Write the inequality

-3 and 4 cannot be the values of x in the given expression

The expression is given as:

[tex]\frac{(x^2-x-6x^2-8x+16)}{(x^2-x-12)}[/tex]

Start by equating the denominator to 0

[tex]x^2 - x - 12 = 0[/tex]

Expand the above equation

[tex]x^2 - 4x + 3x - 12 = 0[/tex]

Factorize the equation

[tex]x(x - 4) + 3(x - 4) = 0[/tex]

Factor out x - 4

[tex](x + 3) (x - 4) = 0[/tex]

Split

[tex](x + 3)= 0\ or\ (x - 4) = 0[/tex]

Remove brackets

[tex]x + 3= 0\ or\ x - 4 = 0[/tex]

Solve for x

[tex]x =- 3\ or\ x = 4[/tex]

Hence, -3 and 4 cannot be the value of x in the given expression

Read more about expressions at:

https://brainly.com/question/2972832

Using the t-distribution, it is found that since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.

At the null hypothesis, it is tested if isolated compounds do not give more counts than those from background, that is:

[tex]H_0: \mu_1 - \mu_2 \leq 0[/tex]

At the alternative hypothesis, it is tested if the give more counts, that is:

[tex]H_1: \mu_1 - \mu_2 > 0[/tex]

Using a calculator, the mean and the standard deviation for each sample are given by:

[tex]\mu_1 = 33.2, s_1 = 6.058[/tex]

[tex]\mu_2 = 24.25, s_2 = 4.35[/tex]

Considering the sample sizes of 5 and 4, respectively, the standard errors are given by:

[tex]s_1 = \frac{6.058}{\sqrt{5}} = 2.71[/tex]

[tex]s_2 = \frac{4.35}{\sqrt{4}} = 2.175[/tex]

For the distribution of differences, the mean and standard error are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 33.2 - 24.25 = 8.95[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{2.71^2 + 2.175^2} = 3.4749[/tex]

The standard error was found from the standard deviation for each sample, hence, the t-distribution is used.

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis, hence:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{8.95 - 0}{3.4749}[/tex]

[tex]t = 2.58[/tex]

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with 5 + 4 - 2 = 7 df and a 0.05 significance level is of [tex]t^{\ast} = 1.895[/tex]

Since the test statistic is more than the critical value for the right-tailed test, it can be conclude that the isolated compound gives more counts than those from background, and hence, we can be 95% confident that the compound is indeed radioactive.

A similar problem is given at brainly.com/question/24826023

Answer:

a

Step-by-step explanation:

a

Answer:

ABCD are the first 4 letters ina alphabet sooooo brooo wheres the parallelogram??

Step-by-step explanation:

Answer:

answer: 0

Step-by-step explanation:

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 (x+4)•(x-1)

 ——————————— • 2 = 0 • 2

      2    

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  (x+4)  •  (x-1)  = 0

7.2    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

simple form

x = 1

x = -4

Answer:

[tex]a = \frac{14 - b}{5}[/tex]

Step-by-step explanation:

The rule to know and follow is:

You can add, subtract, multiply or divide by anything so long as the same thing is done to both sides of the equals sign;

5a + b = 14

If we want to get: "a = ...", then we use the rule to isolate the variable a on one side of the equation;

Firstly, we subtract b from both sides:

5a + b - b = 14 - b

5a = 14 - b

Then, divide both sides by 5:

[tex]\frac{5a}{5} = \frac{14 - b}{5} \\\\ a = \frac{14 - b}{5}[/tex]

Answer:

A (2,2) B (4, -2) C (-4,0)

Step-by-step explanation:

K = 2

K is the scale factor so the y and x distance between the points will double

just take to coordinates and multiply them by 2

A 1,1 new 2,2

B 2, -1 new 4,-2

C -2,0 new -4,0

Answer:

x = 20

Hope you could get an idea from here.

Doubt clarification - use comment section

[tex]\dfrac{\sqrt[3]{343}}{\sqrt[3]{-343}}=\dfrac{\sqrt[3]{343}}{-\sqrt[3]{343}}=-1[/tex]

Answer:

new equation : 1.09t = new price

Step-by-step explanation:

1.09(15.99) = 17.4291

it's about $17

Answer:

15. d(1,3) e(4,4) g(1,-1) f(4,-2)

16. e(2,-1) f(4,-1) g(2,-3) h(4,-5)

Step-by-step explanation:

These are the coordinates to each point (x,y)

I hope this helps!!

Answer:

1/28

Step-by-step explanation:

Answer:

B. 1/3

Step-by-step explanation:

This question is designed to show if you know the exponent rules. Exponent Rules are short cuts. If you are multiplying two terms and they both have the same base (the big bottom number), then you could ADD the exponents (the small font raised numbers) Here the base is 3 in both terms. We keep that base. Then add 2/5 and -7/5 to get -5/5. This is just -1.

Another Exponent Rule is how to use negative exponents. So far we have 3^-1 (that means three to the negative one power)

In order to make that negative exponent positive, you just move it across the fraction bar. So we would lower it below the fraction bar to make it a positive one exponent. So you end up with 1/3

Answer:

Step-by-step explanation:

4x+3=3x+5

x+3=5

x=2

Subsitute: 4x+3=11

XM=11

Answer:

9.3 centimeters

Step-by-step explanation:

Answer:

Continuous

Step-by-step explanation:

Answer:

Solution given in the photo

Answer:

8 yards

Step-by-step explanation:

1 yard is equal to 3 feet, so we just do 24/3 = 8 yards

Answer:

8

Step-by-step explanation:

1 feet is 3 yards so 24 yards is 8

Answer:

-Below.

Step-by-step explanation:

4) When the carton is unopened the number of servings x = 0.

So there are 64-4(0) = 64 ounces in an unopened carton.

5) When all the milk has been poured out no. ounces left (y)  = 0 so

64 - 4x = 0

4x = 64

x = 16

So each serving contains 16 ounces of milk.

Answer: the answer is 7.5

Step-by-step explanation:

Answer:

Step-by-step explanation:

they arent similar because the ratio of 8 to 14 and 10 to 18 arent the same.

The simple interest is $3352.

Using PRT/100, we can find the interest.

Therefore, the simple interest is $3352.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Answer:

3532.59341

Step-by-step explanation:

P= 2150

r= 3.315%

n= 12

t= 15

The given ratio of the volumes indicates that the volume of the cylinder is 9 times the volume of the cone.

Reasons:

The given parameter are;

Ratio of the volume of the cone to the cylinder to the 1 : 9

The height and diameter of the cone  are; 16 cm and 14 cm

The diameter of the cylinder = 28 cm

Required:

To find the height of the cone:

Solution:

[tex]\displaystyle The \ volume \ of \ a\ cone = \frac{1}{3} \cdot \pi \cdot r^2 \cdot h[/tex]

[tex]\displaystyle The \ volume \ of \ the \ cone = \frac{1}{3} \times \pi \times \left(\frac{14}{2} \right)^2 \times 16 = \mathbf{ \frac{784}{3} \cdot \pi}[/tex]

Volume of a cylinder, V = π·r²·h

[tex]\displaystyle Radius \ of \ the \ cylinder = \frac{28 \, cm}{2} = 14 \, cm[/tex]

Volume of the cylinder, V = π × 14² × h = 2,352·π

The volume of the cylinder = 9 × The volume of the cone

Therefore;

[tex]\displaystyle Volume \ of \ the \ cylinder =9 \times \frac{784}{3} \cdot \pi = \mathbf{2,352 \cdot \pi}[/tex]

[tex]\displaystyle Height \ of \ the \ cylinder, \, h = \mathbf{\frac{2,352 \cdot \pi}{14^2 \cdot \pi}} = 12[/tex]

The height of the cylinder, h = 12 cm

Learn more about ratios here:

https://brainly.com/question/4713715

Answer:

63

Step-by-step explanation:

you divide and add then subtract

Answer:

1

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = ( -15 - -14) / ( -11 - (-10))

    = (-15+14) /(-11 + 10)

   = -1 / -1

   = 1

Answer:

The answer is 1

Step-by-step explanation:

Answer:

X= - ¾ X= - 0.75

Step-by-step explanation:

thats all i can do hope it help :D

Answer:

14 and 12

Step-by-step explanation: