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3 years ago

How to make 10 when adding 8+5

Mathematics

1 answer:

VikaD [51]3 years ago

6 0

Required: 10

8+5=13

How to get 10:

13-10=3

Therefore, in order to get 10 from the sum of 8+5, you must subtract 3.

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Solve for x. Help ASAP please!!!

sattari [20]

Answer:

The value of x is 4

Step-by-step explanation:

In a right triangle, if a segment is drawn from the right angle ⊥ to the hypotenuse like the given figure, then

∵ The length of one side of the right triangle = (x + 2)

∵ The length of the hypotenuse = x + 5

∴ (x + 2)² = x (x + 5)

∵ (x + 2)² = (x + 2)(x + 2)

∴ (x + 2)(x + 2) = x(x + 5)

→ Simplify the two sides

∵ (x)(x) + (x)(2) + (2)(x) + (2)(2) = (x)(x) + (x)(5)

∴ x² + 2x + 2x + 4 = x² + 5x

→ Add the like terms in the left side

∴ x² + 4x + 4 = x² + 5x

→ Subtract x² from both sides

∵ x² - x² + 4x + 4 = x² - x² + 5x

∴ 4x + 4 = 5x

→ Subtract 4x from both sides

∴ 4x - 4x + 4 = 5x - 4x

∴ 4 = x

∴ The value of x is 4

3 0

3 years ago

A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

7 0

3 years ago

I need the answer to this question

disa [49]

Answer:

y = 3/4x + 19/2

Step-by-step explanation:

m = 3/4. point (-6,5)

Point slope form:

y-5=3/4(x- -6)

y -5 = 3/4x + 18/4. 18/4 = 9/2

Y = 3/4x + 9/2 + 5. 5 times 2 plus 9 over 2 = 19/2

y = 3/4x + 19/2

6 0

3 years ago

The mass of the parasitic wasp Caraphractus cintus can be as small as 5.00

arsen [322]

Answer:

(c) micrograms (µg)

Step-by-step explanation:

Download docx

3 0

3 years ago

Prove that the triangle EDF is isosceles. Give reasons for your answer.

Gekata [30.6K]

Answer:

$\triangle EDF$ is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are given the following things:

$\angle EDF = y$

$\text{External }\angle DFG = 90 +\dfrac{y}{2}$

Let us try to find out $\angle E$ and $\angle DFE$ . After that we will compare them.

Finding  $\angle DFE$ :

Side EG is a straight line so $\angle GFE = 180$

$\angle GFE$ is sum of internal $\angle DFE$ and external $\angle DFG$

$\angle GFE = 180 = \angle DFE + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)$

Finding  $\angle E$ :

Property of external angle: External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external $\angle DFG$ = $\angle E + \angle EDF$

$\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2} -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)$

Comparing equations (1) and (2):

It can be clearly seen that:

$\angle DFE = \angle E =90-\dfrac{y}{2}$

The two angles of $\triangle EDF$ are equal hence $\triangle EDF$ is isosceles.

8 0

3 years ago