Solve the inequality: a - 4 <10
Α. α >14
B. a < 14
C. a <-14
D. a > 6
E. a<6

HELP!!

The expression 8552/16 is solved using area model below.

What are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

8,552 ÷ 16 = ( ? ÷ 16) + ​(​ 480 ÷ 16 ​)​ + ​(​ ? ÷ 16 ​)​ + (8÷16)

1. 8,552 ÷ 16=8000/16+480/16+64/16+8/16

=500+30+4+1/2

8,552 ÷ 16=534.5

Hence,

           8,552 ÷ 16=534.5

2. 8,552 ÷ 16 = 8000/16 + 30 + 64/16 + 8/16

3. 8,552 ÷ 16 = 534 1/2

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Rounding to the nearest whole number. The correct option is D) 216 m²; 244 m².

Since the prism has a rectangular base, we know that its lateral faces are all rectangles with heights equal to the height of the prism. Let's first find the lateral area of the prism using the formula:

Lateral Area = Perimeter of Base * Height

The perimeter of the base is the sum of the lengths of all four sides of the rectangle. Since there are two bases, we will add their perimeters together. The length and width of each base are 12 m and 7 m, respectively, so:

Perimeter of Base = 2 * (Length + Width) = 2 * (12 + 7) = 38 m

The height of the prism is given as 10 m, so:

Lateral Area = 38 * 10 = 380 m²

Next, we need to find the surface area of the prism. This consists of the lateral area we just found, plus the areas of the two bases. Each base has an area of 12 * 7 = 84 m², so:

Surface Area = 2 * Base Area + Lateral Area = 2 * 84 + 380 = 548 m²

Rounding to the nearest whole number, we get:

Lateral Area ≈ 380 m²

Surface Area ≈ 548 m²

Therefore, the answer is option D) 216 m²; 244 m².

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Answer:

80% of the painters at the construction job are painting the interior of the gallery.

Step-by-step explanation:

To find the percent of painters who are painting the interior of the gallery, you can divide the number of painters painting the interior by the total number of painters, and then multiply the result by 100%.

In this case, you would do the following calculation:

28 painters / 35 painters * 100% = 80%

thus,  80% of the painters at the construction job are painting the interior of the gallery.

Step-by-step explanation:

At a construction job for a gallery there are 35 painters of these 35 painters, 28 of them are painting the interior of the gallery . what percent of these painters are painting the interior?

28/35 = 4/5 = 0.8 = 80%

Answer:

80% of the 35 painters are painting the interior.

The ratio of EG = 36.

Let's assign variables to the lengths of the line segments:

EF = x

FG = 5x

GH = 3x

We know that EH = EF + FG + GH.

Substituting the given values, we have:

54 = x + 5x + 3x

Combining like terms, we get:

54 = 9x

To isolate x, we divide both sides of the equation by 9:

54/9 = x

Simplifying, we find:

6 = x

EF = 6, FG = 5(6) = 30, and GH = 3(6) = 18.

Since EG is the sum of EF and FG, we can calculate it as follows:

EG = EF + FG = 6 + 30

= 36

EG = 36.

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Answer:

\(13\frac{27}{50}\)  

I hope this helps!

The quotient of 2708 and 200 as a mixed number in the simplest form will be 13 27/50.

The quotient of a number simply means we've to divide the given numbers. In this case, the numbers that are given are 2708 and 200.

Also, a mixed number is a number that has both a whole number, a numerator and a denominator. Therefore, dividing the number will be:

= 2708/200

= 13 27/50

Therefore, the correct option is 13 27/50.

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Answer:

Step-by-step explanation:

All the sides are complete, hence we can use the information given to find just 1 triangle

Triangles

From the given information, we have that:

m<B = pi/6 = 30 degres

c = 10

b = 5

This shows that we can use the cosine rule to find the third side b of the triangle. Since all the sides are complete, hence we can use the information given to find just 1 triangle

Answer: All the sides given are complete so we can use the information given to find 1 triangle!!

Step-by-step explanation:

43%=43/100

21/2%=1050

13.6%=136/100

521%=521/100

Answer:

F for number 14

Step-by-step explanation:

Answer:

6x+8=16

or,6x=16-8

or,6x=8

or,x=4 by 3

The  given equation have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p

Given: 2.3p – 10.1 = 6.5p – 4 – 0.01p.

Using this given property, let's write the equation

We can subtract like terms (6.5p– 0.01p = 6.49p) to get:

2.3p – 10.1 = 6.5p – 0.01p – 4

2.3p – 10.1 = 6.49p – 4

Also, we can multiply both sides of the algebraic equation by 100:

(2.3p – 10.1) x 100 = (6.5p – 4 – 0.01p) x 100

230p – 1010 = 650p – 400 – p

Therefore, the equations have the same solution as 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p. The 2nd and 3rd options are the answers

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Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer:

a)100

b) (0, -11 + √(84 - (z - 6)^2), z) and (0, -11 - √(84 - (z - 6)^2), z)

c)(2 + √(64 - (y + 11)^2), y, 0) and (2 - √(64 - (y + 11)^2), y, 0)

Step-by-step explanation:

a)

An equation of a sphere with center (a, b, c) and radius r has the form:

(x- a)^2 + (y - b)^2 + (z - c)^2 = r^2

We are given the center of the sphere as (2, -11, 6) and the radius as 10. Substituting these values into the equation, we get:

(x - 2)^2 + (y + 11)^2 + (z - 6)^2 = 100

So the equation of the sphere is (x - 2)^2 + (y + 11)^2 + (z - 6)^2 = 100.

b) To find the intersection of the sphere with the yz-plane (x = 0), we substitute x = 0 into the equation of the sphere:

(0 - 2)^2 + (y + 11)^2 + (z - 6)^2 = 100

(y + 11)^2 + (z - 6)^2 = 84

This is the equation of a circle with center (0, -11, 6) and radius √84. To find the point(s) of intersection with the yz-plane, we set x = 0 in the equation of the sphere and solve for y and z:

(y + 11)^2 + (z - 6)^2 = 84

y = -11 ± √(84 - (z - 6)^2)

So the two points of intersection with the yz-plane are

(0, -11 + √(84 - (z - 6)^2), z) and (0, -11 - √(84 - (z - 6)^2), z).

c)

To find the intersection of the sphere with the xy-plane (z = 0), we substitute z = 0 into the equation of the sphere:

(x - 2)^2 + (y + 11)^2 + (0 - 6)^2 = 100

(x - 2)^2 + (y + 11)^2 = 64

This is the equation of a circle with center (2, -11) and radius 8. To find the point(s) of intersection with the xy-plane, we set z = 0 in the equation of the sphere and solve for x and y:

(x - 2)^2 + (y + 11)^2 = 64

x = 2 ± √(64 - (y + 11)^2)So the two points of intersection with the xy-plane are (2 + √(64 - (y + 11)^2), y, 0) and (2 - √(64 - (y + 11)^2), y, 0).

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Answer:

$8200

Step-by-step explanation:

rounded to the nearest dollar

The required interest earned is $8200.

Given that,
Suppose Shelly invests $2650 semiannually into an annuity for six years. At the end of this time, she has $40,000.
To determine how much of this balance is from interest.

Simple interest is defined as the percentage of earnings on the lending for a period of time.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
Total balance earned = $40,000
Total investment in 6 year = 6*2*2650
                                            = 31,800
Interest earned = 40,000 - 31800
                          = $8200

Thus, the required interest earned is $8200.

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Answer:

Step-by-step explanation:

\(y = x + 1\\Let ; x =0\\y = 0+1\\y = 1\)

Answer:

y=5

Step-by-step explanation:

Recall that for a linear equation y = mx + b,

the gradient of the line is m and the gradient of a line perpendicular to this line is the negative reciprocal of m,

i.e:

gradient of line perpendicular to gradient m = -1/m

In our case, we are given y = x+1.

