Evaluate.
—4 1/2+3(6.4+3/4)

If you want the answer simplified, its
-36x + 32

Resolviendo una ecuación lineal veremos que que Manuel tiene 36 años.

Vamos a definir la edad de Manuel como x.

Sabemos que la mitad mas el tercio mas la cuarta parte de x es igual que x más 3, entonces:

x/2 + x/3 + x/4 = x + 3

Ahora podemos resolver esta ecuación lineal para x:

x/2 + x/3 + x/4 - x = 3

x*( 1/2 + 1/3 + 1/4 - 1) = 3

x = 3/(1/2 + 1/3 + 1/4 - 1) = 36

Así, concluimos que manuel tiene 36 años.

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Answer:

5 and 9

Step-by-step explanation:

Answer:b

Step-by-step explanation: took the test

The formula for the general term of the sequence is Tn = 4n - 2

The sequence is given as:

{2, 6, 10, 14, 18, . . . }

The above sequence is an arithmetic sequence with the following features:

The formula for the general term is calculated using:

Tn = a + (n - 1) * d

This gives

Tn= 2 + (n - 1) * 4

Expand

Tn = 2 + 4n - 4

Evaluate the like terms

Tn = 4n - 2

Hence, the formula for the general term of the sequence is Tn = 4n - 2

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Answer:

18 and 6

Step-by-step explanation:

18+6=24

18/6=3

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Answer:

[tex]a=27, b=81[/tex]

Step-by-step explanation:

Plug in the values

[tex]a=3^3\\b=3^4\\\\a=27\\b=81[/tex]

Answer:

-3 13/20

Step-by-step explanation:

-3.65=

-3 65/100=

-3 13/20

Answer:

P = [tex]\frac{91}{703}[/tex] ≅ 12.95%.

Step-by-step explanation:

The total amount of chocolates in the box is 8 + 16 + 14 = 38, 14 of which are solid.

Let's calculate the probability of getting a solid chocolate in the first selection:

[tex]P(1S) = \frac{14}{38} = \frac{7}{19}.[/tex]

Given that the first piece was solid, there are now 37 pieces of chocolate in the box, 13 of which are solid. Let's now calculate the probability of selecting another solid chocolate:

[tex]P(2S\,|\,1S) = \frac{13}{37}.[/tex]

Thus, the probability of selecting two solid chocolates in a row is the product of the two probabilities calculated above:

[tex]P = \frac{7}{19}\,.\,\frac{13}{37} = \frac{91}{703}.[/tex]

Gathering information from individuals in a sample is known as : Data collection. ( B )

Statistics is the science of collecting and analyzing data in quantities, especially for the purpose of informing.

Analysis:

sample collection is the first approach to analyzing any information.

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Answer:

C. Vertex (1;-25)

F. x-intercepts: (-4;0), (6;0).

Step-by-step explanation:

1) x-coordinate of the vertex: -b/2a=1; y-coordinate of the vertex: -25;

2) for x-intercepts it needed to solve the equation x²-2x-24=0;

x=6;-4;

3) finally, correct answers are: C. Vertex (1;-25) and F. x-intercepts: (-4;0), (6;0).

Answer: [tex]h'(t)=4t^3 + 6t-1[/tex]

Step-by-step explanation:

Use the power rule for differentiation.

Step-by-step explanation:

[tex] \sec( \alpha ) - \cos( \alpha ) [/tex]

[tex] \frac{1}{ \cos( \alpha ) } - \cos( \alpha ) [/tex]

[tex] \frac{1}{ \cos( \alpha ) } - \frac{ \cos {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]

[tex] \frac{ \sin {}^{2} ( \alpha ) }{ \cos( \alpha ) } [/tex]

[tex] \frac{ \sin( \alpha ) }{ \cos( \alpha ) } \times \frac{ \sin( \alpha ) }{1} [/tex]

[tex] \tan( \alpha ) \sin( \alpha ) [/tex]

4 is the option

Answer:

(0, 22)

Step-by-step explanation:

So you have the equation:

[tex]y-1=-7(x-3)[/tex]

So first let's define what the "y-intercept" is. The y-intercept, of a line is like the name implies, when the line intercepts or "passes" the y-axis. And if you were to take any point on the y-axis, the y-value may vary, but there is one value that doesn't change, and that's the x-value. the x-value is always going to be zero, no matter where you are on the y-axis. So to find the y-intercept simple plug 0 in as x. This gives you the equation:

[tex]y-1 = -7(0-3)[/tex]

[tex]y-1 = -7(-3)[/tex]

[tex]y-1=21[/tex]

[tex]y=22[/tex]

So the y-intercept is at (0, 22)

Answer: B. Reciprocal

Step-by-step explanation:

This is a fact.

The parent function represented by f(x) = -1/x is the reciprocal function.

Therefore, the correct answer is option B.

Reciprocal functions, also known as rational functions, are defined by an algebraic expression where the dependent variable is in the denominator. In this case, the dependent variable is x, and it appears in the denominator as 1/x.

The negative sign in front of the fraction simply indicates that the function is reflected over the x-axis.

The general form of a reciprocal function is f(x) = a/x, where "a" is a constant. In the given function f(x) = -1/x, a is equal to -1.

In the case of f(x) = -1/x, the graph of the function is a hyperbola that opens downwards in the first and third quadrants. It approaches the x-axis as x moves towards positive or negative infinity, and it moves away from the x-axis as x approaches 0.

Therefore, the correct answer is option B, the reciprocal function.

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Answer:

B.concurrency.

Step-by-step explanation:

Three or more lines when met at a single point are said to be concurrent and the point of intersection is point of concurrency.

Answer:

1 day

Step-by-step explanation:

since 7 spider =7 days

1 spider =? day

cross multiply

7 days × 1 spider = 7 spider × ? days

7 spider = 7 spider × ? days

7 spider 7 spider

= 1 days

The table of values is

x -1 0 1 2 3 4 5 6

f(x) -13 -7 -1 11 35 77 143 139

The function is given as:

f(x) = x³ +5x-7

And the values of x are

x = -1, 0, 1, 2, 3, 4 5 and 6.​

Substitute these values in the function

f(-1) = (-1)³ +5(-1) - 7 = -13

f(0) = (0)³ +5(0) - 7 = -7

f(1) = (1)³ +5(1) - 7 = -1

f(2) = (2)³ +5(2) - 7 = 11

f(3) = (3)³ +5(3) - 7 = 35

f(4) = (4)³ +5(4) - 7 = 77

f(5) = (5)³ +5(5) - 7 = 143

f(6) = (6)³ +5(6) - 7 = 239

Hence, the table of values is

x -1 0 1 2 3 4 5 6

f(x) -13 -7 -1 11 35 77 143 139

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Answer:

I think it would be D the last answer on the page I am pretty confident in the answer but if for some reason it's wrong then I'm sorry.

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

Lateral Surface area of cone=πrl=πr×2h=2πrh

Lateral surface area of cylinder=2πrh

Quadrilaterals are plane shapes with four sides. Thus, the required answers are:

a) The first shape is a right trapezoid.

b) The second shape is a parallelogram.

The given properties are that of a quadrilateral, thus both shape is a quadrilateral. A quadrilateral is a family of shapes that have four straight sides. Examples include squares, rhombus, kites, etc.

A. Given that the shape has one right angle and parallel sides. Then considering the given properties, the most likely shape is a right trapezoid.

A right trapezoid is a type of trapezium that has one right angle, and a pair of parallel sides. Thus the shape here is a right trapezoid.

Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.

B. The properties of the required shape as given are: it has two pairs of congruent opposite sides, and 2 pairs of opposite parallel sides. Thus the most likely shape required here is a parallelogram. A parallelogram is a shape with parallel and congruent opposite sides, and no right angle.

Other shapes could be ruled out by comparing their properties with the properties of the shape given in the question.

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Kindly contact a 1-on-1 tutor if more explanations are required.

Answer: [tex]80\pi[/tex]

Step-by-step explanation:

- the equation for the surface area of a cylinder is [tex]A=2\pi rh+2\pi r^{2}[/tex]

- the equation for this cylinder will be [tex]A=2\pi (4)(6)+2\pi (4^{2})\\[/tex]

- so, [tex]2\pi (4)(6) = 150.7964474[/tex] and [tex]2\pi (4^{2})\\ = 150.7964474[/tex]

- then [tex]150.7964474 + 150.7964474= 251.3274123[/tex]

- finally, [tex]251.3274123/\pi = 80[/tex]

- so the answer in terms of [tex]\pi[/tex] is [tex]80\pi[/tex]

hope this helps :)

Answer:534360

Step-by-step explanation:

I did have to remove the multiplication though

The number of 1’s among the draws will be 155.

Binomial distributions consist of n independent Bernoulli trials.

The expected value is given as

E(X) = np

465 draws will be made at random with replacement from the box [0 0 1].

The number of 1’s among the draws will be

p = 1/3

n = 465

Then the expected value is given as

E(x) = 465 × 1/3

E(x) = 155

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The attached graph represents the graph of the line

The given parameters are:

Slope, m = -3

(x1, y1) = (-3, -2)

The equation is calculated as:

y = m(x - x1) + y1

So, we have:

y = -3(x + 3) - 2

Expand

y = -3x - 9- 2

Evaluate the difference

y = -3x - 11

See attachment for the graph of y = -3x - 11

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The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm

The formula for calculating the perimeter of a rectangle is expressed as;

P = 2(l +w)

If the smaller rectangle has a length of 4.3 millimeters and width of 4.5 millimeters while a larger rectangle has a length of x millimeters and width of 24.3 millimeters, then;

4.3/x = 4.5/24.3

Cross multiply

4.5x = 104.49

x = 23.22mm

Perimeter of original rectangle = 2(4.3 + 4.5)

Perimeter of original rectangle = 17.6mm

Perimeter of enlarged rectangle = 2(23.22 + 24.3)

Perimeter of enlarged rectangle = 95.04mm

The perimeter of the original rectangle is 17.6mm. The side length of the enlarged rectangle is 23.22mm and the perimeter of the enlarged rectangle is 95.04mm

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Answer:

17.6mm, 23.22mm, 95.04mm

Step-by-step explanation:

The radius of the base of the vase in cm to 2 dp is 0.08m

The formula for calculating the pressure of a object is expressed as;

Pressure = Force/Area

Area = Force/Pressure

Area = 15/750

Areas = 0.02m²

Since the area of the circular base is πr², then;

πr² = 0.02

r² = 0.02/3.14

r = 0.0798m

Hence the radius of the base of the vase in cm to 2 dp is 0.08m

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Answer:

30 cans :)

Step-by-step explanation:

We need to divide to solve so lets do that now :)

15 x 4 = 60

60/2 = 30

Have an amazing day!!

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Part A: 6 ( 8m + 2) and 48m + 12

Part B: 48m - 48m = 12 - 12

Part C: 6 (10) = 6(10)

1. The two expressions could be gotten thus;

6(m + 2 + 7m)

Collect like terms in the bracket

6 ( 8m + 2) ⇒ first expression

6(m + 2 + 7m)

Expand the bracket

6m + 12 + 42m

Collect like terms

6m + 42m + 12

48m + 12 ⇒ second expression

Part B:

6(m + 2 + 7m) = 48m + 2

Expand the bracket

6m + 12 + 42m = 48m + 2

Collect like terms

48m - 48m = 12 - 12

0 = 0

Part C:

Let the expression from A be 6 ( 8m + 2)

6(m + 2 + 7m) = 6 ( 8m + 2)

Let the number be m = 1

Substitute the values

6(1 + 2 + 7(1) ) = 6 (8(1) + 2)

6 ( 1 + 2 + 7) = 6 (10)

6 (10) = 6(10)

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The confidence interval is (-1.1059, 7.70459).

Image result for what is confidence interval

A confidence interval is the mean of your estimate plus and minus the variation in that estimate.

The sample mean is M=3.3

The sample size is N=44

So, σM= s/√N = 16.6/ √44

= 16.6/ 6.633

= 2.621

and, the degree of freedom

df= n-1

=44-1

=43

So, The t-value for a 90% confidence interval and 43 degrees of freedom is t=1.681.

Now, Margin of error = 2.261* 1.681 = 4.4059

Now, the lower and upper bound of the confidence interval are:

LL = 3.3- 4.40459 = -1.1059

UL = 3.3+ 4.40459 = 7.70459

Hence, the confidence interval is  (-1.1059, 7.70459).

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Answer: 3

8x+10=34

sub 10

8x=24 divide by 8

x=3

Step-by-step explanation: