The fifth term of an arithmetic sequence is 96. Which rule could define the sequence
An=5n+96
An=6n+18
An=18n+6
An=96n+5

Answer:

9.4 cm to nearest tenth.

Step-by-step explanation:

Diagonal of the  6*2 base:

d^2 = 6^2 + 2^2 = 40

d = √40

So the required diagonal:

D^2 = (√40)^2+ 7^2

D^2 = 89

D = √89 = 9.434.

Answer:

15.1

Step-by-step explanation:

To find the length of the rectangular prism' diagonal, use the formula for the length of a diagonal of a right rectangular prism.

d=l2+w2+h2−−−−√

Substitute 7 for l, 6 for w, and 12 for h

Then simplify.

d=72+62+122−−−−√

=49+36+144−−−−√

=229−−−√≈15.1

Therefore, the length of the rectangular prism's diagonal is about 15.1cm.

Answer:

Step-by-step explanation:

The change in the amount of water in the pool is the difference between the amount of water that enters and leaves the pool

Change in volume of water in the pool after 112 minutes is  gallons

Reason:

The given parameters are;

The volume volume of entering the pool = 10 3/4 gallons per minute

The volume of water leaving the pool = 12 1/3 gallons per minute

Answer:

16

Step-by-step explanation:

radius is 1/2 of diameter

Answer:

16 units

Step-by-step explanation:

When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units.

1.) \(y(y + 4) - y = 6\) ✅Are Quadratic Functions.

2.)  \((3x + 2) + (6x - 1) = 0\) ❌ Not a Quadratic Function.

3.) \(4b(b) = 0\) ✅ Are Quadratic Functions.

4.) \(3a - 7 = 2 (7a - 3)\) ❌ Not a Quadratic Function.

Answer:

A & C

Step-by-step explanation:

Got It right on edge.

Answer:

it is 10.3

Step-by-step explanation:

Answer:

b = -1

Step-by-step explanation:

3 - 2(b - 2) = 2 - 7b (Use the distributive property)

3 - 2b + 4 = 2 - 7b (Add 3 and 4)

7 - 2b = 2 - 7b (Add 7b to both sides)

7 - 2b + 7b = 2 (Add -2b to 7b)

7 + 5b = 2 (Subtract 7 from both sides)

5b = 2 - 7 (Subtract 7 from 2)

5b = -5 (Divide both sides by 5)

b = -5/5 (Divide -5 by 5)

b = -1

Work Check: (Substituting b for -1)

3 - 2(b - 2) = 2 - 7b

3 - 2(-1 - 2) = 2 - 7(-1)

3 - 2(-3) = 2 - (-7)

3 - (-6) = 2 - (-7)

3 + 6 = 2 + 7

9 = 9

That is true, so b = -1

In this question we want to find the slope of the tangent line to the parabola \(y=8x-x^{2}\) at the point (1,7) which is 6.

The slope is a measure of the steepness or incline of a line. It describes how much a line rises or falls as it moves horizontally. Mathematically, the slope is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

To find the slope of the tangent line at a given point on a curve, we need to find the derivative of the function and evaluate it at that specific point.

The given equation represents a parabola in the form \(y=ax^{2} +bx+c\), where a = -1, b = 8, and c = 0. Taking the derivative of the function, we get dy/dx = 8 - 2x.

To find the slope at the point (1,7), substitute x = 1 into the derivative: dy/dx = 8 - 2(1) = 8 - 2 = 6.

Therefore, the slope of the tangent line to the parabola at the point (1,7) is 6. This means that at that particular point, the tangent line has a slope of 6, indicating the rate of change of the curve at that point.

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Answer:

You are left with $1.44

Step-by-step explanation:

Subtract the amount of money you payed to how much the cost actually was to get your answer.

using standard z value, 20% of sandwiches are less than 10.58 inches.

In the given question,

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches.

20% of sandwiches are less than...............inches.

The cumulative standardized normal distribution table indicates a z value of -0.84 for 20%.

From the question we know that

Mean(μ) = 11 inches

Standard Deviation(σ) = 0.5 inches

We have to find less than of 20% of sandwiches for z value of -0.84

P(ƶ<z) = 20%

We can write it as

P(ƶ<-0.84) = 20/100

P(ƶ<-0.84) = 0.20

Since z = -0.84

X-μ/σ = -0.84

Now putting the value

X-11/0.5 = -0.84

Multiply by 0.5 on both side

X-11/0.5 *0.5= -0.84*0.5

X-11= -0.42

Add 11 on both side

X-11+11= -0.42+11

X = 10.58

Hence, 20% of sandwiches are less than 10.58 inches.

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Right question is here

Subway sells foot long sandwiches that have a mean of 11 inches and a standard deviation of 0.5 inches. 20% of sandwiches are less than ................. inches. (The cumulative standardized normal distribution table indicates a z value of -.84 for 20%)

(a) 11.500

(b) 11.42

(c) 10.58

(d) cannot be determined from the information given

Answer:Range

Step-by-step explanation:the set of all images of the elements in the domain of a function is called the Range .

The set of all images of the elements in the domain of a function is called the range. The range is the set of all possible outputs or y-values that a function can produce for its corresponding inputs or x-values in the domain.

The range can be determined by either analyzing the function algebraically or by graphing it. It is important to note that not all functions have a defined range, as some may produce infinite or undefined outputs. The range plays a crucial role in understanding the behavior and characteristics of a function, as it helps identify its domain and any possible restrictions or limitations.

The set of all images of the elements in the domain of a function is called the range of the function. The range represents the output values of a function that result from applying the function to every element within its domain. In other words, the range consists of all possible values that the function can produce when it is applied to the elements in its domain.

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Critical value for a 97% confidence interval. For a large sample size, it is approximately 1.96.

(a) In this question, the following notations can be used: p1: Proportion of all male registered voters who voted in the last presidential election in country Y. p2: Proportion of all female registered voters who voted in the last presidential election in country Y. n1: Sample size of the male registered voters. n2: Sample size of the female registered voters. (b) To construct a 97% confidence interval for the difference between the proportion of all male and all female registered voters who were not voted in the last presidential election in country Y, we can use the following steps.

Calculate the sample proportions: phat1: Proportion of male registered voters who voted = 68% = 0.68 ;phat2: Proportion of female registered voters who voted = 65% = 0.65 .Calculate the standard errors for each proportion: SE1 = sqrt((phat1 * (1 - phat1)) / n1); SE2 = sqrt((phat2 * (1 - phat2)) / n2). Calculate the margin of error: ME = Z * sqrt((SE1^2) + (SE2^2)) ;  Z: Critical value for a 97% confidence interval. For a large sample size, it is approximately 1.96. Calculate the lower and upper bounds of the confidence interval: Lower bound = (phat1 -phat2) - ME; Upper bound = (phat1 - phat2) + ME. The 97% confidence interval for the difference between the proportion of all male and all female registered voters who were not voted in the last presidential election in country Y can be expressed using the notations as [ (phat1 - phat2) - ME, (phat1 - phat2) + ME ].

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Answer:

Roses = x = 100

Carnations = y = 110

Lilies = z = 120

Step-by-step explanation:

Roses = $4.50

Carnations = $3.00

lilies = $2.50

Total flowers ordered = 330

Total cost = $1,080

Let

Roses = x

Carnations = y

Lilies = z

x + y + z = 330

4.50x + 3y + 2.50z = 1080

There are 20

more lilies than roses

z = x + 20

Substitute z = x + 20 into the equations

x + y + (x + 20) = 330

4.50x + 3y + 2.50(x + 20) = 1080

x + y + x + 20 = 330

4.50x + 3y + 2.50x + 50 = 1080

2x + y = 330 - 20

7x + 3y = 1080 - 50

2x + y = 310 (1)

7x + 3y = 1030 (2)

Multiply (1) by 3

6x + 3y = 930 (3)

7x + 3y = 1030 (2)

Subtract (3) from (2)

7x - 6x = 1030 - 930

x = 100

Substitute x = 100 into (1)

2x + y = 310

2(100)+ y = 310

200 + y = 310

y = 310 - 200

= 110

y = 110

Substitute the value of x and y into

x + y + z = 330

100 + 110 + z = 330

210 + z = 330

z = 330 - 210

= 120

z = 120

Roses = x = 100

Carnations = y = 110

Lilies = z = 120

Answer:

The answer will be -5a-4

Step-by-step explanation:

Subtract 7a-12a=-5a

Add -8+4=-4

which makes the answer -5a-4

Hope this helps:)

Answer:

a = -4/5

Step-by-step explanation:

7a - 8 - 12a + 4

First, you want to put like terms together. You can rearrange the terms because of the Commutative Property.

