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3 years ago

Write and solve a proportion to answer the question. (Skills Review Handbook) 22. 30 is 15% of what number?

Mathematics

1 answer:

algol133 years ago

3 0

Answer:

The answer is 148.6666667

Step-by-step explanation:

1) Set a linear quation

$\frac{22.30}{x} = \frac{15}{100}$

2) Cross multiply

$15x = 22.30 \times 100$

3) Multiple the right side

$15x = 2230$

4) Divide both side by 15

$\frac{15x}{15} = \frac{2230}{15}$

5) Solve the linear equation

$x = 148.6666667$

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Solve the simultaneous equations:<br> 3x + 2y = 35 <br> 2x + 3y = 30

lesya [120]

Answer:

nuber 1

Simplifying

3x + 2y = 35

Solving

3x + 2y = 35

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2y' to each side of the equation.

3x + 2y + -2y = 35 + -2y

Combine like terms: 2y + -2y = 0

3x + 0 = 35 + -2y

3x = 35 + -2y

Divide each side by '3'.

x = 11.66666667 + -0.6666666667y

Simplifying

x = 11.66666667 + -0.6666666667y

5 0

3 years ago

ou watch a roulette wheel spin 3 consecutive times and each time the ball lands in a red slot. What is the | probability that th

spayn [35]

Answer:

The probability is $\frac{18}{38}=0.4736$

Step-by-step explanation:

The game of roulette wheel consists in spinning a wheel with 38 slots : 18 red, 18 black and 2 green.

If we suppose that the roulette is a fair roulette, then each slot has an equal chance of capturing the ball and given that the ball lands in a red, black or green slot this event doesn't give us information about the following spin. Meaning that exists independence between each spin of the roulette wheel.

In our exercise, we spin the roulette wheel 3 consecutive times and each time the ball lands in a red slot. This doesn't give us information about the fourth spin (because of the independence).

Given that each slot has an equal chance of capturing the ball we can calculate the probability of the ball landing on a red slot on the next spin as :

$P(Red)=\frac{18}{38}=0.4736$

We divide the favourable cases (18 red slots) by the total cases (38 slots) in order to calculate the probability.

The probability is $\frac{18}{38}=0.4736$

6 0

3 years ago

In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. This is the 14

lbvjy [14]

Answer:

We are confident at 99% that the difference between the two proportions is between $0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420$

Step-by-step explanation:

Part a

Data given and notation

$X_{D}=3266$ represent the number people registered as Democrats

$X_{R}=2137$ represent the number of people registered as Republicans

$n=7525$ sampleselcted

$\hat p_{D}=\frac{3266}{7525}=0.434$ represent the proportion of people registered as Democrats

$\hat p_{R}=\frac{2137}{7525}=0.284$ represent the proportion of people registered as Republicans

The standard error is given by this formula:

$SE=\sqrt{\frac{\hat p_D (1-\hat p_D)}{n_{D}}+\frac{\hat p_R (1-\hat p_R)}{n_{R}}}$

And the standard error estimated given by the problem is 0.008

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion of Democrats that approve of the way the California Legislature is handling its job

$\hat p_A =\frac{1894}{3266}=0.580$ represent the estimated proportion of Democrats that approve of the way the California Legislature is handling its job

$n_A=3266$ is the sample size for Democrats

$p_B$ represent the real population proportion of Republicans that approve of the way the California Legislature is handling its job

$\hat p_B =\frac{385}{2137}=0.180$ represent the estimated proportion of Republicans that approve of the way the California Legislature is handling its job

$n_B=2137$ is the sample for Republicans

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.580-0.180) - 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.380$

$(0.580-0.180) + 1.64 \sqrt{\frac{0.580(1-0.580)}{3266} +\frac{0.180(1-0.180)}{2137}}=0.420$

And the 99% confidence interval would be given (0.380;0.420).

We are confident at 99% that the difference between the two proportions is between $0.380 \leq p_{Republicans} -p_{Democrats} \leq 0.420$

5 0

3 years ago

In AABC, MZA = 16°, mZB = 49°, and<br> a = 4. Find c to the nearest tenth.

zhannawk [14.2K]

Answer:

Step-by-step explanation:

The sum of angles in a triangle is 180°, so angle C is ...

C = 180° -A -B

C = 180° -16° -49° = 115°

The measure of side c can be found from the Law of Sines:

c/sin(C) = a/sin(A)

c = a·sin(C)/sin(A) = 4·sin(115°)/sin(16°)

c ≈ 13.2

6 0

3 years ago

Find the perimeter of the square shown below:<br> Area =49 cm2

Ket [755]

Answer:

28 cm

Step-by-step explanation:

If the shape is a square, all the sides are equal. To find the area you multiply the length by the width. Since the area is 49 centimeters, find the square root of 49 to find the length of the length and the height of the square, which is 7. To find the perimeter, you add the lengths of all the sides of the square. 7+7+7+7=28.

5 0

3 years ago