The figure on the right is a scaled copy of the figure on the left.

Answer:

7, 10, 13, 16 and 34

Step-by-step explanation:

\(let \: t_{n} = 3n + 4 \\ when \: n = 1 \\ t_{1} = 3.1 + 4 = 3 + 4 = 7 \\ \\ when \: n = 2 \\ t_{2} = 3.2 + 4 = 6 + 4 = 10 \\ \\ \ when \: n = 3 \\ t_{3} = 3.3 + 4 = 9+ 4 = 13 \\ \\ when \: n = 4 \\ t_{4} = 3.4 + 4 = 12+ 4 = 16 \\ \\ when \: n = 10 \\ t_{10} = 3.10 + 4 = 30+ 4 = 34 \\ \\ \)

Thus the 1st, 2nd, 3rd, 4th and 10th terms are 7, 10, 13, 16 and 34 respectively

Answer:

This is an arithmetic sequence because there is a common difference of 4 between each term

4^2= 16

3^3= 27

27-16=11 so Alia has 11 jelly beans

The linear function through the points (-9,-9) and (-6,0) is given as follows:

y = 3x + 18.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

Considering the two points, we have that when x increases by 3, y increases by 9, hence the slope m is given as follows:

m = 9/3.

m = 3.

Hence:

y = 3x + b.

When x = -6, y = 0, hence the intercept b is given as follows:

0 = 3(-6) + b

b = 18.

Hence the equation is:

y = 3x + 18.

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Answer:

5

Step-by-step explanation:

Coefficient is the number before the variable/letter, for example In 7x, 7 is the coefficient

Using proportions, it is found that one sandwich costs $4.25.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

Considering x as the cost of a sandwich, the total cost is given as follows:

1.08(3x + 1.75) + 5 = 20.66.

The multiplication by 1.08 is because of the sales tax. We solve for x to find the cost of one sandwich, hence:

1.08(3x + 1.75) = 15.66

3x + 1.75 = 14.5

3x = 12.75

x = 12.75/3

x = 4.25.

Hence one sandwich costs $4.25.

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value for c is 2±√52/6 after putting Rolle's theorem

What exactly is Rolle's theorem?

According to Rolle's theorem, "If a function f is defined in the closed interval [a, b] in such a way that it satisfies the following conditions:

If is continuous on [a, b],

ii) f is differentiable on (a, b),

iii) f (a) = f (b),

then there exists at least one value of x, let us assume this value to be c

Rolle's theorem can be stated mathematically as follows:

Let f: [a, b] R be continuous on [a, b] and differentiable on (a, b), such that f(a) = f(b), where a and b are real numbers. Then there is some c in (a, b) such that f'(c)=0

first put the value[-2.2]:

f(-2)= -8-4-(-8)+3

f(-2)= -4+3

f(-2)=-1

for f(2):

f(2)=8-4-8+3

f(2)=4-8+3

f(2)=-1

Hence therefore f(-2)=f(2):

f'(c)=-2

f(x)=x³-x²-4x+3

    =3x²-2x-4=0

ROLLE'S THEOREM:  = -b±√b²-4ac/2a

Here

a = 3

b =-2

c =-4

=2±√4-4×(3)(-4)/2×3

=2±√52/6

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A kilogram of silver contains 5.58×10²⁴ atoms.

From the question given above, the following data were obtained:

Now, we shall convert 1 kg of silver to grams (g).

This can be obtained as follow:

1 kg = 1000g

Therefore, 1 kg of silver is equivalent to 1000g.

Now, let's determine the number of atoms in 1 kg (i.e 1000 g) of silver as follow:

If 107.9 g of silver contains 6.02×10²³ atoms.

Then, 1000 g of silver will contain:

= (1000 × 6.02×10²³) / 107.9

= 5.58×10²⁴ atoms.

Thus, a kilogram of silver contains 5.58×10²⁴ atoms.

