List all two-digit positive integers that satisfy both of the following :
1. The tens and ones digits are consecutive numbers, and
2. The integer is the product of two consecutive numbers.

Please answer it step-by-step.

Answer

a₁ = 4

d = -3

Explanation

a₇ = -14

S₇ = -35

using aₙ = a₁ + (n-1)d

a₇ = a₁ + (7 -1)d

a₇ = a₁ + 6d

substitute a₇ = -14, we have

-14 = a₁ + 6d

a₁ + 6d = -14 --------(i)

Sₙ = n/2[2a₁ + (n-1)d]

S₇ ⇒ n = 7

S₇ = 7/2[2a₁ + (7 - 1)d]

Substitute S₇ = -35, we have

-35 = 7/2[2a₁ + 6d]

Cross multiplying and opening the bracket yields

7(2a₁ + 6d) = -70

Divide both sides by 7

2a₁ + 6d = -70/7

2a₁ + 6d = -10 -------(ii)

Comparing equation (i) and (ii) and substract (i) from (ii)

a₁ + 6d = -14 --------(i)

2a₁ + 6d = -10 -------(ii)

2a₁ - a₁ = -10 - (-14)

a₁ = -10 + 14

a₁ = 4

To find d, substitute a₁ = 4 into equation (i)

Recall (i) a₁ + 6d = -14

4 + 6d = -14

6d = -14 - 4

6d = -18

d = -18/6

d = -3

Answer:

I think it is Yes, SAS

Step-by-step explanation:

The area of the canvas which was covered by the red rose is 333 square inches.

Width of the canvas = 30 inches

Length of the canvas = 37 inches

Area of the canvas = length × width

= 30 × 37

= 1110 square inches

If the painted red rose covered 30% of the painting

Area of the canvas which was covered by the red rose = 30% × 1110

= 0.3 × 1110

= 333 square inches

In conclusion, 333 square inches of the canvas is covered by the red rose.

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Answer:

x=-1.837 or 1.837

Step by Step explanation:

Use the standard form,ax²+bx+c=0 , to find the coefficients of our equation, :

q = 32

b= 0

c= -108

x=-1.837 or x=1.837

I hope this is helpful

pls tag brainliest answer

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grams. Babies of smokers typically ranged in weight from 500 to 4500 grams.

Given,

What is the weight at birth?

Birth weight is the term used to describe a newborn's body weight. Typically, newborns of European heritage weigh between 2.5 and 4.5 kilos, on average 3.5 kilograms, at delivery. Babies from South Asia and China typically weigh 3.26 kg.

Here,

Babies of nonsmokers frequently ranged in weight from 1,000 to 5,000 grams. Babies born to smokers frequently weighed between 500 and 4500 grams.

The usual ranges of birth weights between the two groups do show some notable differences, though. Nearly half of neonates among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grams since there are fewer babies in the lower weight ranges. Fewer babies are in the bigger weight groups, with 40 of 74, or 54%, of the newborns delivered to smokers having birth weights between 2,000 and 3,000 grams.

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If r is < 0, then lambda must be:  Less than 0, Less than 1, Greater than 1  and Greater than 0. The correct answers are: A), B), C), and D).

Recall that the exponential growth or decay model is given by the function:

\(y = y0 * e^(rt)\)

where y0 is the initial value of the function, r is the rate of change (growth or decay), t is the time, and e is the mathematical constant approximately equal to 2.71828.

If r < 0, then the function represents exponential decay, and we have:

\(y = y0 * e^(rt)\)

y/y0 = e^(rt)

Taking the natural logarithm of both sides, we get:

ln(y/y0) = rt

r = (1/t) * ln(y/y0)

Since ln(y/y0) is the natural logarithm of a ratio, it can take any real value. Therefore, r can take any negative value, and there is no restriction on the value of lambda (which is\(e^r\)).

So, the correct answers are: A), B), C), and D).

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Answer:

  7

Step-by-step explanation:

You want the common difference of the arithmetic sequence that starts ...

  15, 22, 29, ...

