marcus' result is likely to be more reliable.

b) Because the sample was bigger.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

The higher the total number of outcomes, the more reliable the probability calculated is.

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The recursive formula for the sequence is a(n) = -4*a(n-1) . where a(1) = 3.

To find the recursive formula for the sequence 3,-12,48,-192, we need to look at how each term relates to the previous term.
Starting with the first term, we have a(1) = 3.
To get to the second term, we multiply the first term by -4. So we have a(2) = -4*a(1) = -4*3 = -12.
To get to the third term, we multiply the second term by -4. So we have a(3) = -4*a(2) = -4*(-12) = 48.
To get to the fourth term, we multiply the third term by -4. So we have a(4) = -4*a(3) = -4*48 = -192.
So we can see that each term is obtained by multiplying the previous term by -4.
Therefore, the recursive formula for the sequence is:
a(n) = -4*a(n-1)
where a(1) = 3.

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Light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808. light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)=               1-0.1808=0.8192.

a. The probability that 1 or less light bulbs are defective among 83 sampled light bulbs can be calculated using the binomial distribution with n=83 and p=0.01. P(X≤1)=0.1808.

b. The probability that 2 or more light bulbs are defective among 83 sampled light bulbs can be calculated as 1 minus the probability that 0 or 1 light bulbs are defective. P(X≥2)=1-P(X≤1)=1-0.1808=0.8192.

In acceptance sampling, a sample is taken from a large batch of items to determine if the entire batch should be accepted or rejected based on the number of defective items in the sample. In this problem, the probability of a light bulb being defective is given as 1%, and we are asked to find the probabilities of having 1 or less defective light bulbs or 2 or more defective light bulbs among a sample of 83 light bulbs. We can use the binomial distribution to calculate these probabilities, where X is the number of defective light bulbs in the sample. The probability of having 1 or less defective light bulbs can be calculated as the sum of the probabilities of having 0 or 1 defective light bulbs, and the probability of having 2 or more defective light bulbs can be calculated as 1 minus the probability of having 1 or less defective light bulbs.

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Prevalence is a commonly used metric in epidemiology and public health to describe the proportion of a population affected by a specific condition or characteristic during a specific period. In this case, it helps to understand the extent of allergies among children in 2020.

The calculation given is an example of a prevalence measure, which is used to determine the proportion or percentage of individuals in a population that have a particular health condition or disease. In this case, the number of children with allergies in 2020 is divided by an estimate of the total number of children in the population to determine the prevalence of allergies in the population.
Prevalence measures are useful for understanding the burden of a particular health condition in a population, as well as for identifying trends over time or differences between different groups within the population. However, it's important to note that prevalence measures are only as accurate as the data used to calculate them, so it's essential to use reliable sources of data and to ensure that the sample of individuals being measured is representative of the entire population.
Prevalence measures are widely used in epidemiology and public health research to understand the distribution of health conditions and diseases in populations. They can be calculated for a wide range of health outcomes, including chronic diseases, infectious diseases, mental health conditions, and more.
In addition to prevalence, other types of measures used in public health research include incidence (which measures the number of new cases of a particular health condition within a population over a specific period of time), mortality (which measures the number of deaths attributable to a particular health condition or disease), and morbidity (which measures the burden of illness associated with a particular health condition or disease, often in terms of disability-adjusted life years or quality-adjusted life years).
Ultimately, the type of measure used in a given study will depend on the research question being asked, the available data sources, and the specific health outcome being studied. However, regardless of the type of measure used, it's important to ensure that the sample of individuals being measured is representative of the entire population, and to use reliable and accurate data sources to calculate the measure.
The calculation you described, which involves dividing the number of children with allergies in 2020 by an estimate of the total number of children in the population, is an example of a prevalence measure.

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Step-by-step explanation:

I believe there is something missing from the description.

I base my solution and explanation on the following assumptions :

in other words, (20, -21) is not just any point on the line, but it is the upper vertex of the triangle.

the baseline of the triangle, which is the radius of the surrounding circle is then the distance from the origin to the point.

Pythagoras (= distance formula) gives us for the distance between 2 points (x1, y1) and (x2, y2) :

distance² = (x1 - x2)² + (y1 - y2)²

in our case

distance² = (20 - 0)² + (-21 - 0)² = 400 + 441 = 841

distance = radius = 29

remember, sine is the up/down leg, cosine is the left/right leg.

so,

sin(theta) = -21/29

FYI : theta ≈ -46.4°

cos(theta) = 20/29

tan(theta) = sin(theta)/cos(theta) = -21/29 / 20/29 =

= -21/20

you were right about tan(theta), not about sin(theta) and cos(theta).

if you mistook theta for a 0, you were still wrong :

sin(0) = 0, cos(0) = 1.

Based on the given sample data, we do not have sufficient evidence to conclude that the population mean is significantly different from 48.

The null hypothesis (H0): The population mean is equal to 48.

