Given a function f(x)=|x+1|-|x -2|
How many solutions has f(x) = a, in respect of a?
If a E {-3, 3}, number of solutions is
if a E (-3, 3) number of solutions is
if a E (-infinity, -3) U (3,infinity) number of solutions is

Exponential functions do not have a vertex.

"Exponential function, as its name suggests, involves exponents. An exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

In mathematics, an exponential function is a function of form [tex]f(x) = a^{x}[/tex], where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0."

"The standard form of a quadratic equation is y = ax² + bx + c and the vertex form of the same is y = a (x - h)² + k. Here, the vertex form has a square in it. So to convert the standard to vertex form we need to complete the square."

We know that, the graph of an exponential function consists of a horizontal asymptote. However, there is no quadratic function available that consists of a horizontal asymptote.

Hence, exponential functions do not have a vertex.

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Answer:

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means      

Step-by-step explanation:

Step(i):-

Given that the first sample size 'n₁' = 22

Given that the mean of the first sample x₁⁻ = 120

Given that the standard deviation of the sample (s₁) = 20

Given that the mean of the second sample x₂⁻ = 100

Given that the standard deviation of the second sample (S₂) = 30

Step(ii):-

T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

     where

             [tex]S^{2} = \frac{n_{1} S_{1} ^{2}+n_{2} S_{2} ^{2} }{n_{1} +n_{2}-2 }[/tex]

            [tex]S^{2} = \frac{22( 20)^{2}+ 15(30) ^{2} }{22 +15-2 }[/tex]

           S² =  637.1428

           S = √637.1428 = 25.24168  

The standard deviation of the sample 'S' = 25.24168   

Step(iii):-

Null Hypothesis:H₀:

There is no difference between the means

Alternative Hypothesis:H₁:

There is a difference between the means

         T-test statistic

               [tex]t = \frac{x^{-} _{1} -x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }[/tex]

              [tex]t = \frac{ 120 -100 }{\sqrt{637.14 (\frac{1}{22 }+\frac{1}{15 } ) } }[/tex]

             t =   2.366

Degrees of freedom

           γ = n₁+n₂ -2 = 22+15-2 = 35

     t₀.₀₅ = 2.0301

The calculated value     t =   2.366 > 2.0301 at 0.05 level of significance

The null hypothesis is rejected

There is a difference between the means          

The correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.

Let we have:

Then, the value of t-test statistic is obtained as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]

If the level of significance is [tex]\alpha[/tex], then as we have:

the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex],

the critical value of t is found to be [tex]t_{\alpha/2}[/tex] , then if we get:

[tex]|t| < t_{\alpha/2}[/tex] we cannot reject the null hypothesis

and if we get [tex]|t| > t_{\alpha/2}[/tex] , then we may reject the null hypothesis and thus, accept the alternate hypothesis.

For this case, we're specified that:

For sample of stray dogs:

For sample of stray cats:

Thus, the t-test statistic for the difference of mean of these two samples is calculated as:

[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}\\\\t = \dfrac{120-100}{\sqrt{20^2/22 + 30^2/15}} = \dfrac{20}{\sqrt{200/11 + 60}}\\\\\\t \approx 2.2619[/tex]

Thus, the correct test statistic for the test of the hypothesis for the considered situation is 2.2619 approximately.

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Answer:

do you have a picture or somthing beacuse i dont understand what your asking

Step-by-step explanation:

Answer: prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent.

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Make a big square and a little one by cutting it. 6x5 is 30 and the small one is 3x2 which is 6....add then you get 36

Answer:

x=4

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

5x – 3= 17 add 3 to both sides

5x = 20 divide both sides by 5

x = 4

Answer:

x^6/2

Step-by-step explanation:

simplify the expression, 4x^4x^3/8x, you make it 4x^7/8x

and it simplifys to 4x^6/8 which then becomes x^6/2

extra note:

a^x * a^y = a^ x+y

(see attachment below)

I hope this helps :)

Answer:

D. A news organization that is not owned by a corporation.

Step-by-step explanation:

Answer:

1. yes     2. no   3. yes

Step-by-step explanation: (put this if you have to show your work)

1.  4*0+2*1.5 (solve with a calculator or by hand)

2 y*5=7*0-5(same as above solve with a calculator or by hand)

3. 1=-2*2+5(same as above solve with a calculator or by hand)

I hope this helps you

Sayi 100A olsun

100A. 0,96=96A

100A-96A=4A

100A da 4A azaldiysa

100 de 4 azalir

Step-by-step explanation:

2x^2 - 4x - 8 = 0

x^2 - 2x - 8 =0

[tex]x = 2 ( - )(+) \sqrt{2 {}^{2} + 4.1.4 } \div 2.1 \\ x = 2( + )( - ) \sqrt{4 + 16} \div 2 \\ x = 2( - )( + ) \sqrt{20} \div 2 \\ x = 2( - )( + )2 \sqrt{5} \div 2 \\ x = 2(1( - )( + ) \sqrt{5} \div 2 \\ thefore \: x = 1 + \sqrt{5} \: or \: x = 1 - \sqrt{5} [/tex]

Answer:

C6.5

Step-by-step explanation:

LOL B-)

Answer: Its C 6.5 I got it right on a test but not sure if its right for you but i think its B also like the other guy said

The answer should be x=-2

Answer:

Y=13/4x-1/4

Step-by-step explanation:

Good luck

Answer:

that it is a cat :')

Step-by-step explanation:

remember, whisker = cat

Answer:

first of all,

Step-by-step explanation:

In triangle ABC one side equal  and two sides equal  

Step-by-step explanation:

We are given a prism whose base is square with sides 8 in and height 12 in.

If we take cross section through vertices A, B and C

We will get a cross section as triangle.

In triangle ABC, sides are AB, BC and AC

AB is diagonal of top square whose side 8 in.

AC is face diagonal of front face.

BC is face diagonal of right face.

AC=BC≠AB

Hence, In triangle ABC one side equal  and two side equal  

Hope this helps!!

Answer:

241.8 cm squared

Step-by-step explanation:

since this is a 5 sided pyramid, we would just need the triangle area calculating formula:

base X Height divided by 2

and then multiply it by 5

after you get the results, don't forget to add the area of the base too.

Answer:

So someone trolled me and deleted my answer. Don’t delete this please!! <3

Step-by-step explanation:

It is a right triangle because it has a 90º angle in it.

answer!

49 cookies were sold!

explaination!

42÷6= 7

42 plus 7 = 49

the amount of cookies sold was 49

(Sorry if it's wrong)

Answer: Sparrows generally fly shorter distances than swifts do.

Step-by-step explanation: hope this right!

Answer:

=> Swifts fly in the upper part of the air column as they hunt; swallows pursue insects closer to the ground or water.

=> If the bird is perched on a nest box, power line, or branch, that's a giveaway: Only swallows have the wherewithal to sit upright. Swifts are just stage-five clingers.

=> The swift has a slightly forked tail, not as long as the swallow's.

[tex] \infty \infty [/tex]

Answer:

E=30H

Melissa earns $330 in 11 hours

Step-by-step explanation:

Answer:

Equation = 30h=E

Melissa's earnings for 11 hours : $363

If you need further explaination I'll be happy to help!!

~ PumpkinSpice1 ♥

Answer:

A. triangle, B. quadrilateral, C. triangle, D. quadrilateral, E. quadrilateral, F. triangle, G. triangle, H. quadrilateral, I. triangle, J. triangle

Step-by-step explanation:

triangles have 3 sides, quadrilaterals have 4 sides

Answer:

A-Triangle

B- Quadrilateral

C- Triangle

D- Quadrilateral

E- Quadrilateral

F-Triangle

G-Triangle

H-Quadrilateral

I- Triangle

J-Triangle

Step-by-step explanation:

If it has 3 sides it’s a triangle, if it has 4 it’s a quadrilateral.

Answer:

20

Step-by-step explanation:

the ratio is 5:3 the you divide the 12 fiction by 3 you get 4 so if the fiction is 4 then you times it by 5 and you get 20

The ratio of fiction books to nonfiction books on the shelf is 5:3, if there are 12 fiction books are on the shelf, then total number of books on the self, 32

A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.

Given that,

The ratio of nonfiction books to fiction books on a shelf is 5:3

There are 12 fiction books on the shelf

Total number of books on the self  = ?

Suppose, the total number of books  = x

Nonfiction = x - 12

Ratio =   nonfiction/fiction

   5/3     =    x-12/12

   x      =    32

Hence, the total number of books is 32

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Answer: +

Step-by-step explanation:

Answer:

$21 per hour

Step-by-step explanation:

To find this answer you do the equation:

630/30 = ?

This equals 21.

Therefore, her hourly rate is $21 per hour.

Answer:

n 1 week, she worked 30 hours. So, she earned $630 for 30 hours. The hourly rate is then 630 / 30 = 21.