What is the distance between 1/3 to 1 for fractions on number line

Find m∠STU and m∠TUA

PIT_PIT [208]

Answers:

angle STU = 65 degrees
angle TUA = 123 degrees

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Explanation:

Let's find the expression for angle TUS in terms of x

Angle TUA has the expression 11x+2. It will add to angle TUS to get 180 degrees

(angle TUS) + (angle TUA) = 180

angle TUS = 180 - (angle TUA)

angle TUS = 180 - (11x + 2)

angle TUS = 180 - 11x - 2

angle TUS = -11x + 178

Now focus on the interior angles of triangle TUS. We have these three angles

T = 5x+10
U = -11x+178
S = 58

For any triangle, the interior angles always add to 180, so,

T+U+S = 180

(5x+10) + (-11x+178) + (58) = 180

(5x-11x) + (10+178+58) = 180

-6x + 246 = 180

-6x = 180-246

-6x = -66

x = -66/(-6)

x = 11

Use this x value to find the angle measures we're after:

angle STU = 5x+10 = 5*11+10 = 55+10 = 65 degrees
angle TUA = 11x+2 = 11*11+2 = 121+2 = 123 degrees

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As an alternative route, you can apply the remote interior angle theorem. This says that adding two interior angles leads to the exterior angle that isn't adjacent to either one.

In this case, we would say

(angle STU) + (angle TSU) = angle TUA

that leads to the equation

(5x+10) + (58) = 11x+2

Solving this should lead to x = 11 to generate the angles mentioned earlier.

6 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 = proportion of households that have three cell phones NOT known.

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 One-sample z-test for proportions;

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, the test statistics = $\frac{0.29-0.30}{\sqrt{\frac{0.30(1-0.30)}{150} } }$

= -0.27

The value of z test statistic is -0.27.

Also, P-value of the test statistics is given by;

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

= 1 - 0.6064 = 0.3936

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

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 we fail to reject our null hypothesis.

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

4 0

3 years ago

darcy needs 1/4 yard of fabric to make a banner. She has 2 yards of fabric. How many banners can she make?

kotegsom [21]

Darcy can make 8 banners.

4 0

3 years ago

Read 2 more answers

Simplify the expression (8x^3y^2/4a^2b^4)^-2

icang [17]

Simplify the following:
((8 x^3 y^2 a^2 b^4)/4)^(-2)
8/4 = (4×2)/4 = 2:
(2 x^3 y^2 a^2 b^4)^(-2)
Multiply each exponent in 2 x^3 y^2 a^2 b^4 by -2:
(x^(-2×3) y^(-2×2) a^(-2×2) b^(-2×4))/(2^2)
-2×3 = -6:
(x^(-6) y^(-2×2) a^(-2×2) b^(-2×4))/2^2
-2×2 = -4:
(y^(-4) a^(-2×2) b^(-2×4))/(2^2 x^6)
-2×2 = -4:
(a^(-4) b^(-2×4))/(2^2 x^6 y^4)
-2×4 = -8:
b^(-8)/(2^2 x^6 y^4 a^4)
2^2 = 4:
Answer: 1/(4 x^6 y^4 a^4 b^8) thus the answer is A

3 0

3 years ago

How many times does to go into 50000

kompoz [17]

Answer: 2500

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers