What is another way to write the equation StartFraction 7 over 8 EndFraction x + three-fourths = negative 6?

Answer:

The probability is P=0.9545.

The empirical rule is consistent, as it would have estimate a probability of 95%.

Step-by-step explanation:

We have a random variable with mean 31.8 in. and standard deviation of 2.4 in.

We have to find the probability that a randomly selected part from this supplier will have a value between 27.0 and 36.6 in.

If we assumed a normal-like distribution, we can calculate the z-score for both values:

[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{27-31.8}{2.4}=\dfrac{-4.8}{2.4}=-2\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{36.6-31.8}{2.4}=\dfrac{4.8}{2.4}=2[/tex]

That can be interpreted as an interval that is 2 standard deviations wide, centered on the mean.

This interval has a probability of:

[tex]P(27.0<x<36.6)=P(-2<z<2)=0.9545[/tex]

If we apply the empirical rule, with 2 standard deviations from the mean, we would have estimate a probability of 95%, which is accurate.

Answer:

x=1, 2, 3, 4, 5, 6

Step-by-step explanation:

Let's use logic. You can not have negative pizzas, and I assume you can not have decimals of pizzas.

That means that with the coupon you can only buy whole pizzas up to 6.

So the domain or x is1, 2, 3, 4, 5, 6

Answer:

We conclude that there is an equal or larger proportion of Republicans in favor of lowering the standards.

Step-by-step explanation:

The complete question is: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:

Number sampled: 1,000 (republican) , 800 (democrats)

Number in favor: 200 (republican) , 168 (democrats)

At the 0.02 level of significance, can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Determine the p-value.

Let [tex]p_1[/tex] = proportion of Republicans in favor of lowering the standards.

[tex]p_2[/tex] = proportion of Democrats in favor of lowering the standards.

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1 \geq p_2[/tex]     {means that there is an equal or larger proportion of Republicans in favor of lowering the standards}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1 < p_2[/tex]     {means that there is a larger proportion of Democrats in favor of lowering the standards}

The test statistics that would be used here Two-sample z-test for proportions;

                         T.S. =  [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]  ~ N(0,1)

where, [tex]\hat p_1[/tex] = sample proportion of Republicans in favor of lowering the standards = [tex]\frac{200}{1000}[/tex] = 0.20

[tex]\hat p_2[/tex] = sample proportion of Democrats in favor of lowering the standards = [tex]\frac{168}{800}[/tex] = 0.21

[tex]n_1[/tex] = sample of Republicans = 1000

[tex]n_2[/tex] = sample of Democrats = 800

So, the test statistics  =  [tex]\frac{(0.20-0.21)-(0)}{\sqrt{\frac{0.20(1-0.20)}{1000}+\frac{0.21(1-0.21)}{800} } }[/tex]

                                     =  -0.52

The value of z test statistics is -0.52.

Now, P-value of the test statistics is given by the following formula;

            P-value = P(Z < -0.52) = 1 - P(Z [tex]\leq[/tex] 0.52)

                          = 1 - 0.6985 = 0.3015

Now, at 0.02 significance level, the z table gives a critical value of -2.054 for left-tailed test.

Since our test statistic is more than the critical value of z as -0.52 > -2.054, 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 there is an equal or larger proportion of Republicans in favor of lowering the standards.

Answer:

orchestra seats: main seats: balcony seats: 160: 400: 240

Step-by-step explanation:

Let number of orchestra seats = x

Let number of main seats = y

Let number of balcony seats = z

As per given statement, total seats are 800

[tex]x +y+z=800 ..... (1)[/tex]

Sales price of each orchestra seat = $40

Sales price of each main seat = $30

Sales price of each balcony seat = $20

If all the seats are sold, total revenue is $23200.

[tex]\Rightarrow 40x + 30y+20z=23200 ...... (2)[/tex]

If all the main and balcony seats are​ sold, but only half the orchestra seats are​ sold, the gross revenue is $ 20 comma 000.

