43÷43×321= can you help me with this ​

Answer:

\(\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=31\)

Step-by-step explanation:

Fractions

We are given the expression:

\(\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}\)

We'll find an equivalent expression that results when simplifying the given fraction.

The numerator is a mixed fraction, which we'll convert into an improper fraction as follows:

\(7\frac{3}{4}=7+\frac{3}{4}=\frac{4*7+3}{4}=\frac{31}{4}\)

Now it follows:

\(\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=\frac{\frac{31}{4}}{\frac{1}{4}}\)

Instead of dividing fraction, we multiply by the reciprocal of the denominator:

\(\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=\frac{31}{4}\cdot \frac{4}{1}\)

Simplifying:

\(\mathbf{\displaystyle \frac{7\frac{3}{4}}{\frac{1}{4}}=31}\)

Answer: slope= -6.0/2.0= -3.0

Step-by-step explanation:

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is -10.000 and for x=2.000, the value of y is -16.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -16.000 - (-10.000) = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

x-intercept = -10/3 = -3.33333

 y-intercept = -10/1 = -10.00000

Answer:

D

Step-by-step explanation:

hope it helps u

The statement is the quotient of 32 and 4 added to the product of fraction 1 over 2 and 16, then subtract 2 describes the expression 32 ÷ 4 + (1/2 x 16) - 2.

The given expression is "32 ÷ 4 + (1/2 x 16) - 2".

"32 ÷ 4" is the division of 32 by 4, which results in the quotient of 8. So, the first part of the expression simplifies to 8.

"(1/2 x 16)" is the product of the fraction 1/2 and 16.

Multiplying these values gives us 8.

Now, we have "8 + 8 - 2". Adding 8 and 8 gives us 16.

Subtracting 2 from 16 results in a final value of 14.

Therefore, the expression "32 ÷ 4 + (1/2 x 16) - 2" simplifies to 14.

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To find the mass of the lamina, we need to integrate the density function over region D. The density function is given by? (x, y) = 7ky, where k is a constant. The region D is bounded by y = \((1 ? x^2)\)  and y = 0, and the limits of integration are \(0 < = y < = (1 - x^2)\) .

So, the mass of the lamina is:

\(m = ∫∫?(x, y) dx dy = ∫∫ 7ky dx dy\\= 7k ∫∫ y dx dy = 7k * ∫ (1 - x^2) dy dx\\= 7k * ∫(0 to 1 - x^2) y dy\\= 7k * (1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/2 * [((1-x^2)^3/3] - 0))= 7k * (1/2 * (1/3 - x^6))\)

To find the center of mass (x bar, y bar) of the lamina, we need to find the x and y coordinates of the center of mass.

The x-coordinate is given by

\((x bar) = 1/m * ∫∫ x ?(x, y) dx dy = 1/m * ∫∫ x * 7ky dx dy \\= 7k * ∫ (x * y) dx dy\\= 7k * (x * 1/2 * ∫(0 to 1 - x^2) y^2 dy)\\= 7k * (x * 1/2 * [y^3/3] evaluated at y = (1-x^2) and y=0)\\= 7k * (x * (1/2 * (1/3 - x^6))\\The y-coordinate is given by\\(y bar) = 1/m * ∫∫ y ?(x, y) dx dy = 1/m * ∫∫ y * 7ky dx dy= 7k * ∫ (y^2) dx dy\\= 7k * (1/3 * ∫(0 to 1 - x^2) y^3 dy)\\= 7k * (1/3 * [y^4/4] evaluated at y = (1-x^2) and y=0)\\= 7k * (1/3 * (1/4 - x^6/2))\)

It's worth noting that the mass and center of mass of the lamina depend on the constant k, which is not specified in the problem.

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Answer:

x + 4√(x + 2) + 6

Step-by-step explanation:

All we need to do is expand by using FOIL (First, Outside, Inside, Last):

x + 2 + 2√(x + 2) + 2√(x + 2) + 4

Then we combine like terms to get our final answer:

x + 2 + 4√(x + 2) + 4

x + 4√(x + 2) + 6

Answer:

96.25%

Step-by-step explanation:

The empirical rule regarding mean and standard deviation is that

Therefore between mean and +2 standard deviation or between mean and -2 standard deviation you will find  approximately 95/2 = 47.5% of the values

Between mean and ± 3 standard deviations you will find approximately 97.5/2 = 48.75% of the values

Therefore between 2 standard deviations above and 3 standard deviations below you will find approximately 47.5 + 48.75 = 96.25% of values

Answer:

Therefore, the correct statements are A, B, and E.

