An architect designs a house that is 10 m wide. The rafters holding up the roof are equal length and meet at an angle of 65°. The rafters extend 0.4 m beyond the supporting wall. How long are the rafters?

The standard score for the given X value is -0.06

Standard Score

Standard score or Z - Score is inversely varies with the standard deviation and directly varies with the difference of the raw score and the mean score.

The formula to calculate standard score is

z - score = (X - μ)/σ

Where

Z = standard score

x = observed value

μ = mean of the sample

σ = standard deviation of the sample

Given,

Here we have the value of X = 83, μ=88.1 and σ=87.

Now, we need to find the standard score for this values and we have also round off the result to two decimal places.

Apply the given values on the z-score formula, then we get,

z-score = (83 - 88.1)/87

When we simplify the numerator, then we get,

z - score = -5.1/87

After the division of these numbers we get the value of z-score as,

z - score = -0.0586

When we round off the result into two decimal place then we get the value of standard score as -0.06.

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First, let's see the progression of the sequence of numbers

As you can see from the second term the sequence continues with a constant change of -13 which means d=-13.

The answers will be the expressions inside the red square box in each case.

Answer:

7 hours

Step-by-step explanation:

25x + 25 = 200.

25x = 175

175/25 = 7.

Answer:

25 + 35h = 200

and

h = 5

(5 hours)

Step-by-step explanation:

you have 200.

costs:

35 per hour

and

25 fee

h will represent the total hours spent renting a boat

25 + 35h = 200

now we will do inverse operations

subtract 25 from both sides

35h = 175

now divide both sides by 35

h = 5

Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a hospital parking lot charges 3.50$ for the first hour and 1.75$ for each additional hour.

The modelled equation representing the above scenerio is -

y = 3.5 + 1.75x

where (x) represents the number of hours for which the car is parked.

Maximum amount with Jose = $19.25

Therefore -

3.5 + 1.75x ≤ 19.25

1.75x ≤ 15.75

x ≤ 9 hours       [Maximum time]

Minimum amount with Jose = $12.25

3.5 + 1.75x ≥ 12.25

1.75x ≥ 8.75

x ≥ 5 hours               [Minimum time]

Therefore, Jose can park his car for the maximum time of 9 hours and the minimum time of 5 hours.

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To simplify the expression

-0.26v + v - 0.07

we will only add the ones with variable v

0.74v -0.07

The correct option is

0.74v - 0.07

The final amount after 3 years compounded semi-annually is $3709.20

To solve this problem, we simply need to use compound interest formula which is given as

[tex]A = p(1 + \frac{r}{n})^n^t[/tex]

where

Lets substitute the values into the formula and solve

[tex]A = p(1 + \frac{r}{n})^n^t\\A = 3000(1 + \frac{0.072}{2})^2^*^3\\ A = 3709.20[/tex]

The amount accrued 3 years from now is $3709.20

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Simplify the equation 4x+9y = -9 in slope-intercept form of equation.

So slope of line is -4/9 and int

Answer:

She worked for 4 hours and made 16 shirts (work below)

Step-by-step explanation:

let h = number of hours worked

and s = number of shirts made :]

28h+2s = 144

4h = s

28h+8h=144

h=4, s=16

:]

Answer:

A - $4060

B - 32 copies

Step-by-step explanation:

A -

P = 1900 + 90c

P = 1900 + 90(24)

P = 1900 + 2160

P = 4060

Total if Ann sold 24 copies: $4060

B -

1900 + 90c = 4780

90c = 4780 - 1900

90c = 2880

c = 32

Total copies: 32

The equation is

Therefore x<-2. The number line representation is

Answer:

7,002

Step-by-step explanation:

The product is the answer of a multiplication problem. You just have to multiply the numbers by using the techniques to solve it. Hope this helps!

Answer:

Numere prime:37,377,769,1243,1999

Sunt numere prime deoare au ca divizori doar 1 si ei insusi

Answer:

378

Step-by-step explanation:

Start with prime factoriazation

18 = 2 * 3 * 3

54 = 2 * 3 * 3* 3

63  = 3 * 3 * 7

2 * 3 * 3 * 3 * 7 = 378  

Problem

At the fast food restaurant, four cheeseburgers and five small fries have a total of 2,310 calories. Three cheeseburgers and two small fries have a total of 1,330 calories. How many calories does each item contain?

Solution

For this case we can set up the following notation

x= number of cheeseburgers

y= small fries

4x +5y= 2310

3x + 2y= 1330

From the first equation we can solve for x and we got:

x= 577.5 - 5/4 y

And now we can replace this into the second equation and we got:

3(577.5 -5/4 y) +2y= 1330

And we can solve for y:

1732.5 - 15/4 y + 2y = 1330

-7/4 y = -402.5

y= 230 cal

And solving now for x we have:

x= 577.5 - 5/4 (230) = 577.5 - 287.5 = 290 cal

Answer: 36

One die has a total outcome of 6 elements (1, 2, 3, 4, 5, 6). Now, if we roll two dice, each time you roll a number on the first die, there are another 6 possible outcomes for the second die.

Therefore, the number of elements in the sample space would be:

There would be 36 elements in the sample space.