[tex]\Rightarrow 40\times \dfrac{x}{2} + 30y+20z=20000\\\Rightarrow 20x + 30y+20z=20000 ...... (3)[/tex]

Here, we have 3 variables and 3 equations. Let us solve them.

Subtracting Equation (3) from equation (2):

[tex]\Rightarrow 20x = 3200\\\Rightarrow x = 160[/tex]

Putting value of x in equations (1) and (2):

Equation (1)

[tex]\Rightarrow 160 +y+z=800\\\Rightarrow y+z=640 ...... (4)[/tex]

Equation (2)

[tex]\Rightarrow 40\times 160 +30y+20z=23200\\\Rightarrow 30y+20z=16800\\\Rightarrow 3y +2z=1680 ...... (5)[/tex]

Equation (5) - 2 [tex]\times[/tex] Equation(4):

[tex]\Rightarrow y =400[/tex]

Putting value of y in equation (4):

[tex]400 +z = 640\\\Rightarrow z =240[/tex]

Hence, answer is:

orchestra seats: main seats: balcony seats: 160: 400: 240

Answer:

I dont know what the answer is exactly

Answer:

The range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].

Step-by-step explanation:

We are given that the lengths of pregnancies in a small rural village are normally distributed with a mean of 262 days and a standard deviation of 17 days.

Let X = lengths of pregnancies in a small rural village

SO, X ~ Normal([tex]\mu=262,\sigma^{2} = 17^{2}[/tex])

Here, [tex]\mu[/tex] = population mean = 262 days

         [tex]\sigma[/tex] = standard deviation = 17 days

Now, the 68-95-99.7 rule states that;

So, middle 68% of most pregnancies is represented through the range of within one standard deviation points, that is;

[ [tex]\mu -\sigma[/tex] , [tex]\mu + \sigma[/tex] ]  =  [262 - 17 , 262 + 17]

                          =  [245 days , 279 days]

Hence, the range in which we can expect to find the middle 68% of most pregnancies is [245 days , 279 days].

Answer:

[tex]49/12[/tex]

Step-by-step explanation:

[tex]6\frac{1}{3} -2\frac{1}{4}[/tex]

[tex]\frac{19}{3} -\frac{9}{4}[/tex]

[tex]\frac{49}{12}[/tex]

Answer:

4 1/12

Step-by-step explanation:

6 1/3 - 2 1/4

Get a common denominator of 12

6 1/3*4/4   - 2 1/4*3/3

6 4/12 - 2 3/12

4 1/12

Answer:

Step-by-step explanation:B is a rational number and therefore when added to 0.5 produces another rational number, 0.75.

Answer:

0.8

Step-by-step explanation:

(2 x 10^-4)

= 0.0002

(4x10^3)

= 4000

0.0002 x 4000 = 0.8

Answer:

312, 313, and 314

Step-by-step explanation:

Since the three numbers are consecutive, each one is one larger than the last. Therefore, we can express them as x, (x+1), and (x+2). Therefore:

[tex]x+(x+1)+(x+2)=939 \\\\3x+3=939 \\\\3x=936\\\\x=312\\\\x+1=313\\\\x+2=314[/tex]

Hope this helps!

Answer:

Step-by-step explanation:

[tex]\sqrt[3]{x^{2} }[/tex] written as a radical expression

The radical is the symbol that is used to represent the root in the expression n√x. The index in the given expression x^(2/3) when rewritten as a radical expression is 3.

The radical is the symbol that is used to represent the root in the expression n√x.

Given the expression [tex]x^{\frac23}[/tex], which can be rewritten in the form of radical as,

[tex]x^{\frac23}\\\\[/tex]

[tex]= x^{2 \times \frac13}\\\\[/tex]

Using the law of exponent, [tex]a^{\frac1x} = \sqrt[x]{a}[/tex], then we can write,

[tex]= \sqrt[3]{x^2}[/tex]

Now, in the given expression 3 is an index, x² is the radicand and the symbol √ is known as the radical.

Hence, the index in the given expression x^(2/3) when rewritten as a radical expression is 3.

Learn more about the Radical here:

https://brainly.com/question/1369233

#SPJ2

Answer:

it takes approximately 11 years and 3 months (11.4 years) for Belinda's investments to double.    

Step-by-step explanation:

To calculate the time it takes for Belinda's money to double, we will use the simple interest formula as shown below:

Simple interest = P × R × T

where:

P = principal = $800

R = Rate in decimal = 8.75% = 0.0875

T = time = ???

simple interest = $800 ( her money doubles)

∴ 800 = 800 × 0.0875 × t

800 = 70 × t

∴ t = 800 ÷ 70 = 11.4 years. (11 years and 3 months)

Therefore after approximately 11 years and 3 months, Belinda's investments doubles

Answer:

8.23

how long would it take belinda's $800 investment to double in value if she has a bond with a 8.75% interest rate?

Answer:

1/9 or 0.11

Step-by-step explanation:

1/3 divided by 3

= 1/3 / 3

= 1/3 / 3/1

= 1/3 x 1/3 (the rule is a/b / c/d = a/b * d/c)

= 1/9 or 0.11(1 continues repeating for ever so just make it 0.11)

Answer:

$0.45+19*$0.35= $7.1

Step-by-step explanation:

first minute= $0.45

subsequent minutes= $0.35

cost per 20 min= $0.45+19*$0.35= $7.1

cost per x min= 0.45+(x-1)*0.35= 0.35x +0.10

Answer:

Step-by✔ 0.45 + 0.35(19)  

✔ $7.10

Answer:

c = 197.2

b = 192.9

Angle C = 90°

Angle A = 12°

Step-by-step explanation:

the side a = 41 and the angle B = 78°, we can use a sine and a tangent to find the hypotenuse and the other side.

Using a sine, cosine, or tangent depends on which side and angle you know.

sin A =opposite/hypotenuse =  a/c

Cos B = adjacent/hypotenuse = a/c

Cos78 = 41/c

c = 41/Cos 78

c  = 41/0.2079

c = 197.21

c = 197.2

Since it is a right angle triangle, let's apply Pythagoras theorem to find the other side.

Hypotenuse ² = opposite ² + adjacent²

c² = a² + b²

197.2² = 41² + b²

b² = 197.2² - 41²

b² = 38887.84 - 1681

b² = 37206.84

b =√37206.84

b = 192.89

b = 192.9

Angle C = 90°

Angle A = 180-(90 +78)

(sum of angles in a triangle =180°)

Angle A = 180-168

Angle A = 12°

(Diagram of the box plots is attached below)

Options:

A. 75% of the volleyball players’ heights are equal to or greater than the median basketball players’ heights

B. 75% of the volleyball players’ heights are equal to or greater than the median basketball players’ heights

C. 25% of the basketball players’ heights are equal to or greater than the median volleyball players’ heights

D. 75% of the basketball players’ heights are equal to or greater than the median volleyball players’ heights

Answer:

D. 75% of the basketball players’ heights are equal to or greater than the median volleyball players’ heights

Step-by-step Explanation:

Based on the box plots given in the diagram attached below, the median height of volleyball players is 79.

Also, from the data set of basketball players, we can approximately infer that the heights from Q2, Q3, and Q4 make up 75% of the data set of the heights of basketball players.

Heights at Q2 in the data set of basketball players starts from 79, which is equal to the median height of volleyball players.

Therefore, from the displays, we can conclude that "75% of the basketball players’ heights are equal to or greater than the median volleyball players’ heights".

Answer:

432

Step-by-step explanation:

Volume is equal to the length*width*height that is 6*6*2*3*6(basically multiply them all in simple terms)=432

Answer:

2 + 3+ 6

Step-by-step explanation:

You are supposed to multiply the length, width, and height not add it.

Answer:

Hello There Again. The correct answer 14.

Explanation: Because you need to do Multpliy 2 and 4 and then add again 8 and 6 to get 14 2x4=8+6=14.