The alternative hypothesis (Ha): The population mean is not equal to 48.

b. To determine the test statistic, we can use the t-test since the population standard deviation is unknown. The formula for the t-test statistic is:

t = (sample mean - hypothesized mean) / (sample standard deviation / √n)

Given:

Sample mean () = (25 + 47 + 32 + 56) / 4 = 40

Hypothesized mean (μ0) = 48

Sample standard deviation (s) = √[( (25 - 40)^2 + (47 - 40)^2 + (32 - 40)^2 + (56 - 40)^2) / (4 - 1)] = √[242] ≈ 15.56

Sample size (n) = 4

Substituting these values into the formula, we get:

t = (40 - 48) / (15.56 / √4) = -8 / 7.78 ≈ -1.028

c. To determine the p-value, we need to find the probability of observing a t-value as extreme or more extreme than the calculated test statistic under the null hypothesis. This can be done using a t-distribution table or statistical software.

For a two-tailed test at the 5% level of significance, we divide the significance level by 2, resulting in an alpha of 0.025. Degrees of freedom (df) = n - 1 = 4 - 1 = 3.

From the t-distribution table or software, we find that the p-value for a t-value of -1.028 with 3 degrees of freedom is approximately 0.381.

Since the p-value (0.381) is greater than the significance level (0.05), we fail to reject the null hypothesis. There is not enough evidence to suggest that the population mean is significantly different from 48 at the 5% level of significance.

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Answer: 49

Step-by-step explanation:

When you have 72 and subtract it by 23 you get 49

The probability that the sample mean would be greater than 135.7 WPM is 0.1686.

Calculate the standard deviation:

The standard deviation of the WPM typed by a speed typist is √100 = 10.

Calculate the z-score

The z-score is calculated by subtracting the population mean (135) from the sample mean (135.7) and dividing it by the standard deviation (10).

z = (135.7 - 135) / 10 = 0.07

Calculate the probability

The probability of the sample mean being greater than 135.7 WPM can be calculated using the z-score.

P(x > 135.7) = 1 - P(x ≤ 135.7)

P(x > 135.7) = 1 - 0.8314 = 0.1686

Therefore, the probability that the sample mean would be greater than 135.7 WPM if 43 speed typists are randomly selected is 0.1686, rounded to four decimal places.

Complete Question:

The mean number of words per minute WPM typed by a speed typist is 135 with a variance of 100. What is the probability that the sample mean would be greater than 135.7 WPM if 43 speed typist are randomly selected? round your answer to four decimal places.

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Answer:

Step-by-step explanation:

[tex]\frac{a^{3}.b^4.5^4}{b^2.5}\\ = a^3.b^2.5^3\\= 125a^3b^2[/tex]

[tex] { {a}^{3} } \times {b}^{2} \times 125[/tex]

When dividing variables with exponents, subtract the bottom exponent from the top. since there is no "a" in the denominator, we would leave it as is. The "b" at the top (numerator) has an exponent of 4, and the one in the bottom (denominator) has an exponent of 2, so we would do 4 - 2, which equals 2, so the exponent on b would be 2. Then, the exponent for 5 in the numerator is 4, and in the denominator, it's 1 (any number that with no visible exponent has an exponent of 1). 4 - 1 is 3, and 5^3 is 125.

The values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent Inequality in terms of d is d ≥ -24.

To make the inequality 3d ≥ -72 true, we need to find values of d that satisfy the inequality.

Dividing both sides of the inequality by 3, we get:

d ≥ -24

Therefore, any value of d that is greater than or equal to -24 will satisfy the inequality.

An equivalent inequality in terms of d would be:

d + 24 ≥ 0

We can simplify this inequality by subtracting 24 from both sides:

d ≥ -24

This is the same inequality we found earlier, which means that any value of d greater than or equal to -24 will make the inequality true.

the values of d that make the inequality 3d ≥ -72 true are all values greater than or equal to -24. An equivalent inequality in terms of d is d ≥ -24.

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The correct option A, "None of the associations listed are correct," is the appropriate response.To determine the association suggested by the two-way table, we need to calculate the relative frequency of the data.

The table provides information about whether individuals have a brother and a sister.

Based on the options given, let's calculate the relative frequencies to see which association is suggested:

Calculate the relative frequency for individuals who have a brother and a sister:Relative frequency = (Number of individuals with both a brother and a sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a brother but no sister:Relative frequency = (Number of individuals with a brother but no sister) / (Total number of individuals)

Calculate the relative frequency for individuals who have a sister but no brother:Relative frequency = (Number of individuals with a sister but no brother) / (Total number of individuals)

Calculate the relative frequency for individuals who have neither a brother nor a sister:Relative frequency = (Number of individuals with neither a brother nor a sister) / (Total number of individuals)

By comparing the relative frequencies, we can determine which association is suggested by the data.Unfortunately, the given two-way table is missing, so we cannot perform the necessary calculations to determine the association.

