What is (7.8×10^3) times (1.0x10^4)

PlZzzzzz help me I’m putting 20 points and give me the exact answer!
PLZZZZZZZ

Answer:

0.2(y-2)

Step-by-step explanation:

factor out 1/5 from the expression

1/5×(y-2)

0.2(y-2)

Answer:

\(3x - 6 = 9\)

Answer:

Approximately 619.42

Step-by-step explanation:

The formula for finding the volume of a cone is  V=1/3hπr². (R is the radius and h is the height.

Answer:

Step-by-step explanation:

C

The mean for this binomial distribution is 12.

In probability theory, the mean of a binomial distribution is the product of the number of trials (n) and the probability of success in each trial (p).

Therefore, to find the mean of a binomial distribution with n = 20 and p = 3/5, we can simply multiply these two values together:

mean = n * p

= 20 * 3/5

= 12

So, the mean for this binomial distribution is 12. This means that on average, we can expect to see 12 successes in 20 independent trials with a probability of success of 3/5 in each trial

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Answer:

2 and 6

Step-by-step explanation:

Adjacent angles require a common vertex, side, and the interiors don't overlap.

Answer:

Step-by-step explanation:

Answer: 6

there are 24 fish and 4 tanks so divide 24 by 4 and you'll have 6

Answer:

the number of fish in each tank is 6

Step-by-step explanation:

becuause 24 divided be 4 is 6

Answer:

91 - 74 = 17

Step-by-step explanation:

The range is the difference between the highest and lowest values in a set of numbers.

Use the appropriate angle rule(s) to solve angles in Mathematical problems.

When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol '∠' stands for the angle. The Latin word "Angulus" is where the term "angle" originated.

These angles are usually measured in degrees like 45°, 30°, 50°, 15°, 110°, 75° and 120° etc.  

Here are some key points and rules to solve angles in Maths

Angles on a straight line

A straight line's angles always add up to 180 degrees. We use this rule to solve angles lying on a straight line.

Angles around a point or angle in a circle

Angles that circle a point always equal 360 degrees. We use this rule to solve angles related to circles, sectors, closed polygons, etc.  

Supplementary angles:

The pair of angles that are added up to 180° are known as Supplementary angles. Example, 150°, 30°;  120°, 60°;  100°, 80° etc.

Complementary angles

The pair of angles that are added up to 90° are known as angles Complementary angle. Examples, 45°, 45°; 50°, 40°; 60°, 40° etc.  

Vertically opposite angles

The angles formed by intersecting two straight lines opposite to each other are known as Vertically opposite angles. In any situation, the vertically opposite angles will equal each other

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If the cost of one paperback book is less than $1, he would receive even more change.

To solve this problem, we need to know the cost of one paperback book. Unfortunately, that information is missing from the question. Without it, we cannot determine the total cost of the 5 paperback books and therefore cannot calculate Prakash's change.

However, we can make an educated guess based on the fact that the question mentions both paperback and hardcover books. Typically, hardcover books are more expensive than paperbacks, so we can assume that the cost of one paperback book is less than the cost of one hardcover book.

Assuming that each hardcover book costs $10, the total cost of 3 hardcover books would be $30. If Prakash gives the clerk $20 bills, he would pay $60 in total. If we subtract the cost of the 3 hardcover books ($30) from the total amount paid ($60), we are left with $30.

This is the maximum amount of change Prakash could receive if each paperback book costs $1.

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Thus, the radius of convergence of the series is 4. That shows  that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4.

To find the radius of convergence of the given series, we can use the ratio test.

The ratio test states that for a series ∑an, if the limit of |an+1/an| as n approaches infinity is L, then the series converges absolutely if L < 1, diverges if L > 1, and inconclusive if L = 1.

So, applying the ratio test to the given series, we get:

|a(n+1)/an| = |(n+1)!x^(n+1) 3 · 7 · 11 · ⋯ · (4n + 3) / n!x^n 3 · 7 · 11 · ⋯ · (4n − 1)|
= |(n+1)x / (4n+3)|
= |x/(4 + 3/n)|

Taking the limit as n approaches infinity, we get:
lim n→∞ |a(n+1)/an| = |x/4|

Since we want this limit to be less than 1, we have:
|x/4| < 1

Solving for x, we get:
-1 < x < 4

Therefore, the radius of convergence of the series is 4. This means that the series converges absolutely for all values of x such that |x| < 4, and diverges for all values of x such that |x| > 4. When |x| = 4, the series may converge or diverge, and further analysis is needed to determine this.