Hope It Helps! :)

Answer:

Well, I think the the right answer is 14. Because, 2 x 8 + 6 - 4 - 5 + 1= 14

Hope This Helps!!~

Good Luck!~

Answer:

90 different ways

Step-by-step explanation:

We have a total of 10 members, and we want to find how many groups of 2 members we can have, where the order of each member in the group of 2 is important, so we have a permutation problem.

To solve this problem, we need to calculate a permutation of 10 choose 2.

The formula for a permutation of n choose p is:

[tex]P(n, p) = n! / (n - p)![/tex]

So we have:

[tex]P(10, 2) = 10! / (10 - 2)![/tex]

[tex]P(10, 2) = 10! / 8![/tex]

[tex]P(10, 2) = 10*9 = 90[/tex]

So there are 90 different ways of choosing a president and a vice-president.

Answer:

321

Step-by-step explanation:

Principal amount = $11,500

Simple interest = 6.7%

time :5 months

as simple interest is calculated for a year, time needs to be calculated in years

12 months comprises 1 year

1 month is equivalent to 1/12 years

thus, 5 month is equivalent to (1/12)* 5 years

time in years = 5/12

Simple interest is calculated by formula

SI = p*r*t/100

where SI is simple interest earned

p is principle amount

r is rate of interest

t is time in years

substituting the value of p, r and t in the formula for SI, we have

SI = (11500*6.7*5)\12*100 = 321.04

interest,the account gained after 5 months is 321.

Answer:

x^2 + y^2 = 3^2

Step-by-step explanation:

Use the standard equation of a circle with center at (h, k) and radius r:

(x - 0)^2 + (y - k)^2 = 3^2, or

x^2 + y^2 = 3^2

Answer:

See explanation and attachment.

Step-by-step explanation:

One of the ways to represent polynomial is the use of algebraic tiles.

To represent the polynomial x²-5x-1, we would use algebraic tiles to represent each of the three terms.

Algebra tiles come with different colors and sizes. Each size is equivalent to a degree of different monomials.

The x² tile is a monomial with degree of 2, the x tile is a monomial with degree of 1 and the unit tile (constant) is a monomial with degree of 0.

Let the shaded tiles represent the positive tiles and the unshaded tile represent the negative tiles.

Find attached the diagram for the tiles.

To represent the polynomial x² - 5x - 1, we would need 1 shaded x² tile, 5 unshaded x tiles and 1 unshaded unit tile. Then we would arrange the tiles to correspond with the polynomial.

Answer:

Answer:

(drag one tile) +x 2 into the product then click check.

(drag five) -x    into the product then click check.

(drag one) - tile into the product and click check..

Step-by-step explanation:

Answer:

yes, the birdhouse has a surface area of 210 inches while the plywood has 1152 inches of surface area

yes the birdhouse is 210 inches while the wood is 1152

Answer:

12.5 feet

Step-by-step explanation:

He only needs 10/12 of a 15 foot long piece of wood. We need to find 10/12 of the length of the wood.

That is:

10/12 * 15 = 12.5 feet

He only needs 12.5 feet of the piece of wood.

Answer:

If 1/5 are chocolate chip, then 4/5 are not chocolate chip because 1 - 1/5 = 4/5. Half of 4/5 are peanut butter. Half of 4/5 is 2/5, so 2/5 of the cookies are peanut butter.

hope it helps!!!!! :]

Answer:

$1.68

Step-by-step explanation:

Remember that cents are in the hundredths place. So think of it as rounding to the nearest hundredth place. 1.6845 ---> 1.68

Answer:

$1.68

Step-by-step explanation:

old rhyme i learnt when i was little but it helps with rounding:

5 or more let it soar, 4 or less let it rest

Answer:

Step-by-step explanation:

1. 30 plants

the rest were confusing sorry

Answer:

184 cm³

Step-by-step explanation:

Volume= base*height

V= 20 cm²*9.2 cm= 184 cm³

Answer:184 cm³

Step-by-step explanation: I took the test a while ago

Answer:

I think "−13.4°C<−13.2°C because −13.2°C is warmer than −13.4°C" is the right answer