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The probability of success of the first two kicks is 0.733

Probability is the likelihood of an event

Since nervous kicker usually makes ​78% of his first field goal attempts. If he makes his first​ attempt, his success rate rises to 94​%. To find the probability that he makes his first two​ kicks, we notice that the events are independent events. So, the probability of independent events A and B is

P(A U B) = P(A)P(B)

Now let

So, the probability of success of the first two kicks is P(F U S) = P(F)P(S)

So, substituting the values of the variables into the equation, we have that

P(F U S) = P(F)P(S)

= 0.78 × 0.94

= 0.7332

≅ 0.733

So, the probability is 0.733

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Using the segment addition postulate, we can find that the value of x is 18.

Explanation: The segment addition postulate states that for three points A, B, and C on a line, if B is between A and C, then AB + BC = AC. In this case, we have three points on a line: E, F, and G, and we are given the lengths of two line segments, EF and FG. Using the segment addition postulate, we can set up the following equation:

EF + FG = EG

Substituting the given values, we get:

(7x+9) + (3x+4) = 143

Simplifying the equation, we get:

10x + 13 = 143

Subtracting 13 from both sides, we get:

10x = 130

Dividing both sides by 10, we get:

x = 13

Therefore, the value of x is 13.

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Answer: A. 7

Step-by-step explanation:

3y-2=19

3y-2+2=19+2 (add 2 to both sides)

3y=21

3y/3=21/3 (divide by 3 on each side)

y=7

los lados faltantes del triángulo rectángulo son de 5.1 y 11.83.

Para resolver este problema, necesitamos recordar las propiedades de un triángulo rectángulo. Primero, sabemos que uno de los ángulos es de 90 grados. Además, el lado opuesto al ángulo recto se llama hipotenusa y los otros dos lados se llaman catetos.

En este caso, sabemos que uno de los ángulos es de 25 grados, por lo que el otro ángulo es de 90 - 25 = 65 grados. Ahora podemos usar la ley de senos para encontrar la longitud del otro cateto.

La ley de senos establece que la longitud de un lado dividida por el seno del ángulo opuesto es igual a la longitud de otro lado dividido por el seno del ángulo opuesto. Entonces, podemos escribir:

12 / sen(90) = x / sen(25)
x = 12 * sen(25) / sen(90) = 5.1

Por lo tanto, el lado faltante tiene una longitud de 5.1. Para encontrar la longitud del otro cateto, podemos usar el teorema de Pitágoras, que establece que la suma de los cuadrados de los catetos es igual al cuadrado de la hipotenusa. Entonces, podemos escribir:

a^2 + b^2 = 12^2 - 5.1^2 = 130.19
a^2 + b^2 = 130.19
b = sqrt(130.19 - a^2)

Donde "a" es la longitud del cateto que conocemos y "b" es la longitud del cateto que queremos encontrar. Podemos usar la ecuación anterior para encontrar la longitud de "b" para diferentes valores de "a". Por ejemplo, si "a" fuera de 4, tendríamos:

b = sqrt(130.19 - 4^2) = 11.83

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Answer:

The volume of 65 kg of the substance is 13 liters.

Step-by-step explanation:

If a substance's mass varies directly from its volume, it means that the ratio of mass to volume remains constant. In this case, we can calculate the continuous ratio and then use it to find the volume.

Given:

Mass1 = 30 kg

Volume1 = 6 liters

Let's denote the constant ratio as k.

Mass1 / Volume1 = k

30 kg / 6 liters = k

k = 5 kg/liter

Now, we can find the volume2 for a mass of 65 kg using the constant ratio:

Mass2 = 65 kg

Volume2 = ?

Mass2 / Volume2 = k

65 kg / Volume2 = 5 kg/liter

To find Volume2, we can cross multiply:

65 kg = 5 kg/liter * Volume2

Volume2 = 65 kg / 5 kg/liter

Volume2 = 13 liters

A parabola is a symmetrical U-shaped curve that can be defined as a set of points in a plane that are equidistant from a fixed point (called the focus) and a fixed straight line (called the directrix). The axis of symmetry is always perpendicular to the directrix and passes through the focus and vertex of the parabola. In a quadratic equation, the coefficient of the x^2 term determines the direction of the opening of the parabola, and the vertex lies on the axis of symmetry.

True. The axis of symmetry is a line that passes through the vertex of a parabola and divides it into two identical halves.

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So, there are 20 different mix-and-match plates that can be created by combining one savory and one sweet dish from Alejandra's Tapas Bar's menu.

To determine the number of different mix-and-match plates that can be created from Alejandra's Tapas Bar's menu, we need to calculate the number of options for both the savory and sweet dishes and then multiply them together.
Let's assume that there are 5 savory dishes and 4 sweet dishes on the menu. To create a mix-and-match plate, we need to choose one savory and one sweet dish. The number of options for the savory dish is 5, and the number of options for the sweet dish is 4. Therefore, the total number of different mix-and-match plates that can be created is:
5 x 4 = 20
Customers can choose any combination they like and can enjoy a unique dining experience each time they visit the restaurant.

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