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Solution

For this case we have the following expression:

We can take common factor and we got:

Then we have two possibilities:

cos x = 0

that happens for:

and the other possibility is:

sin x= 3 (No solution)

then the final answer is:

x= pi/2, 3pi/2

No, the expression (x^3 - 1) / (x^2 - 1) does not simplify to x.

To simplify the expression, let's first factorize both the numerator and denominator.

The numerator can be factorized using the difference of cubes formula: a^3 - b^3 = (a - b)(a^2 + ab + b^2). So, we have (x^3 - 1) = (x - 1)(x^2 + x + 1).

The denominator is a difference of squares: a^2 - b^2 = (a - b)(a + b). Therefore, (x^2 - 1) = (x - 1)(x + 1).

Now, we can simplify the expression by canceling out the common factors in the numerator and denominator:

[(x - 1)(x^2 + x + 1)] / [(x - 1)(x + 1)]

The (x - 1) terms cancel out, leaving us with:

x^2 + x + 1 / (x + 1)

So, the simplified form of the expression is (x^2 + x + 1) / (x + 1), which is not equal to x.

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The constant of proportionality in the equation is 5/4

The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.

The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

In the problem, y = 5/4x

The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values

The term helps in relating x to y

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Answer:

Step-by-step explanation:

From the given information:

Let's first compute the null and alternative hypothesis

Null hypothesis:

\(\mathbf{H_o: \mu_1-\mu_2=1}\)

Alternative hypothesis:

\(H_a :\mu_1 -\mu_2 > 1\)

The number of samples is half in a group of 60

i.e

\(n_1=n_2 = 30\)

the sample mean for sample 1 \(\overline x_1\) = 5.7

the standard deviation for sample 1 \(s_1\) = 3.1

the sample mean for sample 2 \(\overline x_2\) = 3.9

the standard  deviation for sample 2 \(s_2\) = 2.7

degree of freedom  for this test can be computed by using the formula:

\(df = \dfrac{\begin {pmatrix} \dfrac{s_1^2}{n_1} + \dfrac{s^2_2}{n_2} \end {pmatrix}^2 } {\dfrac{ (\dfrac{s_1^2}{n_1}^2)}{ n_1-1} + \dfrac{ (\dfrac{s_2^2}{n_2}^2)}{ n_2-1} }\)

\(df = \dfrac{\begin {pmatrix} \dfrac{3.1^2}{30} + \dfrac{2.7^2}{30} \end {pmatrix}^2 } {\dfrac{ \begin {pmatrix} \dfrac{3.1^2}{30} \end {pmatrix}^2}{ 30-1} + \dfrac{ \begin {pmatrix} \dfrac{2.7^2}{30} \end {pmatrix}^2}{ 30-1} }}\)

df = 114.68

The test statistics can be computed as follows:

\(t = \dfrac{ \overline x_1 -\overline x_2- (\mu_1 -\mu_2)}{\sqrt{ \dfrac{s_1^2}{n_1} +\dfrac{s_2^2}{n_2} }}\)

\(t = \dfrac{ 5.7-3.9- (1)}{\sqrt{ \dfrac{3.1^2}{30} +\dfrac{2.7^2}{30} }}\)

t = 1.07

Using the level of significance of 0.1, the P-value for the test statistics at the df of 114.68 is:

P-value = 0.143

Decision rule: To reject the null hypothesis if the level of significance is greater than the p-value.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance at 0.1.

Thus, it appears that the true average weight loss for the vegan diet does not exceeds that for the control diet by more than 1 kg.

The original fraction is 10/19

Let the fraction be \(\frac{x}{y}\)

Now , according to question

\(\frac{x+2}{y+5}\) =\(\frac{1}{2}\)

⇒ 2(x+2)=y+5

⇒2x-y-1=0-------(1)

and \(\frac{x-4}{y-1}\)=\(\frac{1}{3}\)

⇒3(x-4)=y-1

⇒3x-y-11=0------(2)

subtracting 1 from 2 we get

2x-y-1

3x-y-11

-  +  +

⇒ x=10

putting in (1)

20-y-1=0

y=19

∴ The actual fraction was 10/19

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The domain, range, x-intercept, or y-intercept of g(x) = f(x + 4) + 8. The features of g depend on the corresponding features of f.