Explanation:

Based on my knowledge, a vector is a quantity that has both magnitude and direction. A scalar is a quantity that has only magnitude. When a vector is multiplied by a scalar, the magnitude of the vector is multiplied by the absolute value of the scalar, and the direction of the vector is either preserved or reversed depending on the sign of the scalar.

To answer your question, we need to find the component form, magnitude, and direction of the scalar product –4⇀

.

- The component form of −4⇀

is obtained by multiplying each component of ⇀

by –4. Therefore, −4⇀

= ⟨–8, –12⟩. This means that statement A is true.

- The magnitude of −4⇀

is obtained by multiplying the magnitude of ⇀

by 4. The magnitude of ⇀

is √(2^2 + 3^2) = √13. Therefore, the magnitude of −4⇀

is 4√13. This means that statement B is true.

- The direction of −4⇀

is opposite to the direction of ⇀

because the scalar –4 is negative. This means that statement C is false.

- The vector −4⇀

is in the third quadrant because its components are both negative. This means that statement D is false.

- The direction of −4⇀

is 180° greater than the inverse tangent of its components because it is opposite to ⇀

. The inverse tangent of its components is tan^(-1)(–12/–8) = tan^(-1)(3/2). Therefore, the direction of −4⇀

is 180° + tan^(-1)(3/2). This means that statement E is true.

Therefore, the correct statements are A, B, and E.

The (A ∪ B) ∩ (A ∪ C) ∩ (B ∪ C) ∩ (B ∩ C) ∩ C is an empty set {}.To find the sets A ∪ B, A ∩ B, A ∪ C, A ∩ C, B ∪ C, and B ∩ C, we can perform the following operations:

A ∪ B: The union of sets A and B includes all unique elements from both sets, resulting in {10, 11, 12, 13, 14, 16}.

A ∩ B: The intersection of sets A and B includes only the common elements between the two sets, which are {10, 12}.

A ∪ C: The union of sets A and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 13}.

A ∩ C: The intersection of sets A and C includes only the common elements, which is {10, 11}.

B ∪ C: The union of sets B and C combines all unique elements, resulting in {7, 8, 9, 10, 11, 12, 14, 16}.

B ∩ C: The intersection of sets B and C includes only the common elements, which is an empty set {} since there are no common elements.

Finally, performing the remaining operations:

(A ∪ B) ∩ (A ∪ C): This is the intersection of the union of sets A and B with the union of sets A and C. The result is {10, 11, 12, 13} since these elements are common to both unions.

(B ∪ C) ∩ (B ∩ C): This is the intersection of the union of sets B and C with the intersection of sets B and C. Since the intersection of B and C is an empty set {}, the result is also an empty set {}.

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Answer:

(a)  $897.72:  26 yr

     $1526.49:  10 yr

(b)  See below.

(c)  x = 705

     more, $705, longer it will take

Step-by-step explanation:

Given equation:

\(t=16.708 \ln \left(\dfrac{x}{x-705}\right)\)

where:

\(\begin{aligned}x=897.72 \implies t& =16.708 \ln \left(\dfrac{897.72}{897.72-705}\right)\\& =16.708 \ln \left(4.65815691...\right)\\&=16.708(1.53861985...)\\&=25.70726...\\&=26\; \rm years\end{aligned}\)

\(\begin{aligned}x=1526.49 \implies t& =16.708 \ln \left(\dfrac{1526.49}{1526.49-705}\right)\\& =16.708 \ln \left(1.85819669...\right)\\& =16.708(0.619606496...)\\&=10.352385...\\&=10 \; \rm years\end{aligned}\)

To approximate the total amounts paid (in dollars) over the term of the mortgage, multiply the monthly payment by the term.

Please note I have provided two calculations per monthly payment:

(1) by using the exact term, and (2) using the rounded term from part (a).

\(\implies \$897.72 \times 25.7072605... \times 12 =\$276935.06\)

\(\implies \$897.72 \times 26 \times 12=\$280088.64\)

\(\implies \$1526.49 \times 10.3523853... \times 12=\$189633.75\)

\(\implies \$1526.49 \times 10 \times 12 =\$183178.80\)

To calculate the amount of interest costs (in dollars) in each case, subtract $150,000 from the total amounts paid:

\(\$897.72\implies 276935.06-150000=\$126935.06\)

\(\$897.72 \implies 280088.64-150000=\$130088.64\)

\(\$1526.49 \implies 189633.75-150000=\$39633.75\)

\(\$1526.49\implies 183178.80-150000=\$33178.80\)

The natural logarithm of a negative number cannot be taken.

Therefore, x > 705.

So the vertical asymptote for the model is:

The monthly payment must be more than $705, and the closer to this value the payment is, the longer it will take to pay off the mortgage.

Answer:

Step-by-step explanation:

Move two places to the right.

Answer:

The answer is B

Answer:

Step-by-step explanation:

?

Answer:

26352

Step-by-step explanation:

Answer: 36.1481481481. So approximately 36.1

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

let's use x to represent the unknown number

1/2x is 5 more than 6:

↓

1/2x=5+6

solve to find x

1/2x=11

x=22

next, it asks us what is the value of the number when the number is tripled

since we already found what x is equal to, we can multiply that by 3 to figure out its value when it's tripled

3(22)=66

Using mathematical equation to model the scenario, the value of the number when tripled is 66

Let the number = n

0.5n = 5 + 6

0.5n = 11

Divide both sides by 0.5

n = 22

When n is tripled :

n = 22 × 3

n = 66

Hence, the value of the number when tripled is 66

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Answer:5

Step-by-step explanation:∧

distance=20 miles

time=0.4

speed=20/0.4

     Answer=5

Answer: Smaller side = 14ft

middle side = 33ft

Larger side = 37ft

Step-by-step explanation:

This triangle has 3 sides, defined by the variables:

S = length of the smallest side.

M = length of the middle side.

L = length of the larger side.

And the perimeter of a triangle is equal to the addition of the length of each side of the triangle.

We also know that:

M = 5ft + 2*S

L = 3*S - 5ft

84ft = S + M + L.

The first step is to replace the first and the second equation into the third, so we can solve it for S.

84ft = S + (5ft + 2*S) + (3*S - 5ft)

84ft = 6*S

84ft = 6*S

84ft/6 = 14ft = S.

Now that we found the length of the shorter side, we can replace it in the above equations to find the length of the other two sides:

M = 5ft + 2*S = 5ft + 2*14ft = 33ft

L = 3*S - 5ft = 37ft

Answer:

I think its C

Step-by-step explanation:

Answer:

He began with 14 please mark brainliest

Step-by-step explanation:

13-6 equals 7

7 times 2 equals 14

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Answer + Step-by-step explanation:

\(\frac{5^{10}}{5^{5}} =5^{10-5} = 5^5\)

\(\text{used property :} \ \ \ \frac{a^{m}}{a^{n}} =a^{m-n}\)

_______________________

\((4^8)^3 = a^{8 \times 3}=a^{24}\)

\(\text{used property :} \ \ \ (a^n)^m = a^{n \times m}\)

_______________________

\(10^{-4}=\frac{1}{10^{4}} \ \text{not} \ \frac{1}{4^{10}}\)

_______________________

15⁶ × 15³ = 15⁶⁺³ = 15⁹

_______________________

Recall : If a ≠0  ⇒ a⁰ = 1

Then

Since 6⁸ ≠ 0  ⇒ (6⁸)⁰ = 1  

Answer:

(x-x)/(y-y)

Step-by-step explanation:

Slope is defined by the change in y divided by the change in x, not the change in x divided by the change in y.

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:

your answer will be X=11.1

hope it helps you ...

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Part A: Grocery Store: unit price = $1.65 (Tomatoes)

Farmer's Market: unit price  = $1.75

Part B: Grocery Store offers a better deal because the unit price is less.

Unit price is defined as the price for one of something. For example, if 10 oranges cost $50, the unit price will be $50/10 = $5 i.e.  $5 for one orange.

PART A:

Let's choose tomatoes

Grocery Store

8 tomatoes for $13.20

Unit price = $13.20/8 = $1.65

10 tomatoes for $17.50

Unit price = $17.50/10 = $1.75

Part B:

The location that offers a better deal is Grocery Store. This is because the unit price is less.

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Answer:

Step-by-step explanation:

The next number is 110

Answer:

True

Step-by-step explanation:

If a is negative then the shape of the graph is an upside down U, which intersects the x-axis. If a is positive it will never cross the X axis.

It is true that f(x)=\(a^{x}\)+4 will never cross the x axis if a is positive.

Function is relationship between two or more that are variables expressed in equal to form. In a function each value of x must have a corresponding value of y.

We have been given that f(x)=\(a^{x} +4\) and we have to find whether it will cross x axis or not.

when a line crosses the x axis the value of y becomes negative. We have to first check at y=0.

\(a^{x}+4\)=0

\(a^{x}\)=-4

taking log both sides,

log \(a^{x}\)=log(-4)

x log a=0.602059991+1.3437635i

x=(0.602059991+1.3437635i)/log a

when we put the value of x in f(x) the value of f(x) cannot be negative so it cannot crosses the x axis.

Hence it is true that f(x)=\(a^{x}\)+4 will never cross the x axis if a is positive.

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Answer:

238 B

Step-by-step explanation:

8.5*28    

Answer:

Step-by-step explanation: