11y + 3(2y - 4) slove

Answer:

4x+16

Step-by-step explanation:

Distribute -1/2 to 32 and -40

That gets you -16x+20+20x-4

Combine -16x and 20x which gets you 4x+20-4

subtract 4 from 20

4x+16

One more than two-thirds of a number is no less than 25 is x = -30.

An equation is a mathematical expression that contains two algebraic expressions on either side of the "equals (=)" sign. It shows the equality between the words written to the left and the words written to the right. In all mathematics there is L.H.S = R.H.S (left side = right side). Equations can be solved to find the values ​​of unknown variables that represent unknown quantities or numbers. If there is no "equals" sign in the expression, it means it is not equal. It will be treated as a guide.

let the no. be x

According to the question:-

2/3 × x = 1/2× (x-5)

⇒ 2x/3 = x/2- 5

⇒ 2x/3 - x/2 = -5

⇒ (4x- 3x)/6 = -5

⇒ x/6  = -5

⇒ x = -30.

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Option B is best represents for the answer. A. 84.13%. B. 15.87%. 99.87%. D. 81.86%. To create the distribution curve, we can use the normal distribution formula:  [tex]f(x) = (1/σ√(2π)) * e^(-0.5((x-μ)/σ)^2)[/tex]

where:

f(x) = probability density function at value x

μ = mean = 16.2

σ = standard deviation = 0.3

Using this formula, we can calculate the probabilities for the given scenarios:

a. Probability of a coke having less than 16.5 ounces:

We need to find P(X < 16.5), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 16.5:

z = (16.5 - 16.2) / 0.3 = 1

P(Z < 1) = 0.8413

Therefore, the probability of a coke having less than 16.5 ounces is 84.13%.

b. Probability of a coke having less than 15.9 ounces:

We need to find P(X < 15.9), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.9:

z = (15.9 - 16.2) / 0.3 = -1

P(Z < -1) = 0.1587

Therefore, the probability of a coke having less than 15.9 ounces is 15.87%.

c. Probability of a coke having more than 15.3 ounces:

We need to find P(X > 15.3), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the value of 15.3:

z = (15.3 - 16.2) / 0.3 = -3

P(Z > -3) = 0.9987

Therefore, the probability of a coke having more than 15.3 ounces is 99.87%.

d. Probability of a bag having between 15.9 and 16.8 ounces:

We need to find P(15.9 < X < 16.8), where X is the volume of the coke in ounces.

Using the z-score formula, we can standardize the values of 15.9 and 16.8:

z1 = (15.9 - 16.2) / 0.3 = -1

z2 = (16.8 - 16.2) / 0.3 = 2

P(-1 < Z < 2) = 0.8186

Therefore, the probability of a coke having a volume between 15.9 and 16.8 ounces is 81.86%.

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The rectangular poster is 7 feet tall.

The rectangular shape in two dimensions has four sides, four corners, and four right angles (90°). Equal and parallel opposing sides make form a rectangle. Being a two-dimensional form, a rectangle has length and breadth as its two dimensions.

The procedure for calculating a rectangle's area may be used to get the rectangular poster's height:

Area = length * width

In this case, we know that the area is 35 square feet and the width (or base) is 5 feet. So we can rearrange the formula to solve for the length (or height):

length = Area / width

Substituting the values we get:

length = 35 sq ft / 5 ft = 7 ft

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Answer: a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (4 in 4xy)

Step-by-step explanation: the coefficient is the number or digit that is being multiplied and it is placed before a constant quantity

The missing number in the blank is -5. To find the polynomial that multiplied by 327 is equal to -12s^2 - 62, we need to factorize the expression. We can start by finding the factors of 327. We can see that 327 = 3 x 109. Now, we need to express -12s^2 - 62 in terms of these factors. We can write:

-12s^2 - 62 = -6 x 2 x (s^2 + 5)

Therefore, the polynomial that multiplied by 327 is equal to -12s^2 - 62 is:

(2)(-6)(s^2 + 5)

= -12s^2 - 60

So, the missing number in the blank 322 ( ) = 2st - 62 is -5. We can write the complete polynomial as:

(2)(-6)(s^2 + 5) = -12s^2 - 60

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The time required to earn $300 in interst on a principal of $2,500.00 at an interest rate of 2% per year is 6 years.

Steve puts $2500 in an account that earns 2% interest yearly.

This means principal P = $2500

And interest rate as percentage (R) = 2%

He is trying to earn $300 in interest

I = $300

so, the final amount A = P + I

A = $2800

Now we convert the rate of interest R percent to r a decimal:

r = R/100

r = 2%/100

r = 0.02 per year,

We need to find the number of years t:

We know that the formula for the simple interest is:

A = P(1 + rt)

So, t = (1/r)[A/P - 1]

t = (1/0.02)((2800/2500) - 1)

t = 6

Therefore, the time required to earn $300 in interst = 6 years

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In the trigonometric function , the length of the base of the ramp is

3.69 in.

What is trigonometric function?

The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.

Here Height of ramp = 16in , angle = 13 degrees.

Now The skateboard ramp arrangement looks like a right angled triangle,

then using trigonometric ratio ,

=> tan 13° = opposite/adjacent

=> tan 13° = 16/x

=> x = 16/tan 13°

=> x = 3.69 in

Hence the length of the base of the ramp is 3.69 in.

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Answer: 2.5

Step-by-step explanation:

Given the equation: f = 2.5w

The constant of proportionality is 2.5.

This means that the ration of the cups of flour to the cups of water used in the recipe is 2.5

Answer:

the height is 6 meters

Step-by-step explanation:

v = [tex]\pi r^{2} h[/tex]

471 = 3.14(25)h

471 = 78.5h  Divide both sides by 78.5

[tex]\frac{471}{78.5}[/tex] = [tex]\frac{78.5h}{78.5}[/tex]

6 = h

Helping in the name of Jesus.

the length of the hall is 35 m and the breadth of the hall is 160 m.

To find the length and breadth of the drawing, we need to use the scale given. We know that 1 cm represents 5 m, so we can use this proportion to find the actual dimensions of the school compound:

1 cm : 5 m = x cm : y m

To find the length of the drawing, we can use the given dimensions of the football field, which are 50 m by 30 m:

Length of the drawing = 50 m / 5 m per cm = 10 cm

Breadth of the drawing = 30 m / 5 m per cm = 6 cm

Therefore, the length of the drawing is 10 cm and the breadth of the drawing is 6 cm.

To find the actual length and breadth of the hall, we need to use the scale given. We know that 7 cm represents the length and 32 cm represents the breadth:

Length of the hall = 7 cm x 5 m per cm = 35 m

Breadth of the hall = 32 cm x 5 m per cm = 160 m

Therefore, the length of the hall is 35 m and the breadth of the hall is 160 m.

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The probability that at least two of the six members of a family are not born in the fall is approximately 0.66.

Since there are four seasons and each season has an equal probability of containing a randomly selected person's birthday, the probability that a person's birthday is not in the fall is 3/4. Therefore, the probability that all six family members are born in a season other than fall is (3/4)⁶, which is approximately 0.18.

The probability that only one family member is born in the fall is 6*(1/4)*(3/4)⁵, which is approximately 0.41. To find the probability that at least two family members are not born in the fall, we can subtract the probability that all six are born in the fall or only one is born in the fall from 1: 1 - 0.18 - 0.41 = 0.41.

In conclusion, the chance of having at least two out of the six family members not born in the fall is roughly 66%.

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Answer:

The answer is 6

Answer:

A) 39

B) 900

C) 60%

A) proportion:

21.84 is 56% of x number

x number = 100%

If you want to calculate x you can use proportion. First of all make this kind of system..

x - 100%

21.84 - 56%

Then multiply numbers diagonally.

56x = 2184

Finally solve x

x = 2184/56

x = 39

True. The alpha level for a hypothesis test defines the critical region.

A hypothesis test is a statistical technique that is used to test an assumption or hypothesis regarding a population parameter or distribution.

The critical region refers to the region of the sampling distribution that contains values that are unlikely to have occurred by chance if the null hypothesis is true.

The alpha level is the probability of committing a type I error, which is rejecting the null hypothesis when it is actually true.

The critical region is defined by the alpha level, which is the level of significance or the maximum probability of rejecting the null hypothesis when it is actually true. For example, if the alpha level is set at 0.05, the critical region will be the upper and lower 2.5% of the sampling distribution. If the test statistic falls within this region, the null hypothesis is rejected. On the other hand, if the test statistic falls outside this region, the null hypothesis is accepted.

Therefore, the alpha level plays a crucial role in determining the critical region and making decisions based on the results of the hypothesis test.

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Therefore, the coordinates of the image point B' are (3, -4) when a triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6).

To find the image of point B after performing the given transformations, we need to apply them in sequence.

Reflection over the y-axis:

This transformation will change the sign of the x-coordinate of point B, while leaving the y-coordinate unchanged. Therefore, the image of point B after reflection over the y-axis is (-(-3), 1), which simplifies to (3, 1).

Rotation 90° clockwise:

This transformation will swap the x and y-coordinates of the point and then change the sign of the new x-coordinate. Therefore, the image of point B after rotation 90° clockwise is (1, -3).

Translation (x + 2, y - 1):

This transformation will shift the image of point B two units to the right and one unit down. Therefore, the final image of point B after all three transformations is (1 + 2, -3 - 1), which simplifies to (3, -4).

Therefore, the coordinates of the image point B' are (3, -4).

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(a)The probability that the mean price for a sample of 40 federal income tax returns is within $16 of the population mean is 0.6884, (b)The probability that the mean price for a sample of 60 federal income tax returns is within $16 of the population mean is 0.7805. (c) The probability that the mean price for a sample of 81 federal income tax returns is within $16 of the population mean is 0.8502. (d) The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean

The solution to the given problem is as follows:A) For sample size of 40 Sample size, n=40Sample Mean, x = $273 Standard deviation of the population, σ= $100. Sampling Error = Standard error of mean = σ/√n = 100/√40 = $15.8114 therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.0 1)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/15.81) - P(Z < (256.99 - 273)/15.81)P(Z < 1.012) - P(Z > -1.012) = 0.8453 - 0.1569 = 0.6884. (B) For sample size of 60, sample size, n=60 sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√60 = $12.9155. therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01). Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/12.92) - P(Z < (256.99 - 273)/12.92)P(Z < 1.2389) - P(Z > -1.2389) = 0.8907 - 0.1102 = 0.7805.

C) For sample size of 81Sample size, n=81, sample Mean, x = $273 standard deviation of the population, σ= $100 sampling Error = Standard error of mean = σ/√n = 100/√81 = $11.111. Therefore, the required probability is P(273-16 < x < 273+16) = P(256.99 < x < 289.01)Using the Central Limit Theorem, the standard normal distribution can be used for solving the problem.The required probability is given by;P(Z < (289.01 - 273)/11.11) - P(Z < (256.99 - 273)/11.11)P(Z < 1.4403) - P(Z > -1.4403) = 0.9251 - 0.0749 = 0.8502.D) To ensure that the sample mean is within $16 of the population mean with 95% confidence, we need to find out the sample size that has a probability of 0.95.Probability is given by;P(-1.96 < Z < 1.96) = 0.95The Z-scores are obtained from the standard normal distribution table or calculator. Here, the probability of Z being less than -1.96 is equal to the probability of Z being greater than 1.96. The Z-score for a 95% confidence interval is 1.96. Therefore,1.96 = (289.01 - 273)/σnFor n = 152.94For n = 153, 1.96 = (289.01 - 273)/σ√153The best sample sizes are 153, and 154 so that at least a 0.95 probability that the sample mean is within $16 of the population mean.

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Hank can feed his dog for 40 days with one bag of dog food.

A fraction represents a part of a whole or a ratio between two quantities. It is a mathematical expression that consists of a numerator and a denominator separated by a horizontal line, also called a fraction bar or a vinculum.  

To solve the problem, we need to find how many scoops of dog food are in the bag and divide that by the number of scoops used per day:

Number of scoops in bag = 5 cups ÷ 1/8 cup/scoop = 40 scoops

Number of days he can feed his dog = 40 scoops ÷ 1 scoop/day = 40 days

Therefore, Hank can feed his dog for 40 days with one bag of dog food.

Statement: Hank can feed his dog for 40 days with one bag of dog food.

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(a) GI side of right triangle GHI is the hypotenuse.

(b) GI is the side which is opposite to ∠H

(c) GH is the side that is adjacent to ∠G.

A right-angled triangle is a type οf triangle that has οne οf its angles equal tο 90 degrees. The οther twο angles sum up tο 90 degrees. The sides that include the right angle are perpendicular and the base οf the triangle. The third side is called the hypοtenuse, which is the lοngest side οf all three sides.

(a) GI side of right triangle GHI is the hypotenuse.

(b) GI is the side which is opposite to ∠H

(c) GH is the side that is adjacent to ∠G.

(d) HI is  the side that is opposite to ∠G

(e) HI is the side that is adjacent to ∠I.

(f) GH is the side which is opposite to I.

(g) 5 : 12 is the numerical ratio of the length of the side opposite to G to the length of the side adjacent to ZG.

(h) 12 : 5 is the numerical ratio of the length of the side opposite to I to the length of the side adjacent to I.

(i) 5 : 13 is the numerical ratio of the length of the side opposite to G to the length of the hypotenuse.

(j) 12 : 13 is the numerical ratio of the length of the side adjacent to ZG to the length of the hypotenuse.

(k) 12 : 13 is the numerical ratio of the length of the side opposite to I to the length of the hypotenuse.

(H) 5 : 13 is the numerical ratio of the length of the side adjacent to I to the length of the hypotenuse.

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The required quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

To express the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] in scientific notation, we can write:

[tex]$\frac{1.888 \times 10}{5.9 \times 10^6}$[/tex]

We can simplify the numerator by moving the decimal point one place to the left:

[tex]$\frac{0.1888 \times 10^1}{5.9 \times 10^6}$[/tex]

Now, we can divide the coefficients and subtract the exponents:

[tex]$\frac{0.1888}{5.9} \times 10^{2-6}$[/tex]

[tex]$= 0.031966 \times 10^{-4}$[/tex]

Finally, we can express the result in proper scientific notation by moving the decimal point one place to the right:

[tex]$= 3.1966 \times 10^{-6}$[/tex]

Therefore, the quotient of 1.888 x 10 and [tex]5.9 x 10^6[/tex] expressed in scientific notation is [tex]$3.1966 \times 10^{-6}$[/tex].

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Answer:

Step-by-step explanation:

20 ➗ (4 * (10 - 8)

10 - 8 = 2 * 4 = 8

Then, 20 ➗ 8 = 2.5

Answer:

messageAdam, Ben and Carly work out the mean of their ages.Adam is 4 years older than the mean. Ben is 1 year younger than the mean.Is Carly older or younger than the mean?By how many years?Let's start by finding the mean of their ages. We can do this by adding their ages and dividing by the number of people: Mean = (Adam's age + Ben's age + Carly's age) / 3 Let's call the mean "M" for now. We can use this to create two equations based on the information given: Adam = M + 4 Ben = M - 1 We can substitute these equations into the mean equation to get: M = (M + 4 + M - 1 + Carly's age) / 3 Simplifying this equation gives us: 3M = 2M + 3 + Carly's age Carly's age = M - 3 So Carly's age is younger than the mean by 3 years

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill & \$ 2000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &5 \end{cases} \\\\\\ 2000 = (5000)(\frac{r}{100})(5) \implies 2000=250r\implies \cfrac{2000}{250}=r\implies \stackrel{ \% }{8}=r[/tex]

Therefore, the height of the statue is approximately 192 feet.

Height is a measure of how tall or high something or someone is, typically referring to the vertical distance from the base of an object or person to its highest point. It can be measured in various units such as feet, inches, meters, centimeters, etc. Height is an important physical characteristic of living organisms and is often used as a parameter in many applications, such as architecture, construction, athletics, and medical assessments.

by the question.

let A be the top of the statue, B be the position of the man, and θ be the angle of elevation from the man to the top of the statue. Let AB = h be the height of the statue and let BC = 270 ft be the distance between the man and the base of the statue.

We can use the tangent function to find the height of the statue:

tan(θ) = opp/adj = h/BC

Solving for h, we get:

h = tan(θ) * BC

Substituting θ = 34 degrees and BC = 270 ft, we get:

h = tan (34) * 270

h ≈ 192 ft

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A surgical procedure requires choosing among four alternative methodologies. the first can result in five possible outcomes, the second can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. The total number of outcomes possible is 90.

The first one can result in five possible outcomes, the second one can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. The total number of outcomes possible is a question the student needs an answer to.

To calculate the total number of outcomes, we have to multiply the number of results from the first methodology by the number of results from the second, third, and fourth methodologies. There are four alternative methodologies, and so we multiply the number of results from each methodology to calculate the total number of outcomes.However, we should use a calculator to solve this problem.

The first methodology can result in five possible outcomes, the second methodology can result in two possible outcomes, and the remaining methodologies can each result in three possible outcomes. We can use the following expression to determine the total number of outcomes:

5 × 2 × 3 × 3 = 90

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According to the given information, We will use a right-tailed test. The critical [tex]$z$[/tex]-value is [tex]$z_\alpha = 1.645$[/tex] and the test value is 1.77.

What is right-tailed test?

A right-tailed test, also known as a one-tailed test, is a statistical hypothesis test where the alternative hypothesis is directional and is expressed as an inequality with the greater-than symbol (>), indicating that the parameter being tested is expected to be larger than a specified value.

(a) The null hypothesis [tex]($H_0$)[/tex] and alternative hypothesis [tex]($H_a$)[/tex] are:

[tex]$H_0: \mu = 25$[/tex] (the addition of the mineral does not increase the number of pages read per day)

[tex]$H_a: \mu > 25$[/tex] (the addition of the mineral increases the number of pages read per day)

We will use a right-tailed test because the alternative hypothesis is one-sided (i.e., [tex]$\mu$[/tex] is greater than the hypothesized value).

(b) The critical [tex]$z$[/tex]-value for a one-tailed test with a 5% significance level and 29 degrees of freedom ([tex]df=n-1$, where $n=30$[/tex]) is:

[tex]$z_\alpha = 1.645$[/tex] (from the standard normal distribution table or calculator)

(c) The test value ([tex]$z$[/tex]-value) can be calculated as:

[tex]$z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$$[/tex]

where [tex]$\bar{x}$[/tex] is the sample mean, [tex]$\mu$[/tex] is the hypothesized population mean, [tex]$\sigma$[/tex] is the population standard deviation, and [tex]$n$[/tex] is the sample size.

Plugging in the values, we get:

[tex]$z = \frac{25.5 - 25}{\frac{2.4}{\sqrt{30}}} \approx 1.77$$[/tex]

The test value (1.77) is greater than the critical [tex]$z$[/tex]-value (1.645), so we reject the null hypothesis and conclude that the addition of the mineral is effective in increasing the number of pages read per day.

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