Which numerical pattern is a linear progression? 1 2 , 2 3 , 3 4 , 4 5 , . . . 1 2 , 2 3 , 3 4 , 4 5 , . ⁢ ⁢ . ⁢ . 1, 3, 7, 13, . . . 1, 3, 7, 13, . . . − 10 , − 20 , − 40 , − 80 , . . . − 10 , − 20 , − 40 , − 80 , . ⁢ . ⁢ . 18, 26, 34, 42, . . . 18, 26, 34, 42, . . .

Answer:

Lateral surface area of cuboid = 448 ft²

Step-by-step explanation:

Given:

Height of cuboid(h) = 14 ft

Length of cuboid(l) = 9 ft

width of cuboid(b) = 7 ft

Find:

Lateral surface area of cuboid

Computation:

Lateral surface area of cuboid = 2 h(l + b)

Lateral surface area of cuboid = 2(14)(9 + 7)

Lateral surface area of cuboid = 28(16)

Lateral surface area of cuboid = 448 ft²

Answer:

5%

Step-by-step explanation:

Solving our equation

r = 75 / ( 750 × 2 ) = 0.05

r = 0.05

converting r decimal to a percentage

R = 0.05 * 100 = 5%/year

The interest rate required to

accumulate simple interest of $ 75.00

from a principal of $ 750.00

over 2 years is 5% per year.

Test scores: n = 75, = 46.1, σ = 5.8; 98% confidence, then the correct option is: => (44.5 < μ < 47.7).

given that n = 75 , x = 46.1 , σ = 5.8

98% confidence for z is 2.33

confidence interval formula

=> x +/- z *s/sqrt(n)

=> 46.1 +/- 2.33 * 5.8/sqrt(75)

=> (44.5 < μ < 47.7)

The confidence interval is the amount of conviction you possess about a sample set of information falling inside a scope of values. These values support the confidence level and address the probability of a greater population meeting similar results as your statistical discoveries for the sample. To work out the confidence interval, utilize the accompanying formula:

Confidence interval (CI) = ‾X ± Z(S ÷ √n)

In the formula, ‾X addresses the sample mean, Z addresses the Z-esteem you get from the typical standard circulation, S is the population standard deviation and n addresses the sample size you're surveying.

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Answer:

19

Step-by-step explanation

Let the sum of n terms of A.P. = Sn

The perimeter of the rectangle can be calculated as 2(2x + 5)(7x + 3) which is option B.

The perimeter of a rectangle is the total length of all its sides. In a rectangle, the opposite sides are equal in length, so to find the perimeter, we can add up the lengths of two adjacent sides and then multiply that sum by 2.

If we denote the length of the rectangle as L and the width as W, then the perimeter P is given by:

P = 2(L + W)

In the problem given, the perimeter of the rectangle is given as;

P = 2[(7x + 3) + (2x + 5)]

P = 2[9x + 8]

P = 18x + 16

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Translation: Which option represents the perimeter of the figure?

Answer:

11n

Step-by-step explanation:

Answer:

\( - x + x 2 - 6\)

that's it hope its helpful

The midpoint of a segment in the complex plane with endpoints at 6 - 2i and -4 + 6i is 1 + 2i.

To find the midpoint of a segment in the complex plane, we average the coordinates of the endpoints. The first endpoint is 6 - 2i, and the second endpoint is -4 + 6i.

Adding the real parts and the imaginary parts separately, we get (6 + (-4))/2 = 1 for the real part and ((-2) + 6)/2 = 2 for the imaginary part.

Therefore, the midpoint is given by 1 + 2i. This means that the midpoint of the segment lies on the complex plane at the coordinates (1, 2).

It represents the point equidistant from both endpoints, dividing the segment into two equal parts.

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Answer:

the answer is D) 25 degrees c

Answer: D) 25 degrees c

Step-by-step explanation:

Answer:

23% chance

Step-by-step explanation:

There are a total of 26 students in the class, and 6 of them play basketball and 15 of them play baseball. This means that there are 6 + 15 - 9 = 12 students who play either basketball or baseball, and 9 students who play neither.

Of the 12 students who play either basketball or baseball, 6 of them play basketball and 15 of them play baseball, so there are 6 students who play both basketball and baseball. This means that the probability that a student chosen randomly from the class plays both sports is 6 / 26 = 0.23, or 23%.

Answer:

1:2

Step-by-step explanation:

C. F-test statistic for testing the validity of the regression equation.

In multiple regression analysis, the ratio of MSR (Mean Square Regression) to MSE (Mean Square Error) is used to calculate the F-test statistic.

This statistic is used to test the overall validity of the regression equation, determining whether the regression model as a whole is statistically significant in explaining the variation in the dependent variable.

The F-test assesses whether the regression model as a whole provides a significant improvement over the null model (a model with no independent variables).

A large F-statistic indicates that the regression equation is statistically significant, implying that at least one of the independent variables has a significant effect on the dependent variable.

Therefore, option C, the F-test statistic for testing the validity of the regression equation, is the correct answer.

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Therefore, Chase ran 49/8 miles each day.

To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).

First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.

Now, we can divide 147/4 by 6 to find the distance he ran each day:

(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.

Therefore, Chase ran 147/24 miles each day.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.

So, dividing 147 and 24 by 3, we get:

147/3 / 24/3 = 49/8.

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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.

To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.

Now, we can divide the total distance by the total number of days:

36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.

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Answer:

21 strawberries and 10 smoothies

Step-by-step explanation:

when you divide 28 by 4 you get 7 which is how many strawberries you need for one smoothie. you can now use 7 as a scale factor for the rest of the problem.

Answer:

he the first answer in the strawberry column is 21 and the question in the smoothie box is 10

Step-by-step explanation:

First you divide 28 by 4 (7). You times 7 with 3 (21) thats the first answer

The second you divide 70 with 7 (10 easy math lol) and thats your other answer

By considering ages and equations we have,

Uncle Rob will be 62 years old when Dave is 32.

Dave is listed as being 15 years old, while his uncle Rob is listed as being three times Dave's age. Rob's age as of right now may be calculated using the formula below:

Age of Rob is Dave times three.

Using Dave's age as a plug-in, we obtain following equations,

Rob's age is equal to 15 + 3 = 45.

Rob is currently 45 years old, according to this.

We need to know how many years it will be before Dave turns 32 in order to calculate Rob's age at that time. By deducting Dave's present age from his anticipated age, we may determine this:

Years from now = Dave's age in the future minus Dave's age currently

By entering the specified values, we obtain:

The number of years from now is equal to 32 - 15 = 17 years.

Dave will turn 32 in 17 years, according to this.

We may multiply Rob's current age by the number of years from now to determine his age at that point:

When Dave reaches the age of 32, Rob will be that age plus the number of years.

When we enter the calculated values, we obtain:

When Dave is 32 years old, Rob will be 45 + 17 years old, or 62 years old.

  So, Dave uncle rob 's age will be 62 years old.

As a result, when Dave's age is 32, his uncle Rob's age will be 62.

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Answer:

10\(\sqrt{15}\) + 21\(\sqrt{10}\)

Step-by-step explanation:

-\sqrt{15}(-10-7\sqrt{6})

−

15

​

(−10−7

6

​

)

expand -sqrt15(-10-7sqrt6)

1 Expand by distributing terms.

-(-10\sqrt{15}-21\sqrt{10})

−(−10

15

​

−21

10

​

)

2 Remove parentheses.

10\sqrt{15}+21\sqrt{10}

10

15

​

+21

10

​

Answer:

The diver will hit the water at 1.5 seconds

Step-by-step explanation:

Given

\(h= -16(t-1.5)(t+1)\)

Required (Missing from the question)

When will the diver hit the water?

To do this, we simply solve for t

When the diver hits the water, the height is 0 (at that point)

So, substitute 0 for h in \(h= -16(t-1.5)(t+1)\)

\(0= -16(t-1.5)(t+1)\)

Divide both sides by -16

\(\frac{0}{-16} =\frac{-16(t-1.5)(t+1)}{-16}\)

\(\frac{0}{-16} =(t-1.5)(t+1)\)

\(0 =(t-1.5)(t+1)\)

\((t-1.5)(t+1)=0\)

Split

\(t - 1.5 = 0\) or \(t + 1 = 0\)

Solve for t

\(t = 1.5\) or \(t = -1\)

But time (t) can not be negative.

So:

\(t = 1.5\)

Hence, the diver will hit the water at 1.5 seconds

Answer:

$ 7800

Step-by-step explanation:

P'(t) = 3t² + 10t + 6

\(P(t) = \int\limits^a_b {P'(t)} \, dt\)

For the 4th year, the limits are [3,4]

\(P(t) = \int\limits^4_3 {3t^2 + 10t + 6} \, dt\\\\= [\frac{3t^3}{3} + \frac{10t^2}{2} + 6t]^{^4}__{3}\\\\\)

\(=[\frac{3(4)^3}{3} + \frac{10(4)^2}{2} + 6(4)]-[\frac{3(3)^3}{3} + \frac{10(3)^2}{2} + 6(3)]\\\\=[\frac{3(64)}{3} + \frac{10(16)}{2} + 24]-[\frac{3(27)}{3} + \frac{10(9)}{2} + 18]\\\\= [64 + 5(16) + 24]-[27+5(9) + 18]\\\\= 168-90\\\\= 78\)

= $ 7800

The baby weighed a total of 283 ounces when delivered by the mother.

We must first convert the pounds to ounces and then add up the weights to get the total weight of the babies in ounces.

The total weight of Baby A was 73 ounces, or 4 * 16 + 9.

Baby B weighed 7 pounds, 8 ounces, or 7 x 16 x 8 = 120 ounces.

Baby C weighed 5 pounds, 10 ounces, or 5 x 16 x 10 = 90 ounces.

Let's now add the weights together:

73 ounces (Child A) + 120 ounces (Child B) + 90 ounces (Child C) = 283 ounces.

As a result, the baby weighed a total of 283 ounces when delivered by the mother.

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Answer:

8/9

Step-by-step explanation:

Actually, you're evaluating a problem involving dividing fractions, not 'solving' this problem (there is no '=' sign).

  2

------

  3

==========

  3

------

   4

To divide by a fraction (see 3/4, above), invert the fraction and multiply instead.  We get:

 2          4

------  *  ------    which equals 8/9 (answer)

  3          3

The volume flow rate of the water passing through the pipe increases by a factor of 6.

Assuming that the initial cross sectional area of the pipe is A m² and the initial velocity of the water is V m/s, the water flow rate is:

= initial flow rate = area × velocity = AV m³/s

As the water speed doubles (2V m/s) and the pipe cross-sectional area triples (3A m²), the volume flow rate becomes:

Final flow rate = 2V × 3A = 6AV m³/s

As a result, the volume flow rate of the water moving through it multiplies by a ratio of six.

The basic equation for cases like these is

Q=AV,

where Q is the volume flow rate, A is the cross-sectional area occupied by the flowing material, and V is the average velocity of flow.

V is considered an average since not every component of a flowing fluid flows at the same rate. If you monitor the waters of a river moving slowly downstream at a consistent rate of gallons per second, you will see that the surface has slower currents here and faster currents there.

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The required answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

Subtraction is mathematical terminology that helps and elaborates the decrease in the original value by some value.

Here,
To perform the subtraction, you line up the decimal points and subtract the digits in each place value starting from the right. In this case, you subtract 8 from 6, which requires borrowing 1 from the digit to the left, giving you 16 - 8 = 8 in the one's place. You then subtract 2 from 5, giving you 3 in the tenth place. Continuing this process, you get the result of 82,727.12.

Thus, the answer to the subtraction problem 83,456 - 728.88 is, 82,727.12

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Answer:

Step-by-step explanation:

SOLVING

================================================================

6=-2(7-c)

Use distribution to multiply -2 by parenthesis

6=-14+2c

Add to both sides 14

20=2c

Divide 2 into both sides

10=c

5(h-4)=8

Use distribution to multiply 5 by the parenthesis

5h-20=8

Add to both sides 20

5h=28

Divide 5 into both sides

\(h=\frac{28}{5}\)

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The conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

The question asks us to find the conditional density function ????(????|???? = y) given the joint density function ????(x, y) = 6y(1 − y), 0 ≤ x ≤ y ≤ 1.

To find the conditional density function, we need to divide the joint density function by the marginal density function of y.

The marginal density function of y can be found by integrating the joint density function with respect to x:

????(y) = ∫????(x, y) dx = ∫6y(1 − y) dx = 6y(1 − y) ∫dx = 6y(1 − y) (x) |0≤x≤y = 6y(1 − y) (y - 0) = 6y^2(1 − y)

Now we can find the conditional density function by dividing the joint density function by the marginal density function:

????(????|???? = y) = ????(x, y)/????(y) = 6y(1 − y)/6y^2(1 − y) = 1/y

Therefore, the conditional density function ????(????|???? = y) = 1/y. This is a valid density function because it is non-negative and integrates to 1.

So the answer is ????(????|???? = y) = 1/y.

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Answer:

The answer is D

Step-by-step explanation:

I just took the test three times and it was correct

Answer:

The standard form of a linear equation is Ax+By=CAx+By=C.

5x+3y=2

Answer:

x = 6

Step-by-step explanation:

(3√2)² = 18

using the Pythagorean theorem:

x² = 18 + 18 = 36

x = √36 = 6

Therefore, the directional derivative of f at P=(1,-1,-2) in the direction of A=3i+2j-6k is -2.

To find the directional derivative of f(x,y,z) at P=(1,-1,-2) in the direction of A=3i+2j-6k, we first need to find the gradient of f at P, which is given by:

grad(f) = ∇f = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

Here, f(x,y,z) = xy + yz + zx, so we have:

∂f/∂x = y + z

∂f/∂y = x + z

∂f/∂z = x + y

Thus, at P=(1,-1,-2), we have:

∇f(P) = (∂f/∂x)i + (∂f/∂y)j + (∂f/∂z)k

= (y+z)i + (x+z)j + (x+y)k

= (0+(-2))i + (1+(-2))j + (1+0)k

= -2i - 1j + 1k

Next, we need to find the unit vector in the direction of A:

|A| = sqrt(3^2 + 2^2 + (-6)^2) = 7

u = A/|A| = (3/7)i + (2/7)j - (6/7)k

Finally, we can compute the directional derivative of f at P in the direction of A as:

(DAf) | 1(1,-1,-2) = ∇f(P) · u

= (-2i - 1j + 1k) · (3/7)i + (2/7)j - (6/7)k

= -6/7 - 2/7 - 6/7

= -2

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