7a - 12a - 8 + 4

I will put parentheses around the negative numbers, so it is easier to see the negative numbers.

7a (- 12a)( - 8) + 4

Now you combine the Like Terms

7a-12a     and     -8+4

- 5a - 4

Now you need to get the term with a all by itself on the other side of the equals sign. You can do this by adding the term over to the other side.

-5a - 4

+5a       +5a

Now you have

- 4 = 5a

To get the final answer you need to get a all by itself. You can do this by dividing 5 on both sides.

-4/5=5a/5

So you get

-4/5 = a

as your final answer.

Performing a Chi-Square test is a statistical tool used to determine if there is a significant difference between observed and expected data. The test helps to analyze categorical data by comparing observed frequencies to the expected frequencies. The p-value in a Chi-Square test refers to the probability of obtaining the observed results by chance alone.

If a p-value lower than 0.01 is obtained in a Chi-Square test, it means that the results are statistically significant. In other words, there is strong evidence to reject the null hypothesis, which states that there is no significant difference between the observed and expected data. This means that the observed data is not due to chance alone, but rather to some other factor or factors.

The mean, or average, is not directly related to the Chi-Square test or the p-value. The Chi-Square test is specifically used to determine the significance of the observed data. However, the mean can be used as a measure of central tendency for continuous data, but it is not applicable to categorical data.

In conclusion, obtaining a p-value lower than 0.01 in a Chi-Square test means that there is strong evidence to reject the null hypothesis, and that the observed data is statistically significant.

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Answer:Don’t know I will just get points.Thx

Step-by-step explanation:

Answer:

y=2x+4

Step-by-step explanation:

If the line has a slope of two, that means it goes up 2 on the y axis for every 1 on the x axis. So, if it goes through (1,6), then you can subtract 1 from the x axis and two from the y axis to find the y intercept, (0,4).

Answer:

Step-by-step explanation:

We know that:

Work:

Hence, it takes him 3/5 minutes to finish a full page.

The value of differentiation dy/dt = -4/3.

Given dx/dt = -12, x = 6 and y = -2.

Differentiating both sides of the equation with respect to t:

d/dt(3xy - 4x + 6y³) = d/dt(-108)

Applying the chain rule, we have:

(3x(dy/dt) + 3y(dx/dt)) - (4(dx/dt)) + (18y²(dy/dt)) = 0

Substituting the given values dx/dt = -12, x = 6, and y = -2:

(3(6)(dy/dt) + 3(-2)(-12)) - (4(-12)) + (18(-2)²(dy/dt)) = 0

(18(dy/dt) + 72) + 48 + (72(dy/dt)) = 0

Combining like terms:

18(dy/dt) + 72 + 48 + 72(dy/dt) = 0

90(dy/dt) + 120 = 0

90(dy/dt) = -120

Dividing both sides by 90:

dy/dt = -120/90

Simplifying:

dy/dt = -4/3

Therefore, dy/dt is equal to -4/3.

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assume x and y are functions of . Evaluate dy/dt for 3xy-4x+6y^3=-108 with the conditions dx/dt=-12, x=6, y=-2.

Answer: 1225

Step-by-step explanation:

Just plug in 350 for 'm':

3.5m

3.5m (350)

^^^^^^^^^^

times these two together, to get your final answer!

Multiply:

1225

Answer:

2 distance

Step-by-step explanation:

you solve it and see it's easy know first try I will do it

1.-

In addition equations, we can solve for a variable by subtracting the same number on both sides of the equation.

This is in order to leave the variable we want to solve for alone on one side of the equation.

2.-

The addition equation we have is:

Using the rule of part 1: subtract the same number on both sides to solve for x.

In this case, we have to subtract 3 to both sides:

On the left side, 3-3 cancel each other and we are left only with x:

And on the right side, 7-3 is equal to 4:

Thus, the use of the number family is:

3 is the number we subtract to both sides.

7 is the number to which we subtract 3.

4 is the result of the subtraction.

Answer:

Step-by-step explanation:

Given the function

f(x) = 2x³ -3x²+ 7

putting x=-1 to find f(-1)

f(-1) =  2(-1)³ -3(-1)²+ 7

      = -2 + 3 + 7

      = 8

putting x=1 to find f(1)

f(1) =  2(1)³ -3(1)²+ 7

      = 2 - 3 + 7

      = 6

putting x=2 to find f(2)

f(2) =  2(2)³ -3(2)²+ 7

      = 16 - 12 + 7

      = 11

Therefore,

The parametric equations for the line that is tangent to the curve at t = 0 is x = 1 + t y = 0 + t z = 0 - t.

We are given that;

\(r(t)=eti+(sint)j+ln(1−t)k\) at t=0

Now,

To find parametric equations for the line that is tangent to the curve;

r(t) = eti + (sin(t))j + ln(1 - t)k at t = 0,

Here, line can be obtained by plugging in t = 0 into the given curve:

\(r(0) = e^0i + (sin(0))j + ln(1 - 0)k = i + 0j + ln(1)k = i\)

So (1, 0, 0)  plugging in t = 0:

\(r’(t) = eti + (cos(t))j - (1 / (1 - t))k r’(0) = e^0i + (cos(0))j - (1 / (1 - 0))k = i + j - k\)

So <1, 1, -1> is a direction vector for the line.

Now, using the point and the direction vector, we can write parametric equations for the line as follows;

x = 1 + t y = 0 + t z = 0 - t

Therefore, by the equation the answer will be x = 1 + t y = 0 + t z = 0 - t.

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The average rate of variance of wind chill over each of these 3 intervals is 0.638, 0.523, and 0.332, respectively.

Let's select three respective intervals of wind speed and calculate the mean rates of variance in wind chill inside those ranges.

Interval 1: 3 ≤ w ≤ 10

Average rate of variance runs at: (wind chill at w=10 - wind chill at w=3) / (10 - 3)

= (-17.191 - (-20.475)) / (10 - 3)

= 0.638

Interval 2: 10 ≤ w ≤ 20  

Average rate of variance stands at: (wind chill at w=20 - wind chill at w=10) / (20 - 10)

= (-12.958 - (-17.191)) / (20 - 10)

= 0.523

Interval 3: 20 ≤ w ≤ 30

Average rate of variance boils down to: (wind chill at w=30 - wind chill at w=20) / (30 - 20)

= (-9.635 - (-12.958)) / (30 - 20)

= 0.332

Hence, the average rate of variance of wind chill over each of these 3 intervals is:

0.638, 0.523, and 0.332, respectively.

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The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1), and the expected size of the smallest gap between adjacent cars is 2.

Let us consider that cars of length 2 try to park on a length l road. Each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road.

When no more cars fit, the expected size of the largest gap between adjacent cars is l/(n + 1) and the smallest gap is 2.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1).

Let n be the number of cars parked on the road. Then the total length of the cars parked is 2n.

If the largest gap is a distance g, then the total length of the gaps is l − 2n. Then,gap length:

g (n + 1) ≤ l - 2ng ≤ l − (n + 1)g

Dividing through by (n + 1)g and rearranging:

g ≤ l/(n + 1) (largest gap)g ≥ 2 (smallest gap)

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Answer:

−x2+2x−1=0

Step-by-step explanation:

To write an equation in standard form, move each term to the left side of the equation and simplify.

ax2+bx+c=0

Move 1

to the left side of the equation by subtracting it from both sides.

2x−x2−1=0

Reorder the polynomial.

−x2+2x−1=0

Answer and Step-by-step explanation:

Standard form of an equation is as follows:

Ax + By = C

We have 2x, -\(x^{2}\), and a 1.

Subtract 1 from both sides.

\(-x^{2} + 2x - 1\) = 0 is the equation in standard form.

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