Translate to an algebraic equation then solve. 33. The length of a rectangle is six units longer than the width. Find the length and width if the perimeter of the rectangle is 60 units.

Answer:

D.) [tex]y+1=-3(x-10)[/tex]

Step-by-step explanation:

The original point slope form equation is as follows:

[tex]y - y_1 = m(x-x_1)[/tex]

When you input a negative or positive value into the equation, the sign may or may not change. In this case, we input a negative y value -- this caused the sign to change to '+1' rather than stay at '-1'

Answer:

Probably the engine from their helicopter

Step-by-step explanation:

Answer:

Probability that the sample average time taken is less than 11 minutes for Day 1 is 0.86864.

Probability that the sample average time taken is less than 11 minutes for Day 2 is 0.88877.

Step-by-step explanation:

We are given that the time taken by a randomly selected applicant for a mortgage to fill out a certain form has a normal probability distribution with average time 10 minutes and a standard deviation of 2 minutes.

Also, five individuals fill out the form on Day 1 and six individuals fill out the form on Day 2.

(a) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 1 = 5

Now, the probability that the sample average time taken is less than 11 minutes for Day 1 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{5} } }[/tex] ) = P(Z < 1.12) = 0.86864

The above probability is calculated by looking at the value of x = 1.12 in the z table which has an area of 0.86864.

(b) Let [tex]\bar X[/tex] = sample average time taken

The z score probability distribution for sample mean is given by;

                                Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)

where, [tex]\mu[/tex] = population mean time = 10 minutes

            [tex]\sigma[/tex] = standard deviation = 2 minutes

            n = sample of individuals fill out form on Day 2 = 6

Now, the probability that the sample average time taken is less than 11 minutes for Day 2 is given by = P([tex]\bar X[/tex] < 11 minutes)

         P([tex]\bar X[/tex] < 11 minutes) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{11-10}{\frac{2}{\sqrt{6} } }[/tex] ) = P(Z < 1.22) = 0.88877

The above probability is calculated by looking at the value of x = 1.22 in the z table which has an area of 0.88877.

[tex]\frac{60}{100}[/tex] of a dollar

A fraction is a portion of a whole or, more broadly, any number of equal parts. In everyday English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters.

Kim spent [tex]\frac{40}{100}[/tex] of a dollar on a snack.

So, she has been left with [tex]1-\frac{40}{100}=\frac{60}{100}[/tex] of a dollar on a snack.

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Final answer:

Kim spent 40/100 of a dollar (40 cents) on a snack, so she has 60 cents left.

Explanation:

The question requires converting a fraction of a dollar into a money amount. Kim spent 40/100 of a dollar on a snack. A dollar is equivalent to 100 cents, so Kim spent 40 cents on her snack. To find out how much she has left, we subtract her spending from the total amount of one dollar.

To perform the calculation: 100 cents - 40 cents = 60 cents.

Therefore, Kim has 60 cents left after purchasing the snack.

Answer:

3.22% probability that the sample average is greater than $228,500

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 227000, \sigma = 8500, n = 110, s = \frac{8500}{\sqrt{110}} = 810.44[/tex]

What is the probability that the sample average is greater than $228,500?

This is 1 subtracted by the pvalue of Z when X = 228500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{228500 - 227000}{810.44}[/tex]

[tex]Z = 1.85[/tex]

[tex]Z = 1.85[/tex] has a pvalue of 0.9678

1 - 0.9678 = 0.0322

3.22% probability that the sample average is greater than $228,500

Answer:

D

Step-by-step explanation:

The absolute value parent function is [tex]\mid x \mid[/tex], or answer choice D. Hope this helps!

Answer:

it will hold 25.13 cubic inches of melted ice cream

Step-by-step explanation:

first we get the cone formula because a melted ice cream cone will have a flat top, making it a cone

the cone formula is π*r^2 * h /3

so we input radius and height

π*2^2 * 6 /3

then we simplfy

π * 4 * 6 /3

12.56 *6/3

75.398/3

25.13

Answer:

b = 7.9

Step-by-step explanation:

A = 37       a =

B = 53       b =

C = 90       c = 10

B = 180 - 90 -37 = 53

[tex]\frac{sinB}{b} = \frac{sinC}{c}\\ \frac{sin(53)}{b} = \frac{sin(90)}{10}\\ b = \frac{10 sin(53)}{sin(90)} \\b = 7.9[/tex]

To find the length of side AC in a right-angled triangle ABC with angle A of 37 degrees and hypotenuse 10, we use the cosine function. AC equals the hypotenuse multiplied by the cosine of angle A, resulting in AC being approximately 7.9 units long.

The student wants to know the length of side AC in a right-angled triangle ABC, where angle C is a right angle, angle A is 37 degrees, and the hypotenuse (side BC) is 10. To find the length of side AC, we will use trigonometric functions. Specifically, we will use the cosine function, which relates the adjacent side to the hypotenuse in a right-angled triangle. The cosine of angle A (cos 37°) is equal to the adjacent side (AC) divided by the hypotenuse (BC).

The formula is: Cosine of angle A = AC / BC

This can be rewritten as: AC = BC * Cosine of angle A

By substituting the given values (BC = 10 and angle A = 37°), we get:

AC = 10 * cos(37°)

To find cos(37°), we can use a calculator set to degree mode. The calculation gives us:

AC = 10 * 0.7986 (approximately)

Therefore, AC ≈ 10 * 0.7986 = 7.986

AC is approximately 7.9 units long.

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Answer:18.0625m^2

Step-by-step explanation:

Length =4 1/4 m

Area= length x length

Area=4 1/4 x 4 1/4

Area=(4x4+1)/4 x (4x4+1)/4

Area=17/4 x 17/4

Area=(17x17)/(4x4)

Area=289/16

Area=18.0625m^2

Answer:

The average yearly change in samanthas height was of 3.3 inches.

Step-by-step explanation:

She mesured 40 1/2 = 40.5 inches.

In 5 1/2 years = 5.5 years, she grew to 57 inches.

During the 5 1/2 years, what was the average yearly change in samanthas height?

The total change was of 57-40.5 = 16.5 inches

16.5/5 = 3.3

The average yearly change in samanthas height was of 3.3 inches.

Answer:

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

Step-by-step explanation:

Information provided

[tex]\bar X=1450[/tex] represent the sample mean for the SAT scores

[tex]\mu[/tex] population mean (variable of interest)

[tex]s^2 = 900[/tex] represent the sample variance given

n=25 represent the sample size  

Solution

The confidence interval for the true mean is given by :

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The sample deviation would be [tex]s=\sqrt{900}= 30[/tex]

The degrees of freedom are given by:

[tex]df=n-1=2-25=24[/tex]

The Confidence is 0.954 or 95.4%, the value of [tex]\alpha=0.046[/tex] and [tex]\alpha/2 =0.023[/tex], assuming that we can use the normal distribution in order to find the quantile the critical value would be [tex]z_{\alpha/2} \approx 2.0[/tex]

The confidence interval would be

[tex]1450-2.0\frac{30}{\sqrt{25}}=1450-12[/tex]    

[tex]1450+2.0\frac{30}{\sqrt{25}}=1450+12[/tex]    

And the best option would be:

c. 1450 +/- 12

Answer:

$12 per foot

Step-by-step explanation:

$72.00 divided by 6 is $12

Answer:

The cost per foot of the sandwich is $12.

Step-by-step explanation:

You need to use division for this problem.

Pretend you are cutting the 6-foot sanwhich into 1-foot pieces. You will have 6 pieces. You have to give each piece an equal amount of money. Think about your 6-times tables. What times 6 = 72?

__ x 6 =72

or

72/6 = __

Answer:

Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Step-by-step explanation:

Brian makes a cleaning solution using a ratio of 4 cups of water to 1 cup of vinegar.

Let c be the number of cups of vinegar that Brian should use with 12 cups of water.

1 cup of vinegar uses cup of water = 4

c cups of vinegar uses cup of water = 4c

We are c, the number of cups ofvinegar that Brian should use with 12 cups of water

So, 4c=12

[tex]4=\frac{12}{c}[/tex]

So, equation =[tex]\frac{4}{1}=\frac{12}{c}[/tex]

So, Option B could be used to find c, the number of cups ofvinegar that Brian should use with 12 cups of water

Answer:

D. g(x)=4x^2

Step-by-step explanation:

Answer: g(x)=4x^2

check picture below

Answer:

Standard deviation = 7.76

Step-by-step explanation:

The formula for determining standard deviation when dealing with population proportion is expressed as

Standard deviation = √npq

Where

n represents the number of samples from the population.

p represents the probability of success.

q represents the probability of failure.

From the information given,

n = 500 policyholders

p = 14% = 14/100 = 0.14

q = 1 - 0.14 = 0.86

Standard deviation = √500 × 0.14 × 0.86 = 7.76

Answer: std dev = 0.01552

Step-by-step explanation:

we will solve this by taking a step by step analysis of the problem.

i hope at the end of this section, you will feel confident  to try out other questions.

given that the size of the sample (n) = 500

The Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes.

hence sample proportion of policyholders filing claims involving theft or robbery from their homes (p) = 14% =0.14

let Z be the number of policyholders files involving theft or robbery of personal property from their homes.

so Z~Bin(500,0.14) and p=Z/500

we know from basic mathematics that standard deviation = √(variance)

so variance is  given thus;

V[Z] = 500*0.14*(1-0.14)

or V[p] = V[Z/500] = 500*0.14*0.86/500² = 0.14*0.86/500

so standard deviation is;

sqrt[V[p]]=sqrt(0.14*0.86/500) = sqrt(0.0002408) = 0.01552

∴ the standard deviation = 0.01552

cheers i hope this helps!!!!

Answer:

     [tex]\dfrac{3}{1}=\dfrac{12}{4}[/tex]

Step-by-step explanation:

If you write the proportion as ratios of feet to yards, you have ...

  [tex]\dfrac{3\,\text{ft}}{1\,\text{yd}}=\dfrac{12\,\text{ft}}{4\,\text{yd}}\\\\\boxed{\dfrac{3}{1}=\dfrac{12}{4}}\qquad\text{without the units}[/tex]

__

Please note that a proportion is a true statement. Here, you need only pick the true statement from those offered. For example, here's the first choice written in more readable form:

  [tex]\dfrac{12}{1}=\dfrac{4}{12}\qquad\text{FALSE statement}[/tex]

Answer:

d: 3/1   12/4

Step-by-step explanation:

Final answer:

The equation representing the total monthly cost of the A Fee and Fee plan based on the number of minutes used is y = 0.20x + 29, where y is the total monthly cost and x is the number of minutes.

Explanation:

To find an equation in the form y = mx + b, where x is the number of monthly minutes used and y is the total monthly cost of the A Fee and Fee plan, we first need to determine the slope (m) and the y-intercept (b).

We have two points based on the information given: (290, 87) and (980, 225). The slope (m) is calculated by the difference in cost divided by the difference in minutes:

m = (225 - 87) / (980 - 290)

m = 138 / 690

m = 0.20

Now that we have the slope, we can use one of the points to find b, the y-intercept.

Using the point (290, 87) and the slope 0.20:

87 = 0.20(290) + b

b = 87 - 58

b = 29

The equation representing the total monthly cost (y) based on the number of minutes used (x) is therefore:

y = 0.20x + 29

Answer:

Stratified sampling

Step-by-step explanation:

Members of the population are divided into two or more subgroups called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn. For instance, if we divide the population of college students into strata based on the number of years in school, then our strata would be freshmen, sophomores, juniors, and seniors. We would then select our sample by choosing a random sample of freshmen, a random sample of sophomores, and so on.

This technique is used when it is necessary to ensure that particular subsets of a population are represented in the sample. Since a random sample cannot guarantee that sophomores would be chosen, we would used a stratified sample if it were important that sophomores be included in our sample. Furthermore, my using stratified sampling you can preserve certain characteristics of the population. For example, if freshmen make up 40% of our population, then we can choose 40% of our sample from the freshmen stratum. Stratified sampling is one of the best ways to enforce "representativeness" on a sample.

Yes, a square can be considered as a rhombus and a rectangle both.

The square is a quadrilateral with all sides equal and all angles equals to 90° and having equal diagonals.

Square being a rhombus and a rectangle :-

Rhombus :-

It has it's all sides equal having their diagonals equal and intersect at right angle rhombus is a parallelogram so a square, all the properties that a rhombus holds are also the properties of a square, so we can say a square can be considered as a rhombus.

Rectangle :-

A square is always a rectangle because, it has all the properties of a rectangle, such as parallel and equal opposite sides, vertex angles being a right angle, diagonals being equal.

Hence, a square can be considered as a rhombus and a rectangle both.

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Final answer:

A square is both a rhombus and a rectangle because it has four equal sides and four right angles, fulfilling the criteria for both shapes.

Explanation:

A square indeed has all the properties of a rhombus, which is a parallelogram with four equal sides, and it also has the properties of a rectangle, which is a quadrilateral with four right angles. Since a square has four equal sides and four right angles, it satisfies the criteria to be called both a rhombus and a rectangle. Therefore, the answer is yes; a square is both a rhombus and a rectangle.

Answer:

Deepwater Horizon

good movie too btw

-Hops

Answer:

48 000 gallons / 2 days = 24 000 gallons per day

24 000 gallons / 24 hours = 1 000 gallons per hour

1 000 gallons / 60 minutes = 16.(6) gallons per minute

I had the same question on a quizz, the question was:In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?

Hope that was helpful.Thank you!!!

Answer: C

Step-by-step explanation: It divides the original segment into two equal pieces

The properties that do not apply for the perpendicular bisector should be option c. that it divides the original segment to two equal pieces.

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Answer:

±5sqrt(2) = x

Step-by-step explanation:

50 - x^2 = 0

Add x^2 to each side

50 - x^2 +x^2= 0+x^2

50 = x^2

Take the square root of each side

±sqrt(50) = sqrt(x^2)

±sqrt(25*2)) = x

±sqrt(25) sqrt(2) = x

±5sqrt(2) = x

Answer:

This is a circle with centre (6,-7)  and radius 4.

Step-by-step explanation:

The equation of a circle has the following format:

[tex](x - x_{0})^{2} + (y - y_{0})^{2} = r^{2}[/tex]

In which r is the radius(half the diameter) and the centre is the point [tex](x_{0}, y_{0})[/tex]

In this question:

[tex](x-6)^{2} + (y+7)^{2} = 16[/tex]

So

[tex]x_{0} = 6, y_{0} = -7[/tex]

[tex]r^{2} = 16[/tex]

[tex]r = \pm \sqrt{16}[/tex]

The radius is the positive value.

[tex]r = 4[/tex]

So this is a circle with centre (6,-7)  and radius 4.

Answer:

Given equation

(x-6)^2+(y+7)^2=16

centre (6,-7)  and radius 4.

Step-by-step explanation:

The equation of a circle is (x - a)² + (y - b)² = r²

the radius is r

the centre is (a, b)

Given equation

(x-6)^2+(y+7)^2=16

so ,

a = 6

b = - 7

r² = 16

[tex]r = \pm \sqrt{16}[/tex]

r = 4

Therefore,  the circle with centre (6,-7)  and radius 4.

Answer:[tex]h=\dfrac{kL^2}{8mg}[/tex]

Step-by-step explanation:

Given

Mass of ball is M  is dropped from a height h

spring constant is k

Here we can use conservation of energy

Mass has a Potential energy of E=mgh

and when it falls on the spring then it compresses it a length of 0.5 L

Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .

In this way energy is conserved. So, mass must move to an initial  height h

[tex]mgh=\frac{1}{2}k(\frac{L}{2})^2[/tex]

[tex]h=\dfrac{kL^2}{8mg}[/tex]

considering [tex]h >> 0.5L[/tex]

With u = <-7, 6> and v = <-4, 17>, we have

u + 3v = <-7, 6> + 3 <-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>

We want to find a vector w such that

u + 3v + w = <1, 0>

Subtract u + 3v from both sides to get

w = <1, 0> - (u + 3v) = <1, 0> - <-19, 57>

w = <20, -57>

To get the required vector, subtract u + 3v from the unit vector <1, 0>. The required vector is <20, -57>.

To find the vector that can be added to u + 3v to get the unit vector <1, 0>, we need to subtract u + 3v from the unit vector. This will give us the required vector. Let's calculate:

Unit vector: <1, 0>

u + 3v: <-7, 6> + 3<-4, 17> = <-7, 6> + <-12, 51> = <-19, 57>

Required vector = Unit vector - (u + 3v) = <1, 0> - <-19, 57> = <1 + 19, 0 - 57> = <20, -57>

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Answer:

79

Step-by-step explanation:

Answer:

(1)Base Area= 81 square yards.

(2)

(3)Height=12 Units

Step-by-step explanation:

Question 1

Volume of the rectangular prism=2,592 cubic yards.

Height of the rectangular prism=32 yards

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=2592

32lb=2592

lb=2592/32=81

Base Area= 81 square yards.

Question 2

Volume of the rectangular prism=432 cubic feet.

Height of the rectangular prism=9 feet

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=432

9lb=432

lb=432/9=48

Base Area= 48 square yards.

Any dimension whose product is 48 is a possible choice.

They are:

Question 3

Volume of the rectangular prism=960 cubic units.

Base Area of the rectangular prism, lb=80 Square Units

Volume of a rectangular prism =lbh (where lb is the Base Area)

Therefore:

lbh=960

80h=960

h=960/80=12

Height= 12 units.

Answer:

81 square yards.

Step-by-step explanation:

what the other guy said just less words

Step-by-step explanation:

25.2 + 800 - 427.43 x 2.4 ÷ 13

825.2 - 1025.832 ÷ 13

200.632 ÷ 13

= 15.44

Answer:

357 bears

Step-by-step explanation:

Given;

Population density of bears in the Kenai Peninsula of Alaska = 42 bears per 1000km^2

Area of habitable region of this peninsula = 8500 km^2

how many bears would you expect to find in a habitable region of this peninsula N;

N = population density × area

N = 42/1000 × 8500

N = 357 bears

Answer:

39 children and 13 adults

Step-by-step explanation:

3children = 1 adult

52 = x * (3children + 1adult)

52= x * 4

13 = x

x = 13

total children = 3x

3x = 39

The problem poses a system of linear equations where the number of attendees 'a + c = 52' and 'c = 3a'. Resolving these equations gives 'a = 13' adults and 'c = 39' children.

This is a problem about creating and solving a system of linear equations. Let's denote the number of adults who attended the ball game as 'a' and the children who attended the game as 'c'. According to the problem, we have two parts of information that can be written as equations:

You can substitute the equation for 'c' in the first equation: a + (3a) = 52. Solving this, you find that 'a' equates to 13. Substitute 'a = 13' into the second equation, you will find that 'c = 39'. This indicates that there were 13 adults and 39 children who attended the game.

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