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2 years ago

Here please helppppppppppppp

Mathematics

1 answer:

skelet666 [1.2K]2 years ago

7 0

Answer:

Part 2 - ∠EGF = 105°
Part 3 - ∠D = 65

Step-by-step explanation for Part-2:

We know that:

∠EFG = 32°
∠AEG = 137°
∠EFG + ∠FGE + ∠GEF = 180°

Work:

∠EFG + ∠FGE + ∠GEF = 180°
32 + ∠FGE + (180 - 137) = 180°
=> 32 + ∠FGE + 43 = 180°
=> 75 + ∠FGE = 180°
=> ∠FGE = 180 - 75
=> ∠FGE = ∠EGF = 105°

Hence, the measure of ∠EGF is 105°.

Step-by-step explanation for Part-3:

We know that:

CD = CA
This triangle is an isosceles triangle.
∠D = ∠A

Work:

50 + ∠D + ∠A = 180
=> ∠D + ∠D = 130
=> 2∠D = 130
=> ∠D = 130/2
=> ∠D = 65

Hence, the measure of ∠D is 65°

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Answer:

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Step-by-step explanation:

3. For two equations to have infinite solutions, the equations must be the same.

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1. Michelle rides roller coasters 3 times and plays the super swing 5 times, which means that A = 3 and B = 5.

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3 years ago

The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th

timama [110]

Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

$\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$ = sample proportion.

n= sample size.

$\alpha$ = significance level .

$z_{\alpha/2}$ = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.: x= 54

Sample proportion of Independents $\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108$

Significance level 98% confidence level : $\alpha=1-0.98=0.02$

By using z-table , Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

$0.108\pm (2.33)\sqrt{\dfrac{0.108(1-0.108)}{500}}\\\\=0.108\pm2.33\times0.013880634\\\\=0.108\pm0.03234187722\\\\\approx0.108\pm0.032=(0.108-0.032,\ 0.108+0.032)=(0.076,\ 0.140)$

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)

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3 years ago

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snow_tiger [21]

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3 years ago

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3 years ago

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svetlana [45]

Answer:

a) The equation (10s + 8w) represents the calories Bridget ate on Monday and the equation (20s + w) represents the calories she ate the next day.

b) The number of calories in each strawberry is 4 and the number of calories in each vanilla wafer cookie is 19. The solution is s= 4 and w = 19.

Step-by-step explanation:

For part A, Bridget ate 10 strawberries and 8 vanilla wafer cookies on Monday. Since the the number of calories in a strawberry is s and the number of calories in a vanilla wafer cookie is w , the number of calories Bridget ate on Monday is 10s + 8w. The next day, Bridget ate 20 strawberries and 1 vanilla wafer cookie. Hence, the number of calories Bridget ate on the next day is 20s + w.

For part B,

we will create two different simultaneous equations.

Equation 1: 10s + 8w = 192

Equation 2: 20s + w = 99

We need to find one of the terms first to solve the other term. For this case, I will solve for w first.

Multiply the first equation by 2.

Equation 3: 20s + 16w = 192*2 = 384.

Now, subtract equation 2 from this new equation.

Equation 4:

(20s + 16w) - (20s + w) = 384 - 99

20s + 16w - 20s - w = 285

15w = 285

This leaves only w left and we can solve w.

w = 285 / 15 = 19

Now, we can solve for s using equation 2.

20s + 19 = 99

20s = 99-19 = 80

Hence,

s = 80/20 = 4

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