The common difference is the difference between a term and the one before. It is "common" because the difference is the same for all successive term pairs.

  22 -15 = 7

  29 -22 = 7

The common difference is 7.

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The decimal equivalent in base 10 of the largest number a system can represent depends on the number of digits available and the base value.

In any number system, the largest number that can be represented depends on the number of available digits and the base value. For example, in the decimal system (base 10), we have ten digits from 0 to 9. With these digits, the largest number we can represent with n digits is (10ⁿ- 1).

In general, if a system has a base value of b and n digits available (0 to b-1), the largest number it can represent is (bⁿ - 1). This is because the value of each digit position increases exponentially with the base value. The leftmost digit represents the base raised to the power of (n-1), the second leftmost digit represents the base raised to the power of (n-2), and so on.

For example, in the binary system (base 2), we have two digits 0 and 1. With just one digit, we can represent the numbers 0 and 1. With two digits, we can represent (2² - 1) = 3, which is the largest number in base 2 with two digits.

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Answer:

x = (A t)/4 + (p t)/4

Step-by-step explanation:

Solve for x:

A = (4 x)/t - p

A = (4 x)/t - p is equivalent to (4 x)/t - p = A:

(4 x)/t - p = A

Add p to both sides:

(4 x)/t = A + p

Multiply both sides by t/4:

Answer: x = (A t)/4 + (p t)/4

Answer: The asnwer is 8

Step-by-step explanation:

Answer:

456748

Step-by-step explanation:

you 463uy2iuswhk then 13456

Answer:

\(-\frac{1}{2}\)

Step-by-step explanation:

Gradient Formula= \(m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}\)

\(y_{2}=4\\y_{1}=2\\x_{2}=0\\x_{1}=4\)

\(=>\frac{4-2}{0-4}\)

\(=> -\frac{1}{2}\)

That's it. Hope that helped.

The probability that a randomly selected patient is affected by COVID-19 is 70%. The probability that a test is not accurate is 21.4%. If we select an affected patient, the probability that they tested negative is 20%.

1. The probability that a randomly selected patient is affected by COVID-19 can be calculated as the proportion of positive cases in the sample. In this case, it is 70%.

2. The probability that the test is not accurate can be calculated by considering the false positive and false negative rates. In this case, the false positive rate is 1.4% (patients who tested positive but are not affected), and the false negative rate is 20% (patients who tested negative but are affected).

So, the probability of the test not being accurate is the sum of these rates, which is 1.4% + 20% = 21.4%.

3. If we select an affected patient, we are looking for the probability that the patient tested negative. This can be calculated by considering the false negative rate among the affected patients.

In this case, the false negative rate is 20%. Therefore, the probability that an affected patient tested negative is 20%.

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Answer: 28.275cm^3

Step-by-step explanation: The density equation is mass/volume, and you can rearrange the equation to figure out what the volume is. By rearanging the equation, you get that volume= mass/ density. So 11.31/0.40=28.275cm^3

Answer:

B

Step-by-step explanation:

-240 +65 = -175

(We use a -240 instead of 240 because it's below water.) :)

Answer:

7x^2 - 7x + 6

Step-by-step explanation:

Rearrange equation so its easier

-2x^2 + 9x^2 - 8x + x +3 + 3

Then simplify

7x^2 - 7x + 6

Answer:

C

Step-by-step explanation:

Trust me and vote brainliest

Equivalent expression for the expression ( log 2 - log 6 ) is,

⇒ - log 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log 2 - log 6

Now, Simplify the expression by using logarithmic rule as;

⇒ log 2 - log 6

⇒ log 2 / 6

⇒ log 1/3

⇒ log 3⁻¹

⇒ - log 3

Therefore, We get;

Equivalent expression for the expression ( log 2 - log 6 ) is,

⇒ - log 3

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Answer:

Step-by-step explanation:

In this problem we are going to first solve for 10% of $35 an add it to the wholesale price to get the retail price

10% of $35

\(\frac{10}{100}*35= 0.1*35= 3.5\)

The retail price is 3.5+35= $38.5

Answer:

$38.50

Step-by-step explanation:

Answer:

molar mass of carbon-12

Step-by-step explanation:

Keno

\(|\Omega|=10^2=100\\|A|=6\cdot4=24\\\\P(A)=\dfrac{24}{100}=\dfrac{6}{25}=24\%\)

Angelita

\(|\Omega|=10\cdot9=90\\|A|=6\cdot4=24\\\\P(A)=\dfrac{24}{90}=\dfrac{4}{15}\approx26,7\%\)

Therefore, the answer is Angelita.

