Select the correct answer. what are the solutions of this quadratic equation? x2 − 10x = -34

The volume of the similar cone that is twice as large as the first cone is 5600 cubic meters.

Let's denote the volume of the first cone as V₁ and the volume of the second cone as V₂.

We know that the first cone has a volume of 350 cubic meters, so V₁ = 350.

Now, since the second cone is twice as large, its dimensions (radius and height) will be twice those of the first cone.

Let's denote the dimensions of the first cone as r₁ and h₁, and the dimensions of the second cone as r₂ and h₂.

Since the second cone is twice as large, we have r₂ = 2 × r₁ and h₂= 2 × h₁.

Now, we can use the formula for the volume of a cone:

V = (1/3) × π ×r² × h

Plugging in the values for the second cone, we have:

V₂ = (1/3) × π × (2 × r₁)² × (2 × h₁)

= (1/3) × π×4 × r₁² × 4 × h₁

= (1/3) × π × 16 × r₁²  ×  h₁

= 16 × V₁

So, the volume of the second cone (V₂ ) is 16 times the volume of the first cone (V1).

Therefore, the volume of the similar cone that is twice as large as the first cone is 16 × 350 = 5600 cubic meters.

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To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Answer:

6a. 26

6b. 60%

6c. 33.3% or just one-thrid

7. 80.925 rounded is $80.93

8. 240

9. 25

10. 54%

Step-by-step explanation:

brainliest please!

Answer:

Step-by-step explanation:

chocolate donuta= 35% of 40

=\(\frac{35}{100} *40\)

=\(\frac{1400}{100}\)

=14

chocolate donuts=14

a.donuts that are not chocolates=40-14

=26

b.donuts with sprikles=24

percent of donjts with sprikles=24/40 *100%

=(2400/40)%

=60%

c.donuts that have cream filling out of donut that have sprikles=8

percent of donuts which have sprikles with cream filling=8/24*100%

=(800/24)%

=33.33%

7.final cost=35% of $124.50

=35/100 *$124.50

=$4357.5/100

=$43.575

8.48% 0f 500

=48/100 *500

=48*5

=240

9.let the number be x

15=60% 0f number

15=60/100 *x

15/x=60/100

do cross multiplication

x*60=15*100

x=1500/60

x=25

therefore the number is 25.

10.let the percent be y%

90=y% of 60

90=y/100 *60

90*100=60y

9000/60=y

y=150 %

therefore 150% 0f 60 is 90

Line segment BD is 12 units

Using the pythagorean theorem a^2 + b^2 = c^2

Answer:

Lani saved during 12 months

Answer:

12

Step-by-step explanation:

194-50=144

144/12=12

Answer:

12 hours

Step-by-step explanation:

We can start with an equation: 12x+50 = 194 (x being number of hours)

solving gives 12x = 144

x = 144/12

x = 12

Answer:

A

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

Neglecting friction, a similar ride with 12 passengers aboard would take 6 minutes.

The time it takes for a roller coaster ride is directly proportional to the mass of the passengers. If we assume that each passenger has the same mass, then the time it takes for the ride is proportional to the number of passengers.

Let T1 be the time for the ride with 6 passengers, and T2 be the time for the ride with 12 passengers. Then, we have:

T2 = (12/6) * T1

Simplifying this expression, we get:

T2 = 2 * T1

We are given that T1 = 3 minutes, so we can substitute this value into the equation above to find T2:

T2 = 2 * 3 minutes = 6 minutes

Therefore, a similar roller coaster ride with 12 passengers aboard would take 6 minutes, as opposed to the 3 minutes it takes with 6 passengers aboard. The answer is 6 minutes.

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Answer: 66 skirts

Step-by-step explanation:

Since research shows that they will be able to sell at most three times as many skirts as dresses, and a dress will take 10 hours to produce and a skirt will take 1 hour,

Let the time of production be in 3:1

For the production of the skirts and the dress.

If 3 hours are used to produce 3 skirts, then 10 hours will be used for 1 dress.

3 + 10 = 13

286/13 = 22

That is 22 dresses will be produced and 22 × 3 = 66 skirts will be produced.

Therefore, they should sew 66 skirts in order to maximise the profit.

Therefore, it would take about 3322 years for the Gregorian and tropical years to be out of step by exactly one day.

Length is a physical quantity that describes how long or how far apart two points or objects are from each other in space. It is typically measured in units such as meters, feet, or inches, and is one of the basic dimensions used to describe the size and position of objects in the physical world.

given by the question.

The difference between the length of the Gregorian year and the tropical year is:

365.242500 - 365.242199 = 0.000301

This means that every year, the Gregorian calendar gains 0.000301 days on the tropical year. To be out of step by exactly one day, the Gregorian calendar needs to gain one full day on the tropical year, which would take:

1 / 0.000301 = 3322.26 years.

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Answer:

  the function is either increasing or decreasing

Step-by-step explanation:

For m ≠ 0, the function must be either increasing or decreasing. If the function is increasing, it will have its maximum value at the right end of the interval. If it is decreasing, its maximum value will be at the left end of the interval.

Answer:

64 cans

Step-by-step explanation:

If two puppies eat 2 cans in two days then you can imagine one puppy eats one and the other puppy eats the other. so if 8 puppies eat in 8 days you would want to do 8 * 8 = 64 cans

Answer:

Faris' arrival time = 3:30 pm + 3 h 54 mnt = 7:24 pm

Answer:

19.24

Step-by-step explanation:

Answer:

\(y = \frac{3}{2} x + 2\)

Step-by-step explanation:

\(2y - 3x = 4\)

\(y - \frac{3}{2} x = 2\)

\(y = \frac{3}{2} x + 2\)

The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications.

Perimeter refers to the total outside length of an object,

here, we have,

the radius = r = 14 inch.

we know,

circumference = 2*pi* r

so, calculating we get,

circumference = 87.96 inch.

Hence, The solution is, the circumference of the circle with radius 14in. is  87.96 inch.

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The statement describes the incidence measure of occurrence, which refers to the number of new cases of a disease or condition that occur in a defined population over a specific period of time.

This statement describes the incidence rate of flu among students living in Dunedin hostels.
The incidence rate is a measure of occurrence that calculates the number of new cases (in this case, students getting sick with the flu) in a specific population (150 students in Dunedin hostels) over a specific time period (3 months). This rate helps us understand the frequency at which the flu is affecting this particular group of students

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The function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

To find f(t) from the Laplace transform ℋ(f(t)), we need to apply the inverse Laplace transform ℒ⁻¹ to ℋ(f(t)).

Given ℋ(f(t)) = ℋ{s(t)}, we have:

ℒ⁻¹{ℋ(s(t))} = ℒ⁻¹{ℋ[(s + 1)²/s]} = ℒ⁻¹{ℋ[s/s] + ℋ[2s/(s+1)²] + ℋ[1/(s+1)²]}

Using the properties of Laplace transforms and taking the inverse Laplace transforms, we get:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

where u(t) is the unit step function.

Therefore, the function f(t) corresponding to the Laplace transform ℋ(f(t)) = ℋ{s(t)} is:

f(t) = u(t) + 2te^(-t) + t^2/2 u(t)

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We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

18. ∆PQR =~ ∆RPA ( by SAS )

19. ∆DQR =~ ∆PQR ( by AAS )

20. ∆ARO =~ ∆PQO ( by AAS )

The flux of the vector field F = x²z i - xyz j + x²y³ k out of the surface of the cube between (0,0,0) and (2,2,2) using Gauss's theorem is  

8/3 - 4/3 - 16.

What is the polynomial equation?

A polynomial equation is an equation in which the variable is raised to a power, and the coefficients are constants. A polynomial equation can have one or more terms, and the degree of the polynomial is determined by the highest power of the variable in the equation.

To compute the flux of the vector field F = x²z i - xyz j + x²y³ k out of the surface of the cube between (0,0,0) and (2,2,2) using Gauss's theorem, we need to calculate the divergence of the vector field and evaluate the triple integral over the volume enclosed by the cube.

The divergence of the vector field F is given by:

div(F) = ∇ · F = ∂(x²z)/∂x + ∂(-xyz)/∂y + ∂(x²y³)/∂z

= 2xz - xz - 3x²y²

Now, let's evaluate the triple integral of the divergence of F over the volume enclosed by the cube.

The volume V of the cube between (0,0,0) and (2,2,2) is given by V = (2-0)(2-0)(2-0) = 8.

Using Gauss's theorem, the flux of F through the surface of the cube is equal to the triple integral of the divergence of F over the volume V:

Flux = ∭V (div(F)) dV

Since the divergence of F is already calculated as 2xz - xz - 3x²y², the flux becomes:

Flux = ∭V (2xz - xz - 3x²y²) dV

Now, we evaluate the triple integral over the volume of the cube:

Flux = ∫[0 to 2] ∫[0 to 2] ∫[0 to 2] (2xz - xz - 3x²y²) dx dy dz

Integrating with respect to x, we get:

Flux = ∫[0 to 2] ∫[0 to 2] [(xz² - (1/2)x²z - x³y²)] dx dy dz

Next, integrating with respect to y, we have:

Flux = ∫[0 to 2] [∫[0 to 2] (xz² - (1/2)x²z - x³y²) dx] dy dz

Simplifying the inner integral with respect to x:

Flux = ∫[0 to 2] [(x/3)z² - (1/6)x³z - (1/4)x³y²] evaluated from x=0 to x=2 dy dz

Flux = ∫[0 to 2] [(2/3)z² - (4/6)z - (8/4)y^2] dy dz

Integrating with respect to y:

Flux = [(2/3)z² - (4/6)z - (8/4)y³] evaluated from y=0 to y=2 dz

Flux = [(2/3)z² - (4/6)z - (8/4)(2)³] evaluated from z=0 to z=2

Flux = (2/3)(2)² - (4/6)(2) - (8/4)(2)³ - [(2/3)(0)² - (4/6)(0) - (8/4)(0)³]

Flux = (8/3) - (8/6) - (64/4) - 0

Flux = 8/3 - 4/3 - 16

Hence, the flux of the vector field F = x²z i - xyz j + x²y³ k out of the surface of the cube between (0,0,0) and (2,2,2) using Gauss's theorem is  

8/3 - 4/3 - 16.

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There is a 5% chance that we have wrongly rejected the null hypothesis and that the new ingredient does not actually reduce the drying time.

Hypothesis testing is a statistical method used to determine whether an assumption about a population parameter is supported by the sample data. In this case, the product developer is interested in determining whether the new ingredient in the primer paint reduces the drying time.

The null hypothesis assumes that there is no difference between the population means of drying time for the two formulations, while the alternative hypothesis assumes that the new ingredient reduces the drying time.

To determine the effectiveness of the new ingredient, the product developer can perform a hypothesis test.

Let's assume that the null hypothesis (H₀) is that the new ingredient does not reduce the drying time, and the alternative hypothesis (Hₐ) is that the new ingredient reduces the drying time.

H₀: μ₁ - μ₂ = 0

Hₐ: μ₁ - μ₂ > 0

Where μ₁ and μ₂ are the population means of drying time for formulation 1 and formulation 2, respectively.

Since the population standard deviation (σ) is known and the sample size is large enough (n = 10), we can use a two-sample z-test.

The test statistic can be calculated as:

z = (x₁ - x₂) / [σ × √(1/n₁ + 1/n₂)]

Where x₁ and x₂ are the sample means of drying time for formulation 1 and formulation 2, respectively.

Plugging in the given values, we get:

z = (121 - 112) / [8 × √(1/10 + 1/10)] = 4.14

Using a one-tailed test and a significance level of α = 0.05, the critical z-value is 1.645.

Since the calculated z-value (4.14) is greater than the critical z-value (1.645), we can reject the null hypothesis and conclude that there is evidence that the new ingredient reduces the drying time.

However, it's important to note that this conclusion is subject to a type I error, which is the probability of rejecting the null hypothesis when it is actually true. The probability of type I error is equal to the significance level (α), which in this case is 0.05.

Therefore,

There is a 5% chance that we have wrongly rejected the null hypothesis and that the new ingredient does not actually reduce the drying time.

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3/5 part of an hour passes in between two times given.

What is fraction?

A fraction represents a vicinity of a full or, a lot of typically, any variety of equal elements. once spoken in everyday English, a fraction describes what number elements of a precise size there ar,

Main body:

The time given are = 4:56 and 5:32

Total time spent between = 4+ 32

                                           = 36 minutes

Total minutes in 1 hour = 60

So parts spent = 36/60

now simplifying we get.

= 3/5

Hence the answer is 3/5 .

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Answer: Well 100g is 100 grams so 100 grams?

Step-by-step explanation:

The statement that, If the value of the sum of squares due to regression (SSR) can never be larger than the value of the sum of squares total (SST)  is True.

To explain this, let's define both terms:

1. Sum of squares due to regression (SSR): This represents the variation in the dependent variable that is explained by the independent variable(s) in the regression model.

2. Sum of squares total (SST): This represents the total variation in the dependent variable, without considering any explanatory variables.

Now, let's consider their relationship.

The total variation in the dependent variable (SST) can be decomposed into two components: the variation explained by the regression model (SSR) and the unexplained variation, which is the sum of squares due to error (SSE).

In other words:

SST = SSR + SSE

Since SSE represents the unexplained variation and is always non-negative, SSR can never be larger than SST. This confirms that the statement is True.

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Answer:

the value of the 7 in the number 506,087 is ONES. 

Step-by-step explanation:

This statement is False.

The formula provided in the statement is used to calculate the variance of the sample mean difference between two independent samples, but it is not necessarily true that the sample variances, and , are independent of one another.

The sample variances are calculated based on the data from their respective samples, and thus their relationship will depend on the specific data and the underlying population distributions.

For example, let's consider two samples of size n = 25, one from a normal population with mean 100 and variance 10, and another one from a normal population with mean 110 and variance 20. The sample variances for each sample are:

S1² = 9.6 and S2² = 20.8

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The quadrilateral is a trapezoid, the value of  x is  5  in given trapezoid.

An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid. See the diagram below. It indicates that sides c and d are of equal length and opposite sides a and b (the base of the trapezoid) are parallel to each other.

The given trapezoid is An isosceles trapezoid .

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

(21+27)/2 = 5x -1

24 = 5x-1

x=5

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The given question is incomplete, the complete question is:

The quadrilateral is a trapezoid. What is the value of x?

A)48

B)4

C)25

D)5

and the Question image is attached in image section.

The formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

The formula =IF(A1="A",1,IF(A1="B",2,IF(A1="D",4,5))) is a nested IF statement that checks the value of cell A1 and returns a corresponding value based on the conditions.

In this case, the value of A1 is "C". Therefore, the first condition, A1="A", is not true, so the formula moves on to the second condition, A1="B". This condition is also not true, so the formula moves on to the third condition, A1="D". However, this condition is also not true, because the third condition has a typo, where there is an extra space before the "D". Therefore, the formula evaluates the final "else" option, which is 5.

Thus, the formula will return 5, because none of the conditions in the nested IF statement are true for the value of A1 being "C".

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Answer: 9

Step-by-step explanation:

First solve the system (using elimination):

x-y=7...(1)

3x+2y=26...(2)

Multiply equation 1 by -3

 -3x+3y=-21

+ 3x+2y=26

 -----------------

     5y=5

      y=1

Substitute y=1 into equation 1

x-y=7

x-(1)=7

x=8

Let a=8 (x=a) and y=1 (y=b)

a + b

= (8) + (1)

= 9

Information provided with us :

What we have to calculate :

Performing Calculations :

Here we have been given with two equations,

From the first equation we would be getting a value of x and that value of x we would substitute in the second equation.

⇒ x - y = 7

⇒ x = 7 + y

Now, substituting it in the second equation :

⇒ 3x + 2y = 26

⇒ 3 (7 + y) + 2y = 26

⇒ 3 × (7 + y) + 2y = 26

⇒ 21 + 3y + 2y = 26

⇒ 21 + 5y = 26

⇒ 5y = 26 - 21

⇒ 5y = 5

⇒ y = 5 / 5

⇒ y = 1

★ Therefore, value of y is 1.

Now, substituting this value of y as 1 in the first equation.

⇒ x - y = 7

⇒ x - 1 = 7

⇒ x = 7 + 1

⇒ x = 8

★ Therefore, value of x is 8.

Value of a + b :-

⇒ x = a = 8

⇒ y = b = 1

Now,

⇒ a + b

⇒ 8 + 1

⇒ 9

Henceforth, value of a + b is 9.