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Answer:

9b + 3c

Step-by-step explanation:

1. Combine like terms:

(7b + 2b) + 3c

2. Simplify.

9b + 3c

Answer:

9b + 3c or 9b^2 + 3c

Step-by-step explanation:

Add 7b & 2b:

9b or 9b^2

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Answer:

The population at the beginning of 2016 is 55,326.

Step-by-step explanation:

Giving the following information:

Population 2010 (PV)= 42,000

Growth rate (g)= 4.7% = 0.047

Number of years (n)= 6 years

To calculate the population at the beginning of 2016, we need to use the following formula:

FV= PV*(1+g)^n

FV= 42,000*(1.047^6)

FV= 55,326

The population at the beginning of 2016 is 55,326.

The displacement of the compressor is 628 cubic centimeters. Other factors that affect the performance of a compressor include its operating pressure, flow rate, efficiency, and power consumption.

To find the displacement of the compressor, we need to use the formula:
Displacement = (pi/4) x bore^2 x stroke
Here, the bore is 8 centimeters and the stroke is 10 centimeters. So, substituting these values in the formula, we get:
Displacement = (pi/4) x 8^2 x 10
Displacement = (3.14/4) x 64 x 10
Displacement = 628.32 cubic centimeters

A compressor is a mechanical device that is used to increase the pressure of a gas or air by reducing its volume. It works by compressing the gas or air in a cylinder and then transferring it to a storage tank or other equipment. The displacement of a compressor is a measure of the volume of gas or air that is displaced or compressed during one complete cycle of the compressor. Therefore, the displacement of the compressor is 628 cubic centimeters. This means that during one complete cycle of the compressor, it displaces or compresses 628 cubic centimeters of gas or air. The displacement is an important parameter of a compressor, as it determines its capacity or the amount of gas or air that it can compress in a given time.

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The displacement of the compressor is 160π cubic centimeters.

To find the displacement of the compressor, we first need to understand what displacement means. Displacement is the change in position of an object in a specific direction. In this case, the compressor has a bore of 8 centimeters and a stroke of 10 centimeters. The displacement of the compressor can be calculated as the product of the bore area (πr^2) and the stroke length.

Displacement = π(4^2) * 10 = 16π * 10 = 160π cubic centimeters.

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Answer:

B

Step-by-step explanation:

1. The total distance of the race is 44 miles. 2. There are 13 female senators and 71 female members of the House of Representatives in Congress. Jane will pay $387.50 per month.

1. We are given that Mark ran half the distance and swam a quarter of the distance before starting to bike the remaining 11 miles. Let's represent the total distance of the race as "D."

The distance Mark ran is half of D, so it is D/2.

The distance Mark swam is a quarter of D, so it is D/4.

After Mark's break, he started biking the remaining 11 miles.

Since the total distance of the race is the sum of the distances Mark ran, swam, and biked, we can set up the following equation:

D/2 + D/4 + 11 = D

To solve for D, we can simplify the equation and solve for D:

Multiply the equation by the common denominator, which is 4:

2D + D + 44 = 4D

3D + 44 = 4D

Subtract 3D from both sides:

44 = D

Therefore, the total distance of the race is 44 miles.

2. In the second problem, we are given that there are 84 female officials in Congress, and the number of female members of the House of Representatives is 58 more than the number of female senators. Let's represent the number of female senators as "S" and the number of female members of the House of Representatives as "H."

We are given that the total number of female officials is 84, so we can write the equation:

S + H = 84

We are also given that the number of female members of the House of Representatives is 58 more than the number of female senators:

H = S + 58

To solve for the values of S and H, we can substitute the second equation into the first equation:

S + (S + 58) = 84

2S + 58 = 84

Subtract 58 from both sides:

2S = 26

Divide both sides by 2:

S = 13

Substitute the value of S back into the equation for H:

H = 13 + 58

H = 71

Therefore, there are 13 female senators and 71 female members of the House of Representatives in Congress.

3. In the third problem, Jane and her two friends will rent an apartment for $775 a month, but Jane will pay double what each friend does because she will have her own bedroom. Let's represent the amount each friend pays as "F" and the amount Jane pays as "J."

We are given that Jane will pay double what each friend pays, so we can write the equation:

J = 2F

The total amount they will pay is $775, so we can write the equation:

F + F + J = 775

Substituting the value of J from the first equation into the second equation:

F + F + 2F = 775

4F = 775

Divide both sides by 4:

F = 193.75

Substitute the value of F back into the equation for J:

J = 2(193.75)

J = 387.50

Therefore, Jane will pay $387.50 per month.

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The solution to the given separable differential equation for u, with the initial condition u(0) = 7.

To solve the separable differential equation for u, we start by rearranging the equation f as:

(1/u) du/dt = e^(3u)/u + 10t/u

We can now integrate both sides of the equation with respect to t and u, separately. Starting with the left-hand side, we have:

∫(1/u) du = ln|u| + C1

where C1 is the constant of integration. For the right-hand side, we can use u-substitution by letting v = 3u, dv/du = 3, and du/dv = 1/3u. Substituting these values into the equation f and simplifying, we have:

(1/3) ∫e^v dv = (1/3) e^v + C2

where C2 is another constant of integration. Substituting v = 3u back into the equation and combining the constants of integration, we get:

ln|u| = e^(3u)/3 + 10t/3 + C

where C = C1 + C2. To solve for u, we exponentiate both sides of the equation:

|u| = e^(e^(3u)/3 + 10t/3 + C)

We can drop the absolute value since u(0) = 7 > 0, and simplify the exponential expression by using the properties of exponents:

u = e^(e^(3u)/3) * e^(10t/3 + C)

Finally, we use the initial condition u(0) = 7 to solve for C:

7 = e^(e^(3(7))/3) * e^(10(0)/3 + C)
7 = e^(e^21/3) * e^C
ln(7/e^(e^21/3)) = C

Substituting this value of C back into the equation for u, we get:

u = e^(e^(3u)/3) * e^(10t/3 + ln(7/e^(e^21/3)))

This is the solution to the given separable differential equation for u, with the initial condition u(0) = 7.

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For the the inequality –3(2x – 5) < 5(2 – x) the correct options are: x < 5, –6x + 15 < 10 – 5x

What is inequalities?

In mathematics, an inequality is a mathematical statement that indicates that two expressions are not equal. It is a statement that compares two values, usually using one of the following symbols: "<" (less than), ">" (greater than), "≤" (less than or equal to), or "≥" (greater than or equal to).

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

x < 5 (obtained by simplifying the inequality and solving for x)

–6x + 15 < 10 – 5x (obtained by distributing the terms and simplifying the inequality)

Therefore, the correct options are:

x < 5

–6x + 15 < 10 – 5x

The options that describe number lines are not applicable to this inequality since they represent a single value, whereas an inequality represents a range of values that satisfy the inequality.

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Answer:

$2.45*4/7=$1.4

So felipe gets $1.4

Step-by-step explanation:

$2.45*4/7=$1.4

So felipe gets $1.4

a false association between two variables that is actually due to the effect of a third variable is called a confounding variables.

In the context of a mathematical problem or experiment, a variable is anything that may be altered. Typically, a variable is denoted by a single letter. Common generic symbols used for variables include the letters x, y, and z. An attribute that can be measured and have a wide range of values is called a variable. Size, age, wealth, place of birth, academic standing, and kind of housing are a few examples of factors. Both categorically and numerically can be used to categorise variables into two primary groups.

Third factors that affect both the independent and dependent variables are referred to be confounding variables. You risk overestimating the correlation between your independent and dependent variables if you don't take confounding factors into account.

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Answer:  the sample proportion for those who favor Candidate Two is approximately 0.422 or 42.2%.

Step-by-step explanation:

To find the sample proportion for those who favor Candidate Two, we need to subtract the number of voters who favor Candidate One from the total number of voters and divide it by the total number of voters.

Total number of voters: 1,065

Number of voters who favor Candidate One: 615

Number of voters who favor Candidate Two: 1,065 - 615 = 450

Sample proportion for those who favor Candidate Two: 450 / 1,065 ≈ 0.422 (or approximately 42.2%)

The cooking time for a 20 lb turkey in an electric roaster can vary depending on several factors, including the specific model of the roaster and the desired level of doneness.

As a general guideline, it is recommended to cook a turkey in an electric roaster at a temperature of 325°F (163°C). The estimated cooking time for a 20 lb turkey in an electric roaster is approximately 3.5 to 4.5 hours. However, it's essential to use a meat thermometer to ensure the turkey reaches a safe internal temperature of 165°F (74°C) in the thickest part of the thigh.

To determine the exact cooking time for your turkey, it is best to consult the manufacturer's instructions for your specific electric roaster model, as they may provide more accurate guidelines based on the appliance's features and specifications.

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Answer:

D). Mode

Step-by-step explanation:

I hope this helps!! Have a good day!

Answer:

they all are.

Step-by-step explanation:

They all are a measure of central tendency Standard deviation is not. Hope this helps :D

Answer:

121 feet

Step-by-step explanation:

By graphing the equation we can see the maximum y value is 121

Answer:

a=9

b=-6

Step-by-step explanation:

The statement that is true among the given options is that both false position and secant methods are in the open method category.

The methods mentioned in the options are numerical methods used for finding roots of equations. Let's evaluate each statement to determine which one is true:

1. Method of false position always converges to the root faster than the bisection method: This statement is not true. The convergence rate of the method of false position and the bisection method depends on the specific equation being solved. In some cases, the false position method may converge faster, while in others, the bisection method may converge faster. The convergence rate can vary depending on the behavior of the function and the initial interval.

2. Method of false position always converges to the root: This statement is not true. The method of false position may not always converge to the root. There can be cases where the method fails to converge, such as when the function is highly nonlinear or has multiple roots within the initial interval.

3. Both false position and secant methods are in the open method category: This statement is true. The false position method and the secant method are both categorized as open methods because they do not require a bracketed interval to start the iteration. They can be applied with a single initial guess and iteratively approach the root.

4. Secant and Newton's methods both require the actual derivative in the iterative process: This statement is not true. While Newton's method requires the derivative of the function, the secant method approximates the derivative using two function evaluations without explicitly requiring the actual derivative.

Based on the explanations provided, the statement that is true is that both false position and secant methods are in the open method category.

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x=-13

x=2

Answer:

Solution given:

5-2x=\(\sqrt{2x²+x-1}-x\)

keep square root alone

5-2x+x=\(\sqrt{2x²+x-1}\)

5-x=\(\sqrt{2x²+x-1}\)

squaring both side

(5-x)²=2x²+x-1

25-10x+x²=2x²+x-1

2x²+x-1-25+10x-x²=0

x²+11x-26=0

doing middle term factorisation

for this

coefficient of first and last terms should be multiplied

here

1*26=26

factor product

26=2*13*1

remember that check the sigh of last term

in here it is - so

we need to get 11 by subtracting factor of 26

we get

13-2=11

keep 13-2 value in place of 11

x²+(13-2)x-26

now

distribute

x²+13x-2x-26=0

take common from each two term

x(x+13)-2(x+13)=0

(x+13)(x-2)=0

either

x=-13

or.x=2

Answer:

A and B

Step-by-step explanation:

we would like to solve the following equation:

\( \rm\displaystyle 5 - 2x = \sqrt{ {2x}^{2} + x - 1 } - x\)

to do so isolate -x to the left hand side and change its sign:

\( \rm\displaystyle 5 - 2x + x = \sqrt{ {2x}^{2} + x - 1 } \)

simplify addition:

\( \rm\displaystyle 5 - x = \sqrt{ {2x}^{2} + x - 1 } \)

square both sides:

\( \rm\displaystyle (5 - x {)}^{2} = (\sqrt{ {2x}^{2} + x - 1 } {)}^{2} \)

simplify square of the right hand side:

\( \rm\displaystyle (5 - x {)}^{2} = {2x}^{2} + x - 1 \)

use (a-b)²=a²-2ab+b² to expand the left hand side:

\( \rm\displaystyle {x}^{2} - 10x + 25= {2x}^{2} + x - 1 \)

swap the equation:

\( \rm\displaystyle {2x}^{2} + x - 1 = {x}^{2} - 10x + 25\)

isolate the right hand side expression to the left hand side and change every sign:

\( \rm\displaystyle {2x}^{2} + x - 1 - {x}^{2} + 10x - 25 = 0\)

simplify:

\( \rm\displaystyle {x}^{2} + 11x - 26= 0\)

rewrite the middle term as 13x-2x:

\( \rm\displaystyle {x}^{2} + 13x - 2x - 26= 0\)

factor out x:

\( \rm\displaystyle x({x}^{} + 13)- 2x - 26= 0\)

factor out -2:

\( \rm\displaystyle x({x}^{} + 13)- 2(x + 13)= 0\)

group:

\( \rm\displaystyle (x- 2)(x + 13)= 0\)

by Zero product property we obtain:

\( \displaystyle \begin{cases}x- 2 = 0\\ x + 13= 0 \end{cases}\)

solve for x:

\( \displaystyle \begin{cases}x = 2\\ x = - 13 \end{cases}\)

to check for extraneous solutions we can define the domain of equation recall that a square root of a function is always greater than or equal to 0 therefore

\( \rm\displaystyle 5 - x \geq0\)

solve the inequality for x:

\( \rm\displaystyle x \leqslant 5\)

since 2 and -13 is less than 5 both solutions are valid for x hence,

\( \displaystyle \begin{cases}x _{1} = 2\\ x_{2} = - 13 \end{cases}\)

and we're done!

Step-by-step explanation:

15y-14y=1y

14 years is stracted from 15 years

Answer: One way is Rise/Run or Y/X

Step-by-step explanation:

You first find two points on the graph and Y2-y1 gives you the rise and X2-X1 gives you the run you then put the rise on top and the run below to get Y/X or rise over run

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