Answer:

A

Step-by-step explanation:

Adding the equations,

[tex]2y=10 \implies y=5 \\ \\ \therefore 2x+3(5)=1 \implies x=-7[/tex]

The money was invested for 8.60 years

Given:

Amount in the savings account = $2750

Amount invested = $2000

rate = 4.36% = 0.0436

To find:

the time it took to invest the money to obtain the amount in the account

The investment was done using simple interest. So to get the time, we will apply simple interest formula

3xy-5x+9y-45

Step-by-step explanation:

Step by Step Solution

STEP1:STEP2:Pulling out like terms

 2.1     Pull out like factors :

   3y - 15  =   3 • (y - 5) 

Equation at the end of step2: (x • (3y - 5)) + 9 • (y - 5) STEP3:Equation at the end of step 3 x • (3y - 5) + 9 • (y - 5) STEP4:Trying to factor a multi variable polynomial

 4.1       Split       3xy-5x+9y-45 

 4.1       Split       3xy-5x+9y-45 

             into two 2-term polynomials

             -5x+3xy   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy-5x   and    +9y-45

             This partition did not result in a factorization. We'll try another one:

             3xy+9y   and    -5x-45

             This partition did not result in a factorization. We'll try another one:

             3xy-45   and    +9y-5x

             This partition did not result in a factorization. We'll try another one:

             -45+3xy   and    +9y-5x

             This partition did not result in a factorization. We'll try 

Answer:

15.9 hours.

Step-by-step explanation:

speed = distance / time.

230 = 3647 / time.

time = 3647 / 230.

time = 15.9 hours.

Given:

Required:

To find the probability that the dart land will be in the shaded region.

Explanation:

Area of the circle is given by the formula:

Where r = radius

Thus the area of the circular region

The area of the square is given by the formula:

Thus the area of the given square

The probability of an event is given by the formula:

The probability that the dart land will be in the shaded region

Thus probability

Final answer:

Thus the probability that the dart land will be in the shaded region is 0.349.

2.

The reason for 2 is 'the angles are vertical'.

3. In the diagram below, we can identify the alternate interior angles more easily

Therefore, Therefore, the statements of the third step are

Finally, the corresponding angles of triangles GRA and TRE are all congruent; thus, the two triangles are congruent because of the AA similarity criterion. The answer is AA similarity criterion. The length of the sides is not involved in the demonstration.

ANSWER

EXPLANATION

Given:

Desired Outcome:

1. Domain

2. Range

Determine the domain of the function

Note: We want to include only input values that do not require the denominator to be 0 when there is a denominator. As a result, we'll set the numerator to 0 and solve for x.

We'll now remove 4 from the domain. All of the answers are real numbers x > 4 or x < 4. We will also use Union notation to combine the two sets.

That is:

Determine the range of the function

Set x to 4 to find y

We'll also remove 3 from the range. All of the answers are real numbers y > 3 or y < 3. We will also use Union notation to combine the two sets.

That is:

Calculate the given division, as shown below

ANSWER

EXPLANATION

We want to write the equation of the circle in vertex form:

The first step is to group the x terms and y terms together and take the constant to the right-hand side of the equality sign:

Now, complete the square for the x terms:

Repeat the process for the y terms:

That is the equation of the circle in vertex form.

Answer:

y = 1/6x + 1

Step-by-step explanation:

Add 2x to both sides of the equation.

12y = 12 + 2x

Divide each term in 12y = 12 + 2x by 12 and simplify.

y = 1 + x/6

Write in y=mx+b form.

y = 1/6x + 1

The first equation given in the question as, y = 1^x is not exponential.

What do you mean by exponential?

A mathematical function with the form f (x) = a^x is an exponential function. "x" is a variable, while "a" is a constant that serves as the function's base and must be bigger than 0. The transcendental no., or roughly 2.71828, is the most often used exponential function on regular basis.

The equation, y = 1^x is not an exponential because for any integer value of x, y always equals to zero. Which makes it simple equation and not an exponential equation.

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The number that should go in the gap to factorise the given expression is 2

From the question, we are to determine the number that should go in the gap in order to factorise the given expression.

The given expression is

6x + 14

To determine the number that should go in the gap,

First we will factorize the given expression

6x + 14

The greatest common factor (GCF) of 6 and 14 is 2

Thus,

We can factor out 2 as follows

2(3x + 7)

The factored form of the expression is 2(3x + 7)

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The price will increase if number of students increase

By multiplying the  number of students with cost

Number of students varies in this example

The expression shown for trip amount is c = 10+13x.

The cost for 10 students is 140

The cost for 17 students is 231

Finding the value of an algebraic expression when a specified integer is used to replace a variable is known as evaluating the expression. We use the given number to replace the expression's variable before applying the order of operations to simplify the expression.

1). The price will increase if number of students increase.

2). By multiplying the  number of students with cost.

3). Number of students varies in this example.

4). Let the number of students

Then total amount(c) of the trip is given by

c = 10+13x  ------ equation (1)

5). Put x = 10 in equation (1)

c = 10+13(10)

c = 140

6).  Put x = 17 in equation (1)

c = 10+13(17)

c = 231

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If Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

The deposited amount = $500

The simple interest = 7.5%

The interest she earned = $225

Then the final amount = The deposited amount + The interest she earned

= 500+225

= $725

The equation of simple interest

A = P(1+rt)

Where A is the final amount

P is the initial amount

r is the interest rate

t is the time period

725 = 500(1+(7.5/100)×t)

(1+0.075t) = 1.45

0.075t = 0.45

t = 0.45/0.075

t = 6 years

Hence, if Gloria deposited $500 into a bank account that earned 7.5% simple interest each year and she earned $225 in interest before closing the account, then the number of years that the money in the account is 6 years

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Solution

- The probability of him getting 1 queston correctly given tahat there is only one correct option out of 4 optins,

- Since here are questions, it implies that there are multiplye trials the student has.