Compared to the general equation above, gradient m = 1

hence the gradient of a perpendicular line = -1/m = -1/1 = -1

therefore the perpendicular line will take the form:

y = (-1) x + b

y = -x + b, where b is the y-intercept.

We are also given that the perpendicular line passes through (4,1), we simply substitute x = 4, y = 1 into the equation

y = -x + b

1 = -4 + b   (add 4 to both sides)

1 + 4 = b

b = 5

Hence the y-intercept is y=5

Answer:

\(\displaystyle [-2, 7]\)

Step-by-step explanation:

You want to eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

\(\displaystyle \left \{ {{4x + 2y = 6} \atop {-2x + 2y = 18}} \right.\)

{½[4x + 2y = 6]

{−2x + 2y = 18

>> \(\displaystyle \left \{ {{2x + y = 3} \atop {-2x + 2y = 18}} \right. \\ \\ \frac{3y}{3} = \frac{21}{3} \\ \\ \\ y = 7\)

Plug this back into the system to get the x-value of \(\displaystyle -2.\)

I am joyous to assist you at any time.

Answer: $1500 + 3% + $82,975= 84475.03

Step-by-step explanation:

Given:

The probability of finding an elephant in a national park is 0.7.

The probability of finding a cheetah in a national park is 0.4.

The probability of finding an elephant or Cheetah or both is 0.8.

a) The probability that both the animals will be spotted is,

b) The probability of Neither of the animal will be spotted is,

Answer:

a) probability is 0.3.

b) probability is 0.7.

Answer:

a) To solve the differential equation y''-2y'-3y= e^4x, we first find the characteristic equation:

r^2 - 2r - 3 = 0

Factoring, we get:

(r - 3)(r + 1) = 0

So the roots are r = 3 and r = -1.

The general solution to the homogeneous equation y'' - 2y' - 3y = 0 is:

y_h = c1e^3x + c2e^(-x)

To find the particular solution, we use the method of undetermined coefficients. Since e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = Ae^4x

Taking the first and second derivatives of y_p, we get:

y_p' = 4Ae^4x

y_p'' = 16Ae^4x

Substituting these into the original differential equation, we get:

16Ae^4x - 8Ae^4x - 3Ae^4x = e^4x

Simplifying, we get:

5Ae^4x = e^4x

So:

A = 1/5

Therefore, the particular solution is:

y_p = (1/5)*e^4x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^3x + c2e^(-x) + (1/5)*e^4x

b) To solve the differential equation y'' + y' - 2y = 3xe^x, we first find the characteristic equation:

r^2 + r - 2 = 0

Factoring, we get:

(r + 2)(r - 1) = 0

So the roots are r = -2 and r = 1.

The general solution to the homogeneous equation y'' + y' - 2y = 0 is:

y_h = c1e^(-2x) + c2e^x

To find the particular solution, we use the method of undetermined coefficients. Since 3xe^x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax + B)e^x

Taking the first and second derivatives of y_p, we get:

y_p' = Ae^x + (Ax + B)e^x

y_p'' = 2Ae^x + (Ax + B)e^x

Substituting these into the original differential equation, we get:

2Ae^x + (Ax + B)e^x + Ae^x + (Ax + B)e^x - 2(Ax + B)e^x = 3xe^x

Simplifying, we get:

3Ae^x = 3xe^x

So:

A = 1

Therefore, the particular solution is:

y_p = (x + B)e^x

Taking the derivative of y_p, we get:

y_p' = (x + 2 + B)e^x

Substituting back into the original differential equation, we get:

(x + 2 + B)e^x + (x + B)e^x - 2(x + B)e^x = 3xe^x

Simplifying, we get:

-xe^x - Be^x = 0

So:

B = -x

Therefore, the particular solution is:

y_p = xe^x

The general solution to the non-homogeneous equation is:

y = y_h + y_p

y = c1e^(-2x) + c2e^x + xe^x

c) To solve the differential equation y" - 9y' + 20y = x^2*e^4x, we first find the characteristic equation:

r^2 - 9r + 20 = 0

Factoring, we get:

(r - 5)(r - 4) = 0

So the roots are r = 5 and r = 4.