Given the function g(x) = f(x + 4) + 8, let's examine its features:

Domain:

The domain of the function g will be the same as the domain of the function f, which depends on the restrictions or constraints of f.  However, it is important to note that shifting the input by 4 units (x + 4) does not inherently change the domain unless there are specific restrictions imposed by f.

Range:

Similar to the domain, the range of the function g will depend on the range of the function f.

x-intercept:

The x-intercept of a function is the point where the graph intersects the x-axis, meaning the y-coordinate is zero (y = 0). To find the x-intercept of g(x), we set g(x) = 0 and solve for x.

0 = f(x + 4) + 8

By subtracting 8 from both sides:

-8 = f(x + 4)

Since the exact value of x that makes f(x + 4) equal to -8. The x-intercept will depend on the behavior of f.

y-intercept:

The y-intercept of a function is the point where the graph intersects the y-axis, meaning the x-coordinate is zero (x = 0). To find the y-intercept of g(x), we substitute x = 0 into the function:

g(0) = f(0 + 4) + 8

g(0) = f(4) + 8

Again, the specific value of f(4) will depend on the behavior of the function f.

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Yes, it is possible for an object to have zero momentum. Momentum is defined as function the product of mass and velocity, so an object with zero mass or zero velocity will have zero momentum.

Momentum is a physical property of an object that is equal to the product of its mass and velocity. It is measured in kilogram meters per second (kg m/s) and is a vector quantity, meaning it has both magnitude and direction. In order for an object to have zero momentum, it must have either zero mass or zero velocity. An object with zero mass will always have zero momentum regardless of its velocity, while an object with zero velocity will only have zero momentum if its mass is also zero. An object with nonzero mass but zero velocity still has nonzero momentum if its mass is not zero. Therefore, it is possible for an object to have zero momentum.

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the complete question is

is it possible for an object to have no (zero) momentum? use the mathematical definition of momentum (p) to explain

It is possible for an object to have No (Zero) momentum because Momentum is the product of mass and velocity, so the object with zero mass or zero velocity will have No momentum.

What is Momentum ?

The Momentum of an object is a vector quantity that is defined as the product of the mass and velocity , the unit of measurement if Kg m/s .

So , for the object to have No (zero) momentum, the object must have either zero mass or zero velocity. that means the object with zero mass will always have No (zero) momentum regardless of velocity of the object ,

whereas the object with 0 velocity will only have No (zero) momentum if the  mass is also 0 .

Therefore , By the Mathematical Definition of momentum , Yes , it is possible for the object to have No(zero) momentum .

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Answer:

what kind of math are you working on?

Step-by-step explanation:

I'm pretty good at math, I graduate next year

Hey Emma, the same way that you asked this question, you can ask questions on this site, and someone will answer.

Answer:

x = -1

Step-by-step explanation:

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

use the distributive property to get rid of the parentheses. on -2 and -1 they cancel each other out so it becomes + 2. now you have:

3x + 3 = -2x + 2 - 4 (+2 and -4 are like terms so they become -2. so technically its 3x + 3 = -2x -2)

get +3 on the other side by subtracting it from itself and then subtracting it from -2 so it becomes -5.

3x = -2x - 5

get -2x on the other side by adding 2x to itself then adding 2x to 3x so it becomes 5x

5x = -5

divide 5 from -5 and you get x = -1

Answer:

It's 1/2

Step-by-step explanation:

Answer:

the aqnswer is one half

Step-by-step explanation:

Answer:

47.5

Explanation:

The mean is 3.4 f and the standard deviation is 0.5 kg.

Then, if we want the percentage of babies born between 3.4 kg and 4.4 kg, we want the percentage between the mean and two standard deviations from the mean because

mean + 2(standard deviation) = 3.4 kg + 2(0.5 kg)

mean + 2(standard deviation) = 4.4 kg

By the empirical rule, the percentage between two standard deviations of the mean is 95%, so the percentage between the mean and two standard deviations from the mean is

95%/2 = 47.5%

Therefore, the answer is

47.5%

Answer:

yeah, it is 35.77

Step-by-step explanation:

:)))))

Answer:

758, 578, 857, 785, 875, 587

Answer:

The first event is represented by a dot. From the dot, branches are drawn to represent all possible outcomes of the event. The probability of each outcome is written on its branch.

Step-by-step explanation:

Answer:

33.49 cubic centimeters

Step-by-step explanation:

Equation for volume: 4/3*π*r^3

Substitute 2 for r and 3.14 for π

4/3*3.14*2^3

To the nearest hundredth is 33.49

Answer: well you’d want to do -2 times 2x and 1 but keep it as -4x + -2 - then multiply 3 by x and 3 making it -4x+-2-3x+9 add like terms -4x - -3x = 7 x and 2+9 = 11 then you got 7x-11

Step-by-step explanation:

To complete the sequence "7444> →→19-", we need to find the missing terms that fit the pattern established by the given numbers. Let's analyze the sequence and identify any discernible pattern or rule.

Looking at the sequence, we can observe that each number is decreasing by a certain value. In this case, the first number is 7444, and the second number is 19, indicating a decrease of 7425. Now, we need to continue this pattern.

To find the third missing term, we subtract 7425 from 19, resulting in -7406. Therefore, the third missing term is -7406

To find the fourth missing term, we subtract 7425 from -7406, resulting in -14831. Therefore, the fourth missing term is -14831.

To find the fifth missing term, we subtract 7425 from -14831, resulting in -22256. Therefore, the fifth missing term is -22256.

Therefore, the completed sequence is:

7444> →→19- → -7406 → -14831 → -22256

Each term in the sequence is obtained by subtracting 7425 from the previous term.

It's important to note that this solution assumes a linear pattern in which the same subtraction value is applied to each term. However, without additional context or information about the sequence, there could be alternative patterns or interpretations.

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Answer:

Step-by-step explanation:

Let,

The req. number be = x

So,

Two - thirds of the number

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

Then, it is reduced by 13

\( = \frac{2}{3} x - 13\)

After that,

The req. result we get is = 7

Therefore,

By the problem,

\( = > \frac{2}{3} x - 13 = 7\)

\( = > \frac{2}{3} x = 7 + 13\)

\( = > \frac{2}{3}x = 20\)

\( = > \frac{2}{3} x \times \frac{3}{2} = 20 \times \frac{3}{2} \)

=> x = 30

Hence,

The req. number is 30.

Given that :

To Find :

Solution :

Let's assume the number as x

According to the question :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 = 7 }\)

Adding 13 to both sides we get :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x - 13 + 13 = 7 + 13 }\)

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x = 20 }\)

Now, Multiplying both sides by \( \dfrac{3}{2} \) we get :

\(\qquad \sf \: { \dashrightarrow \dfrac{2}{3}x \times \dfrac{3}{2} = 20 \times \dfrac{3}{2} }\)

\(\qquad \sf \: { \dashrightarrow \dfrac{ \cancel2}{ \cancel3}x \times \dfrac{{ \cancel3}}{ \cancel{2}} = \cancel{20} \times \dfrac{3}{ \cancel{2}} }\)

\(\qquad \sf \: { \dashrightarrow x = 10 \times {3} }\)

\(\qquad \bf \: { \dashrightarrow x = 30 }\)

Therefore, The number is 30.

Answer:

A) -27+36n

Step-by-step explanation:

3(12n-9)

36n-27