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lesya692 [45]
3 years ago
5

What does H equal? -h + 11h - 16 = 74

Mathematics
2 answers:
umka2103 [35]3 years ago
6 0

Answer:

9

Step-by-step explanation:

1. combine the h

2. move the -16 to the other side and combine (the -16 becomes positive)

solve for h

10h=90

Serhud [2]3 years ago
4 0

Answer:

h=9

Step-by-step explanation:

-h + 11h - 16 = 74

             +16   +16

        -h+11h = 90

           10h=90

         \frac{10h}{10h} =\frac{90}{10h}

          90/10h= 9

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Express a decimal number ( ie 0.768) - process description please - as a rational number (96/125)?
Stels [109]

The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as

1\cdot10^2+2\cdot10^1+3\cdot10^0+4\cdot10^{-1}+5\cdot10^{-2}+6\cdot10^{-3}

10^{-n}=\dfrac1{10^n} for any n, so the above is the same as

100+20+3+\dfrac4{10}+\dfrac5{100}+\dfrac6{1000}=\dfrac{100000+20000+3000+400+50+6}{1000}=\dfrac{123456}{1000}

Similarly, we can write

0.768=\dfrac{768}{1000}

Now it's a question of reducing the fraction as much as possible. We have \mathrm{gcd}(768,1000)=8 so

\dfrac{768}{1000}=\dfrac{96\cdot8}{125\cdot8}=\dfrac{96}{125}

5 0
3 years ago
Suppose a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%. A cell phon
leva [86]

Answer:

We conclude that the actual percentage of households is equal to 30%.

Step-by-step explanation:

We are given that a consumer group suspects that the proportion of households that have three cell phones NOT known to be 30%.

Their marketing people survey 150 households with the result that 43 of the households have three cell phones.

Let p = <u><em>proportion of households that have three cell phones NOT known.</em></u>

So, Null Hypothesis, H_0 : p = 30%      {means that the actual percentage of households is equal to 30%}

Alternate Hypothesis, H_A : p \neq 30%     {means that the actual percentage of households different from 30%}

The test statistics that would be used here <u>One-sample z-test for proportions;</u>

                                T.S. =  \frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }  ~ N(0,1)

where, \hat p = sample proportion of households having three cell phones = \frac{43}{150} = 0.29

           n = sample of households = 150

So, <u><em>the test statistics</em></u>  =  \frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }  

                                     =  -0.27

The value of z test statistic is -0.27.

<u>Also, P-value of the test statistics is given by;</u>

              P-value = P(Z < -0.27) = 1 - P(Z \leq 0.27)

                            = 1 - 0.6064 = <u>0.3936</u>

<u>Now, at 1% significance level the z table gives critical value of -2.58 and 2.58 for two-tailed test.</u>

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <em><u>we fail to reject our null hypothesis</u></em>.

Therefore, we conclude that the actual percentage of households is equal to 30%.

4 0
3 years ago
In circle K shown below, points B, C, D, and E lie on the circle with secants HBD and HCE drawn. Prove:
Alexxx [7]

Answer:

By exterior angle theorem, we have;

∠DBE = ∠H + ∠HEB = ∠ECD = ∠H + ∠HDC

∴ ∠H + ∠HEB = ∠H + ∠HDC

By addition property of equality, we have

∠HEB = ∠HDC

∠H = ∠H by reflexive property

∴ ΔHCD ~ ΔHEB by Angle Angle AA similarity postulate

∴ HE/HD = EB/DC, by the definition of similarity

Therefore, by cross multiplication, we have;

HE × DC = EB × HD

Therefore, by commutative property of multiplication, we have;

HE × DC = HD × EB

Step-by-step explanation:

3 0
3 years ago
(Score for Question 3: ___ of 5 points) The measure of ∠2=8x+10 and the measure of ∠4=42+6x. Find the measure of ∠4. Show your w
Svetradugi [14.3K]

Answer:

∠4 = 78°, assuming out measurements have been taken in degrees.

Step-by-step explanation:

If ∠2 = 8x + 10 and

∠4 = 42 + 6x

We will assume that x in both cases is represented by the same number, therefore, we will first need to solve for x. We will do so by equating both angle measurement expressions.

8x + 10 = 42 + 6x        Take away 6x from both sides

2x + 10 = 42                Take 10 away from both sides to combine like terms

2x = 32                        Divide both sides by 2 to isolate x

x = 16

Knowing x, we can solve for the measure of ∠4 by plugging in 16 for x

∠4 = 42 + 6x

∠4 = 42 + 6(6)

∠4 = 42 + 36

∠4 = 78°, assuming out measurements have been taken in degrees.

4 0
3 years ago
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