The general solution to the homogeneous equation y" - 9y' + 20y = 0 is:

y_h = c1e^4x + c2e^5x

To find the particular solution, we use the method of undetermined coefficients. Since x^2*e^4x is a solution to the homogeneous equation, we try a particular solution of the form:

y_p = (Ax^2 + Bx + C)e^4x

Taking the first and second derivatives of y_p, we get:

y_p' = (2Ax + B)e^4x + 4Axe^4x

y_p'' = 2Ae^4x +

Answer:

Yes. There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

Step-by-step explanation:

We want to test the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

To perform this test we have a sample of 500 students which have paid their balance in full each month. The sample mean is $825 and the estimated sample deviation is considered $200.

Then, the null and alternative hypothesis are:

\(H_0: \mu=905\\\\H_a:\mu< 905\)

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=825.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{200}{\sqrt{500}}=8.94\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{825-905}{8.94}=\dfrac{-80}{8.94}=-8.94\)

The degrees of freedom for this sample size are:

\(df=n-1=500-1=499\)

This test is a left-tailed test, with 499 degrees of freedom and t=-8.94, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=P(t<-8.94)=0\)

As the P-value (0) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that college students who pay their credit card balance in full each month have a mean balance that is lower than $905.

We should add 25 both side by method of completing the square.

We have to given that;

A student is solving the problem

x² + 10x + _ = 16 + _

Now, We can completing the square as;

⇒ x² + 10x + 5² = 16 + 5²

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 16 + 25

Hence, We should add 25 both side by method of completing the square.

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2. The transformations are given as follows:

3. The transformations are given as follows:

For item 2, the transformations in this problem are given as follows:

For item 3, the transformations are given as follows:

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Answer:

x = 31.3

Step-by-step explanation:

100° and (3x + 6)° are vertical angles. Vertical angles are congruent.

To find the value of x, set both equal to each other.

3x + 6 = 100

3x = 100 - 6 (subtraction property of equality)

3x = 94

x = 94/3 (division property of equality)

x = 31.3 (nearest tenth)

Answer:

a. unbounded

e. x ≤ 9

Step-by-step explanation:

The interval means all real numbers less than or equal to 9.

Since all numbers to negative infinity are included, it is unbounded.

a. unbounded

e. x ≤ 9

A sketch looks like a number line with a solid dot at 9 and an line pointing left with an arrowhead at the left pointing left.

Answer:

b. unbounded

e. x ≤ 9

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

A bounded interval is an interval that includes both its endpoints.

For the interval (-∞, 9]:

Therefore, the given interval is unbounded.

Inequality notation

Therefore, the given interval is represented by the inequality x ≤ 9.

To sketch the graph on a number line:

To sketch the graph on a coordinate plane:

Answer:

two sides have the length of 7m

third side is 11m

Step-by-step explanation:

perimeter is the sum of all sides

let 'n' = length of congruent sides

let '2n - 3' = length of third side

25 = n + n + 2n - 3

25 = 4n - 3

28 = 4n

n = 7m

2(7) - 3 = 11m

Answer:where is the attachment?

Step-by-step explanation:

Answer:

2/5+(-3/5)

Step-by-step explanation:

2/5+(-3/5)

2/5 + 3/5

If you want the answer to it it's 1, and if I did it wrong then tell me what I did wrong.

Answer:

The answer is D.) 48

Step-by-step explanation:

I made X stand as 3 so my equations would go as follows.

AC=4(3)+12 and 2(3)+18=BC

After solving for both they both become 24 and since C looks like its half way All I did was add 24 and 24 to get 48 as the answer.

Hope this helps.

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