Answer:

50 N

Step-by-step explanation:

force = mass X acceleration

= 5 X 10

= 50 N

The cube root of -1 is -1, and the cube root ∛(-125) is -5.

To find the real nth roots of a number a, we can use the formula:

\(√(a) = a^(1/n)\)

For the case where n=3 and a=-125, we have:

\(√(-125) = (-125)^(1/3)\)

We can simplify this using the fact that

\((-a)^(1/n) = -(a^(1/n)):\)

√(-125) = - (√125)

Now we need to find the cube root of 125. We can factor 125 as 555, so:

√(-125) = - (√125) = - (√(555)) = - (5√5)

Therefore, the real cube root of -125 is -5√5.

The cube root of -125 is the real number x that satisfies the equation

\( {x}^{3} \)

= -125.

We can rewrite -125 as -1*5^3, which means we can write the cube root of -125 as ∛(-1)*∛(5^3).

The cube root of -1 is -1, and the cube root of 5^3 is 5, so ∛(-125) = -1*5 = -5.

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Answer: 0.9973 .

Step-by-step explanation:

Given: Weights of students in a junior college follows normal distribution with a mean = 100 lbs and a standard deviation =18 lbs.

Let X denotes the random variable that represents the weights of students .

Then, the probability that a student drawn at random will weigh less than 150 lbs will be :

\(P(X<150)=P(\dfrac{X_\mu}{\sigma}<\dfrac{150-100}{18})\\\\=P(Z<2.78 )\ \ \ \ [Z=\dfrac{X_\mu}{\sigma}]\\\\ =0.9973\ \ \ [\text{By p-value table for z}]\)

Hence, the e=required probability is 0.9973 .

-0.216 is a decimal itself I guess?

An equation of the plane that passes through the points P(1, 0, 2), Q(3, -1, 6), and R(5, 2, 4) is -10x - 12y - 4z + 18 = 0

surface area of z = √√x² + y² over the region D bounded by 0≤x≤ 4, 1≤ y ≤ 6. Surface Area = ∫[1 to 6]∫[0 to 4] √((2x² + y²) / (x² + y²)) dx dy

(a) To find an equation of the plane that passes through the points P(1, 0, 2), Q(3, -1, 6), and R(5, 2, 4), we can use the equation of a plane in vector form.

Let's first find two vectors that lie in the plane by subtracting the coordinates of two points from P: Q - P and R - P.

Q - P = (3 - 1, -1 - 0, 6 - 2) = (2, -1, 4)

R - P = (5 - 1, 2 - 0, 4 - 2) = (4, 2, 2)

Now, we can find the cross product of these two vectors to obtain the normal vector of the plane.

N = (2, -1, 4) × (4, 2, 2)

= ((-1 * 2 - 4 * 2), (2 * 2 - 4 * 4), (-1 * 2 - 2 * (-1)))

= (-10, -12, -4)

The equation of the plane in vector form is given by:

N · (P - P0) = 0, where P0 is any point on the plane.

Using point P(1, 0, 2), the equation becomes:

(-10, -12, -4) · (P - (1, 0, 2)) = 0

Expanding the dot product:

-10(x - 1) - 12(y - 0) - 4(z - 2) = 0

Simplifying:

-10x + 10 - 12y - 4z + 8 = 0

-10x - 12y - 4z + 18 = 0

Therefore, an equation of the plane that passes through the points P(1, 0, 2), Q(3, -1, 6), and R(5, 2, 4) is -10x - 12y - 4z + 18 = 0

.

(b) To find the surface area of z = √√(x² + y²) over the region D bounded by 0 ≤ x ≤ 4 and 1 ≤ y ≤ 6, we can set up the integral for the surface area using the formula for the surface area of a surface given by z = f(x, y):

Surface Area = ∬√(1 + (f_x)^2 + (f_y)^2) dA,

where f_x and f_y are the partial derivatives of f with respect to x and y, respectively, and dA is the area element.

In this case, f(x, y) = √√(x² + y²), so we need to calculate f_x and f_y.

f_x = (∂f/∂x) = (∂/∂x)(√√(x² + y²)) = (√(x² + y²))^(-1/2) * (1/2) * (2x) * (√(x² + y²))^(-1/2) = x / (√(x² + y²))

f_y = (∂f/∂y) = (∂/∂y)(√√(x² + y²)) = (√(x² + y²))^(-1/2) * (1/2) * (2y) * (√(x² + y²))^(-1/2) = y / (√(x² + y²))

Now, we can calculate the surface area using the integral:

Surface Area = ∬√(1 + (f_x)^2 + (f_y)^2) dA

= ∬√(1 + (x / (√(x² + y²)))^2 + (y / (√(x² + y²)))^2) dA

= ∬√(1 + x² / (x² + y²) + y² / (x² + y²)) dA

= ∬√((x² + x² + y²) / (x² + y²)) dA

= ∬√((2x² + y²) / (x² + y²)) dA

To evaluate this integral, we need to determine the limits of integration. We are given that 0 ≤ x ≤ 4 and 1 ≤ y ≤ 6. Therefore, the region D is a rectangle in the xy-plane bounded by the lines x = 0, x = 4, y = 1, and y = 6.

Using these limits, we can set up the integral:

Surface Area = ∫[1 to 6]∫[0 to 4] √((2x² + y²) / (x² + y²)) dx dy

Unfortunately, this integral does not have a simple closed-form solution and needs to be evaluated numerically using techniques such as numerical integration or software tools.

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The area of the sheet of paper in correct metric units is 602.6c\(m^{2}\).

A region's size on a plane or curved surface is expressed by the term "area," which is a mathematical concept. As opposed to surface area, which refers to the area of an open surface or the boundary of a three-dimensional object, plane region or plane area refers to the area of a form or planar lamina. Area can be thought of as the volume of material, at a particular thickness, required to create a model of the shape, or as the volume of paint required to paint the surface in a single coat. It is equivalent to the volume of a solid or the length of a curve in two dimensions (a three-dimensional concept).

Calculations:

The length of a 8 X 11 paper in metric unit is 27.9 cm and width of 8 X 11 paper in metric unit is 21.6 cm.

Area of sheet of paper=length*width

               =27.9*21.6

               =602.6 c\(m^{2}\)

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A) The rectangular equation for the path of the projectile is

y = 6 + x - 0.008x².

B) To find h, v0, and θ, we can compare the given rectangular equation with the parametric equations. By equating the coefficients of x², x, and the constant term, we can derive the values.

C) Using a graphing utility, we can plot the rectangular equation

y = 6 + x - 0.008x² and confirm the shape of the projectile's path. Additionally, we can sketch the curve represented by the parametric equations x = t(v0 cos(θ)) and y = h + (v0 sin θ)t - 16t² to visually verify the result.

In the given problem, the parametric equations describe the motion of a projectile launched at height h and angle θ with an initial velocity of v0. By eliminating the parameter t, we obtain the rectangular equation y = 6 + x - 0.008x², which represents the path of the projectile. To find the values of h, v0, and θ, we compare the coefficients of x², x, and the constant term between the rectangular equation and the parametric equations. By solving these equations, we can determine the values of h, v0, and θ.

To confirm the obtained values, we can use a graphing utility to plot the rectangular equation y = 6 + x - 0.008x². The graph will show the shape of the projectile's path. Additionally, we can sketch the curve represented by the parametric equations x = t(v0 cos(θ)) and y = h + (v0 sin θ)t - 16t² to compare it with the graph of the rectangular equation. This visual confirmation will ensure the accuracy of the calculated values.

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